Geographie delineated forth in two bookes Containing the sphericall and topicall parts thereof, by Nathanael Carpenter, Fellow of Exceter Colledge in Oxford.

GEOGRAPHIE: THE FIRST BOOKE. (Book 1)

CHAP. I. Of the Terrestriall Globe, the matter and forme.

1 GEOGRAPHIE is a science which teacheth the descrip∣tion of the whole Earth.

The Nature of Geographie is well expressed in the name: For Geographie resolued according to the Greeke Ety∣mologie, signifieth as much as a des∣cription of the Earth; so that it differs frō Cosmographie, ••s a part from the whole. Forasmuch as Cosmographie according to the name, is a description of the whol•• world, cōprehending vnder it as well Geographie, as Astronomie. Howbeit, I confesse, that amongst the ancient Writers, Cosmographie hath been taken for one & the selfe-same science with Geographie; as may appeare by sundry treatises meerely Geographicall,* 1.1 yet intituled by the name of Cosmographie. This Science (according to our appro∣ued Ptolomie) is distinguished from Chorographie foure wayes.

First, because Geographie describeth the whole Spheare of the Earth, according to its iust quantity, proportion, figure, and dis∣positions, which the principall parts of it haue; as well in respect of one another, as of the whole Terrestriall Globe: so that it on∣ly vndertakes the chiefe and most noted parts, such as are sines, creekes, nations, cities, promontories, riuers, and famous moun∣taines. But the Chorographer separatly handleth the lesser parts, and matters of smaller moment, such as are hillocks, brooks, lakes, townes, villages, and Parishes, without any respect at all to the places adioyning, as conferring them with the Sphaericall fabricke of the whole Earth: Which by the same Author is well illustrated by an example, drawne from the Painters Art: For wee see that a Painter, desirous to draw out and represent the head of any liuing creature, will first draw out the lineaments of the first and greatest parts; as the eyes, eares, nose, mouth, forehead, and such like; only caring that they may challenge a due and iust proportion and symmetrie one with the other, not regarding the lesser particles and ornaments in each of these, wanting perhaps space competent to accomplish it. But if the same Painter would striue to expresse only an eye, or an eare, he might take space enough to designe out euery smaller linea∣ment, colour, shadow, or marke, as if it were naturall: for in this he cares not to make it correspondent to the whole head, & o∣ther parts of the body: So happens it to the Geographer, who willing to delineate out any part of the Earth, (as for example, our Realme of England) he would describe it as an Iland, en∣compassed round with the sea, & figured in a triangular forme, only expressing the principall and greater parts of it. But the Chorographer vndertaking the description of some speciall and smaller part of England; as for example, the City of Oxford, descends much more particularly to matters of small quantity and note: such as are the Churches, Colledges, Halls, Streets, Springs; giuing to each of them their due accidents, colours, li∣neaments, and proportion, as farre forth as Art can imitate Na∣ture. Neither in this kind of description needs there any con∣sideration of the places adioyning, or the generall draught of the whole Iland. The second difference betweene Geographie and

Chorographie assigned by Ptolomie, consists in this; that Choro∣graphie is commonly conuersant in the accidentall qualities of each place, particularly noting vnto vs, which places are bar∣ren, fruitfull, sandy, stony, moist, dry, hot, cold, plain, or moun∣tainous, and such like proprieties. But Geographie lesse regar∣ding their qualities, inquires rather of the Quantities, measures, distances, which places haue aswell in regard one of the other, as of the whole Globe of the Earth: assigning to each region its true longitude, latitude, clime, parallell, and Meridian. 3^ly, Geo∣graphie and Chorographie are said to differ, because Geographie stands in little need of the Art of Painting, for as much as it is conuersant the most part about the Geometricall lineaments of the Terrestriall Globe, clayming great affinity with the Art called of the Greekes, Ichnographie; whose office is to expresse the figure and proportion of bodies, set forth in a plain superfi∣cies. But contrariwise Corographie requires, as a help necessary, the Art of Painting; forasmuch as no man can fully and perfectly expresse to the eye the true portraict of cities, townes, castels, promontories, and such other things, in their true colours, liuely∣hood, and proportion; except they bee skilled in the Art of Painting. So that this part is by some likened to that Art which the Greekes call Sciographie, or S••enographie. Fourthly, and last∣ly, Geographie is distinguished from Chorographie, in that the former considering chiefly the quantity, measure, figure, site, & proportion of places, as well in respect one of the other, as of the Heauens, requires necessary helps of the Sciences Mathemati∣call, chiefly of Arithmeticke, Geometrie, and Astronomie, without which a Geographer would shew himselfe euery-where lame & impotent, being not able to wade thorough the least part of his profession: whereas a man altogether vnpractised in those fa∣culties, might obtaine a competent knowledge in Chorography. As we find by experience, some altogether ignorant in the Ma∣thematicks; who can, to some content of their hearers, Topogra∣phically, and Historically discourse of Countries, as they haue read of in books, or obserued in their trauaile. Notwithstanding all these differences assigned by Ptolomie, I see no great reason why Chorography should not bee referred to Geography; as a

part to the whole; forasmuch as the obiects on which hee hath grounded his distinction, differ only as a generall and a speciall; which being not opposite, but subordinate (as the Logicians vse to speake) cânnot make two distinct Sciences, but are redu∣ced to one and the selfe-same: at least the differences thus assig∣ned, will not be Essentiall but Accidentall. Wherfore my scope in this Treatise shall bee to ioyne them both together in the same, so far forth as my Art and leisure shall be able, to descend to particulars; which being in Chorographie almost infinite, wil not all seeme alike necessary in the description of the vniuer∣sall Globe of the Earth. The name of Geographie thus distingui∣shed, wee define it to be a Science which teacheth the Measure and Description of the whole Earth. It is properly tearmed a Science, because it proposeth to it selfe no other end but know∣ledge; whereas those faculties are commonly tearmed Arts, which are not contented with a bare knowledge or speculati∣on, but are directed to some farther worke or action. But here a doubt seemes to arise, whether this Science be to be esteemed Physicall, or Mathematicall? Wee answer, that in a Science two things are to bee considered: first▪ the matter or obiect whereabout it is conuersant; secondly, the manner of handling and explication: For the former, no doubt can bee made, but that the obiect in Geographie is for the most part Physicall, con∣sisting of the parts whereof the Spheare is composed: but for the manner of Explication, it is not pure, but mixt; as in the former part Mathematicall, in the second rather Historicall; whence the whole Science may be alike tearmed Mathematical & Historicall▪ not in respect of the Subiect which we haue said to be Physicall, but in the manner of Explication. For the obiect of Geographie (as we haue intimated) is the whole Globe of the Earth: where we are to obserue, that the Earth may bee consi∣dered 3 manner of wayes: First, as it is an Element, out of which mixt Bodies are in part compounded: In which sense it apper∣taines to Naturall Philosophie, whose office is to treat of all na∣turall bodies, their principles and proprieties. Secondly, as it is supposed to be the center of heauenly motions, and so it is vn∣dertaken by Astronomers. Thirdly according to its Sphaericall

superficies, as it is proposed to bee measured or described, in which manner it is the subiect of Geographie, so far forth as the parts of it haue a diuerse situation, as well in regard one of ano∣ther, as in respect of the Heauens. Which restriction, although agreeing well to some part of it, will hardly square with all the rest: because many things herein are handled besides the Earths naturall site or position, as hereafter shall be taught. For which cause wee haue rather defined the subiect of Geographie to bee the Earth, so far as it is to bee measured and described, as wan∣ting one word to expresse the whole manner of considera∣tion.

2 Geographie consists of 2 parts, the Spheri∣call, and Topicall: The Sphericall part is that which teacheth the naturall constitution of the Terrestriall Spheare.

The common and receiued diuision of this Science amongst Geographers, is into the Generall or vniuersall part; and the spe∣ciall. Which diuision, I dare not vtterly reiect; being strengthe∣ned with the authority of ancient and approued Authors. Yet seems it more aptly to be applyed to the Historicall part, then to the whole Science, as we shall after make apparant. In the mean time the diuision of it into Sphericall & Topicall parts, seemes to be preferred in reason: Forasmuch as the Terrestriall Globe, which we suppose to be the subiect of the Science, is proposed to vs vnder a twofold consideration; first in regard of the Ma∣thematicall lineaments and circles, whereof the Spheare is ima∣gined to consist; out of which wee collect the figure, quantity, site, and due proportion of the Earth, and its parts: Secondly, of the places Historically noted and designed out vnto vs, by certaine names, markes, and characters. The former receiueth greatest light from Astronomie, whence some haue called it the Astronomicall part: The later from Philosophie and Historicall obseruation, being (as we haue said) a mixt Science, taking part of diuers faculties.

3 The Terrestriall Spheare is a globous or round Body, comprehended within the super∣ficies of the Earth and Wate••.

Some haue nicely distinguished betwixt a Spheare & an Orbe, that a Spheare is a round massie body, contained in one surface, which is conuexe or outward as a Bowle. The other concaue, or hollow, in manner of an Egge-shell emptyed. But this di∣stinction seemes too curious, as sauouring to much of Scho∣lasticall subtility, because the name of Orbe and Spheare are ma∣ny times promiscuously vsed, without difference, amongst good Writers. This Spheare which wee make the subiect of our Sci∣ence, wee call Terrestriall, not because it consists meerely of Earth; (the contrary of which wee shall hereafter shew:) but because the Earth is the chiefest in the composition; whence by a tropicall kind of speech, the whole Globe may bee called Ter∣restriall.

4 The handling of the Terrestriall Spheare is is either Primary, or Secundary. The Primary consists in such affections as primarily agree to the Earth.

The Geographicall Affection may be considered two wayes; either simply and absolutely in themselues; or eomparatiuely as they are conferred and compared the one with the other. As for example, the circles of the Spheare, such as are the Parallels and Meridians, may be considered either absolutely in themselues; or comparatiuely as they concurre to the longitude, latitude, di∣stance, or such like accidents, which arise out of the comparison of one Circle with another.

5 The Terrestriall Spheare primarily conside∣red, is either Naturall, or Artificiall. The Na∣turall is the true Globe in it selfe, without i∣mage or representation.

6 Herein againe are to be considered two things; First, the Principles and constitution of the Spheare; Secondly, the Accidents and pro∣prieties: The principles whereof the Spheare is composed are two; viz: Matter and Forme.

7 The Matter is the substance whereof the Spheare is made, viz: Earth, and Water.

My meaning is not in this Treatise to handle the nature and propieties of these two Elements, Water, & Earth, farther then may seeme necessary for the Geographicall constitution of the Terrestriall Spheare, leauing the rest to the Naturall Philosopher; because it is supposed that few men vndertake the study of this Science, without some insight in the other. And to speake truth, this begins where the Naturall Philosopher ends. Yet because some light in each learning is necessarily required▪ ••nd all men are not willing to seeke farther into the grounds of Naturall Philosophie; it will not seeme altogether impertinent, to lay the foundation farther off, that the building thereon erected may stand surer and stronger. Wherefore taking some begin∣ning from the matter of the Earthly Globe, wee haue distingui∣shed it into Earth, and Water, as those parts whereof the whole Globe is not essentially compounded, as one intire body in it selfe; but rather co••ceruated and compacted together, each part retaining its owne nature and proprieties, without any pro∣per mixture. To expresse more fully the constitution of this Spheare, we are here to distinguish betwixt the first and second matter. The first matter was that vniuersall chaos, or masse, out of which, all bodies both Celestiall and Elementary were made and formed, as wee read in the first of Genesis. Which whether it be the same with Aristotle's Materia prima, as some haue ima∣gined, I leaue to others to dispute. The second matter of the Globe is either Proper or Accidentall. The proper we call that

whereof the Globe of the Earth most properly consists, such as are the two Elements of Earth and Water. The Accidentall mat∣ter is vnderstood of all other bodies, contained in the superficies of the said Spheare, as Stones, Mettals, Minerals, and such like materials, made of a Terrestriall substance, and engendred in the wombe of the Earth. Concerning the Earth and Water, which we make the most proper and essentiall parts of the Spheare, we will set downe these two Theoremes.

1 In the Terrestriall Spheare is more Earth then Water.

The Theoreme may bee proued by sundry reasons drawne from Nature and Experience. Whereof the first may bee taken from the depth of the waters, compared with the whole thick∣nes of the Earth. For the ordinary depth of the Sea is seldome found to be aboue 2 or 3 miles, and in few places 10 furlongs, which make a mile and a quarter. And albeit some late Writers haue imagined the obseruation to be vnderstood only of straight and narrow Seas, and not of the maine Ocean: yet granting it to amount 〈◊〉〈◊〉 10, 20, or 30 miles, it cannot reach to so great a quantity, as to come neere the greatnes of the Earth. For the whole circle of the Terrestriall Spheare being 21600 English miles, (allowing 60 English miles to a degree of a greater circle) wee shall find the Diameter to bee about 7200 miles: Whose semi-diameter, measuring the distance betweene the center and the superficies of the Earth, will be 3600 miles. And if any man suppose some of the quantity to be abated, because of the Sphericall swelling of the Water aboue the Earth, whose Circle must be greater than that of the Earth: We answer; first that this may challenge some abatement, but not come neere any equality of the Water with the Earth. Secondly it is to bee ima∣gined that the surface of the Sea, howsoeuer as it is painted in Globes and Charts, it seeme for a great part empty and vnfurni∣shed of Ilands; yet this for the greatest part, seeme rather to bee ascribed to mans ignorance, and want of true discouery, be∣cause many quillets and parcels of land lye yet vnknowne to our Christian World, and therefore omitted, and not figured in

ou•• ordinary Mappes. So wee find a great quantity of Earth which lay hid and vnknowne without discouery, in the daye•• of Ptolomy, which caused him to contract & curtaile the Earth in his Geographicall descriptions. Which defect hath been since that time supplyed by the industrious trauailes and Nauigations of later time: such as were of Portugals, English, and Hollanders, especially of Columbus the Italian, who (as one wittily allu∣ding to his name) like Noah's Doue plucking an oliue branch from this Land, gaue testimony of a portion of Land as yet vn∣knowne, and left naked vnto discouery. And no question can be made, but a great quantity of land, not yet detected by our Eu∣ropean Nauigators, awaites the industry of this age. To which alludes the Poët in these Verses:* 1.2

Venient annis secula seris, Quibus Oceanus vincula rerum Laxet, & ingens pateat tellus, Typhi••{que} nouos detegat orbes, Nec sit terris vltima Thule.

In after-yeeres shall Ages come, When th'Oecean shall vnloose the bands Of things, and shew vast ample lands; New Worlds by Sea-men shall be found, Nor Thule be the vtmost bound.

Another reason to proue the Earth to be greater in quantity, may bee drawne from the mixture of Earth and Water: for if these two Elements should meet in the same quantity, & chal∣lenge an equality; questionlesse the whole Earth would proue ouer-moist, ••lymie, and vnapt for habitation. Which any man may easily obserue by his owne experience. For let a portion of Earth, & another of Water be mixt together in the same quan∣tity, the whole masse will seeme no other than a heap of mire or slime, without any solid or consisting substance. Moreouer the Water being no other than a thin and fluid body,* 1.3 hardly con∣taining it selfe within its own bounds or limits (as Aristotle tea∣cheth

vs) must needs require a hard and solid body, whereon to support it selfe, which body must of necessity bee greater in quantity.

2 The Earth and Water together make one Spheare.

It may bee probably collected from sundry places of holy Scripture, that in the first Creation, the surface of the Earth; be∣ing round and vniforme, was ouerwhelmed and compassed round with Waters, as yet vnfurnished of liuing Creatures. Se∣condly, it appeares that Almighty GOD afterwards made a se∣paration betwixt the Waters and Dry-Land. This separation (a•• farre as reason may bee admitted as Iudge) seemes to bee effe∣cted one of these two wayes: Either by giuing super-naturall bounds and limits vnto the Waters, not suffering them to inuade the Dry-land: or els by altering the superficies of the Earth, ca∣sting it into inequall parts, so that some-where, some parts of it being taken away, empty channels or concauities might be left to receiue the Waters; other-where by heaping vp the parts so taken away, whence were caused Mountaines and eminent pla∣ces on the earth. The former of these wayes seemes altogether improbable; forasmuch as it is very vnlikely to imagine, that God in the first institution of Nature, should impose a perpe∣tuall violence vpon Nature, as hereafter in place more conueni∣ent shall bee demonstrated. Wherefore taking the later as more consonant to reason; we shall find that the Water & the Earth separated and diuided, make not two separate and distinct 〈◊〉〈◊〉 Globes, but one and the same Spheare; forasmuch as the conca∣uities and hollowgapings of the Earth, are euery-where choa∣ked and filled vp with Water, whose superficies is Sphaericall; and therefore helpes, together with the Earth, to accomplish & perfect this Terrestriall Spheare. To confirme which opinion▪ these reasons out of common experience may be alleadged: The first is drawn-from the parts of Earth and Water; For we may euery-where obserue, that a portion of Earth, and another of Water being let fall, will descend in the same right line toward the same center: whence we may euidently conclude, that the

Eearth & Water haue one and the selfe-same center of their mo∣tion, and by a consequence conspire to the composition of one and the selfe-same Spheare. Secondly, to a like Arch or space in the Heauens, is found answerable alike Arch in the Terrestriall Globe, whether it bee measured by the Earth or Water: which could not happen, were they not accounted parts of the same Spheare. The third reason may bee drawne from the Ecclipse of the Moone, wherein the part of the Moone shadowed & obscu∣red, is obserued to be one Sphaericall or round-figure. This sha∣dow, by the consent of all Astronomer's is caused by the Terre∣striall Spheare, interposed betwixt the Sun and the Moone, inter∣cepting the Sun-beames, which should illuminate the Moone; and the shadowes imitate the opacous bodies, whence they a∣rise: But in the Ecclipse we find only the shadow of one body or Spheare, and therefore according to the ground of the Opticks, we may conclude the body whereof such a shadow proceedeth, to be but one and the selfe-same Spheare.

8 The Forme of the Terrestriall Spheare, is the naturall Harmony or order, arising from the parts working together.

We ought here to remember what we said before; that the Earth and the Water concurre together to make one Terrestri∣all Spheare: wherefore the whole being accounted one coacer∣nated and collected Body, made of two other; we are not to ex∣pect an Internall, Essentiall, and Specificall Forme, such as Ari∣stotle recounts amongst the principles of a Naturall Body: but only such a one as in it self is Externall and Accidentall; yet con∣curring (as it were) Essentially to the constitution of the Terre∣striall Spheare, whose Fabricke and first composition, cannot well be vnderstood without it. Some haue imagined the whole Globe of the Earth to bee informed with one Internall and Es∣sentiall Forme; which opinion seemes to haue much affinity with that of Plato's, concerning the Soule of the World: Not that Plato and his followers were so absurd to defend, that the World with all his parts was animated with a true vitall Soule, in the nature of a liuing Creature: but that all the members of

it were vnited together, quickned, and disposed by a certaine Energeticall power or vertue, which had great resemblance and representation of the Soule of man. Which assertion seemes to be restored and embraced by our late Magneticall Philosophers, whose opinion we shall discusse and examine hereafter in place conuenient. In the meane time, grounding our discourse on knowne principles; we can admit no other Forme in the Spheare of the Earth, then the mutuall Harmony, order and concent of the parts, concurring together, and working the perfection & perpetuation of the whole. A fit resemblance whereof we may obserue in an artificiall Clock, Mill, or such like great Engine, wherein euery part duly performing its owne office, there will arise and result a naturall Harmony, whch not vnaptly may bee termed the Forme of the whole Engine. Why the World should not consist of an Internall and Essentiall Forme, sundry reasons haue been alleadged by our common Philosophers: First, because Nature neuer attempteth any thing in vaine, or without a de∣terminate end; But the particular Formes of speciall Bodies (say these Philosophers) are sufficient for the vnity and conformati∣on of this Terrestriall Globe: so that to grant an vniuersall Forme of the whole, were to multiply causes without any necessity, & make Nature the Mother of superfluity, which to all Philoso∣phers seemes most absurd. Secondly, if this were admitted; the whole Spheare of the Earth would bee as one continuate Body, whose parts should (as it were) suffer a fellow-feeling one of the other. Thirdly, it were a difficult matter to assigne, to what kind such a Forme might be reduced, whether Animate, or In∣animate. If Inanimate, whether it were simple, or compound. If Animate, whether Vegetatiue, Sensitiue, or Rationall; vnder the which are couched many great difficulties, as yet vndisclo∣sed. Whether these reasons bee of any great force to ouerthrow the aduerse opinion, I leaue it to further inquiry: intending here a Geographicall, not a Physicall Discourse.

CHAP. II. Of the conformity of parts in the constitution of the Terrestriall Spheare.

1 IN the former we haue treated of the Natu∣rall constitution of the Terrestriall Spheare, aswell in Matter as Forme: It is needfull in the next place to treat of such Affections and proprieties as nece••sarily arise out of such a Constitution.

2. Those Affections or Proprieties are of two sorts, Reall or Imaginarie; Reall I call such as agree to the Terrestriall Globe by Nature▪ Imaginary, such as agree to it by vertue of our vnderstan∣ding.

3 Againe the Affections Really or Naturally a∣greeing to the Terrene Spheare, are assigned either in respect of the Earth it selfe, or in res∣pect of the Heauens.

4 These Affections are said to agree to the Earth in respect of it selfe, which may be expressed and vnderstood without any comparing of it with the celestiall Bodies.

5 These againe are twofold; either Elemen∣tarie, or Magneticall. Elementary I terme

such as haue commonly been knowne or ob∣serued by ordinary Philosophers. Here is chief∣ly to bee considered the conformity of the Terrestriall parts, in the making and constitu∣tion of the whole Spheare.

In the former Chapter we haue shewed, that the Forme of the Terrestriall Spheare, is nothing els but the concinnity and apt conspiration of the parts whereof the whole is compoun∣ded. This conformity being diuers and manifold, as well in re∣gard of the parts conforming themselues, as the manner; of the conformity, we shall particularly and distinctly treat of, so far as appertaines to a Cosmographer. Here by the way I cannot but taxe some defect in most of our common Cosmographers, who taking the Sphaericall roundnes of the Earth for a granted supposition, are nothing curious to search into the first grounds and causes of this rotundity, whereby it first became a globous Body; and afterwards retaines in it selfe a Naturall vigour or power (if any violence should be offered) to restore her selfe to her former right and perfection. All which are very pleasant & profitable, to giue an industrious Learner some satisfaction. To explaine this before we descend to particulars, we will lay this ground and Theoreme;

1 The parts of the Terrestriall Spheare, doe natu∣rally conforme and dispose themselues, aswell to the production and generation, as to the conti∣nuance and preseruation of it.

The forme of the Terrestriall Spheare, albeit (as wee haue shewed) it be Externall in respect of the whole Globe: yet may we call it naturall; forasmuch as it issueth and ariseth from the naturall disposition and inclination of all the parts. To vnder∣stand which clause the better, wee are to consider that a thing may bee called Naturall two manner of wayes: first in regard of the primary intent of Nature; as the neerest and immediate

end or scope to which shee is directed. Secondly, in respect of her secundary intent or purpose, as that which must of necessity follow the former. True it is that euery Terrene Body, accor∣ding to Natures first intention, seeks and works it's owne per∣fection and conseruation. Neuerthelesse according to her secun∣dary Intent, it concurres to the perfection and good of the whole vniuerse; which we shall plainely see in a stone or clodd of earth; which separated and remoued from it's mother, the Spheare of the Earth, by his descent and falling downewards, seeks first his owne conseruation, by reuniting it selfe to the Earth whence it was taken: Secondly, of the whole Globe of the Earth, which by this vnion and addition, no doubt, is made more compleat and perfect. This conformity of the Terrestriall parts, out of which ariseth the Earths Sphaericity; I call the natu∣rall inclination they haue to moue and settle themselues in such a site or position, as may bring forth a Sphaericall consistency: so that if it were possible (as what cannot be to Gods Almighty power?) that the whole Globe of the earth were dissolued and rent into little peeces; yet were that vigor and motiue inclina∣tion remaining in the parts, whereby they might settle and con∣forme themselues to the same Sphaericall nature, and compositi∣on which it formerly enioyed. For all the parts thus supposed to be distracted, would (no question) meet together & conforme themselues to the same point or Center; and so equally poising themselues, would restore the same Spheare so dissolued. So that wee here note a double inclination and motion of earthly bodies; first by a Right line, of the parts tending towards the Center; the other Sphericall of the whole Spheare, whereof the first in nature preceedes the composition of the Spheare, the other followes. But this latter motion I leaue doubtfull, till place conuenient.

6 The conformity of the Terrene parts is two∣fold; Primarie, or Secondary. The former is that whereby all earthly bodies are by a right line carried and directed to the Center

of the Terrestriall Globe.

As in an Artificiall Spheare or circle, drawne by a Geome∣trician, their principall parts are expressed, to wit, the Center, Ray, and circumference: so in the Naturall Globe of the Earth, these three, as it were Naturally & Really discouer themselues vnto vs. For first there is set a fixt point, to which all heauy bo∣dies moue and conforme themselues. Secondly, there is set the line or Radius, in which such bodies are carryed and conueyed. Thirdly, the confluence of all these parts, begets the roundnesse and Sphaericall forme. To begin first with that which is first in nature, we will take these grounds.

1 All Earthly Bodies incline and approach to the Center as neere as they can.

This proposition so farre forth as it concernes the two Ele∣ments of Earth and Water, is confirmed by common experience, and therefore needs no long demonstration. For we see plainly, that not only these two doe incline (as much as may be, all ob∣stacles being remoued) to the Center of the Earth; but also all mixt bodies compounded of them, being ouerswayed with the most predominant element, doe challenge to thēselues the same motion. I say not that all these Terrestriall bodies driue & mee•• in the Center (for that were impossible, that all this massy Spheare should bee contracted to one point) but that all the parts haue a mutuall inclination to approach as neere the Cen∣ter, as the necessity of the place, and the concurrence of them amongst themselues will suffer. By these Terrestriall Bodies which inioye this motion and inclination, wee vnderstand first the two Elements of Earth and Water, with all other bodies arising out of their mixture. To these I may adde the Ayre, which by reason of his affinity with the Earth and Water, and naturall cōformity to the same Center, we may well tearme an earthly body. It is commonly reported that the Ayre is l••ght, and therefore carried vpwards, not inclining at all to the Cen∣ter of the Terrestriall Globe; as the parts of these two Elements are. But this assertion, although bolstred vp, both with antiqui∣ty and authority; I take either to bee false, or misunderstood,

and that I speake no more herein than I can proue; I will pro∣duce some reasons (strong enough, as I thinke) to perswade that the Ayre is a heauy body, hauing a due inclination and confor∣mity to the Center of the Earth: First therefore will I produce this experiment. When a Well or deepe Trench is digged vp in the earth, I would willingly demand whether the Aire des∣cends to fill up this Trench or concauity; or else a void space is left vnfurnished of any naturall body to fill it? If they admit the latter, they will consequently bring in againe that vacuum, or void space which Arist. and all sound Philosophers haue long since proscribed the confines of nature. If they affirme the for∣mer, that the Ayre descends to fill vp this empty space, I will aske againe, whether this descent of the Ayre be violent or naturall: If they say Naturall, they admit our assertion, that the Ayre na∣turally descends towards the Center, and so by consequence that it is heauy and not light by nature. Neither according to our Peripateticall-Philosophy can wee ascribe more than one moti∣on to the Aire, because it is a ground generally receaued among Aristoteleans: that One simple body can claime but one simple motion: much lesse one simple forme, as that of the Aire, can produce two opposite and contrary motions, such as are Ascent and Descent of the same body. If they chance to light on the o∣ther member of our distinction, and say that the motion of the Aire in this sort is violent, it must needs follow, that it must haue some externall cause or principle whence it should pro∣ceed; because all such motions proceed from externall causes. But here no such cause can be assigned: For the cause would bee either the Earth which is so made hollow, or the emptinesse, or vacuum, or at least the other parts of the Aire. That it is not the Earth, may be proued; first because no Philosopher hath e∣uer shewed any such Attractiue power to reside in the Earth, but rather the contrary; because the Earth and Ayre by most haue beene thought opposite in nature, and repugnant one to the other. Secondly, because Philosophy teacheth, that no agent can worke vpon a separate and distinct patient, except there be a meeting of the Agent and Patient in some meane▪ But here in this supposition, the Earth is imagined to drawe and attract

the Aire, which as yet it toucheth not. That this externall cause is not the Vacuum or Emptinesse, is plaine; because it was ne∣uer granted to haue any being or existence, much lesse any cau∣sality in nature. Some perhaps will say, that not the vacuum it selfe, but the euitation and auoiding it, is the cause of the mo∣tion. I deny not but this may in some sort be interpreted a cause, but the doubt is not answered: For wee seeke not a Finall but an Efficient cause; and a curious searcher into Nature, will hard∣ly rest in a meere finall cause. For the finall cause, so farre forth as it is a cause preceding the effect, can no otherwise bee con∣ceiued than in the intention of the Agent: then must enquiry bee made againe what the Agent should bee, and so will the probleme rest vncleered. 1. Because one parcell of the Aire could not moue another, except the same were first moued it selfe, and so a new Agent must of necessity bee found out. 2 The Agent and the thing moued or Patient, ought to bee two sepa∣rate and distinct bodies: But the parts of the ayre meeting to∣gether, become one continuate body. No shift is there left for these Philosophers but one distinction, wherein they distinguish betwixt the Vniuersall and Speciall forme, The Aire, as they affirme, according to his Speciall forme, asc••nds vpward from the Center of the Earth: yet by the Vniuersall, for the conser∣uation of the whole vniuerse, it may sometimes suffer a contra∣ry motion, as to moue downeward toward the Center. In which distinction they suppose they haue cut the throat of all contra∣ry reasons. But who so vnderstands himselfe, shall finde it but as a weake reed, to hurt his hand which rests on it: for a second enquiry will bee made, what this vniuersall forme should bee. For by it they vnderstand of necessity either an Internall forme or Nature; or an Externall resultancie and harmony of the parts, such as wee haue described in the first Chapter of this booke. If they vnderstand this latter, it cannot any way bee a cause of this motion; because it followes and ariseth out of this motion concurring with the rest, and no way preceeds it: wher∣as on the contrary part euery cause is to goe before his effect: Secondly, this vniuersall forme or nature compared with the speciall, there would arise a Subordination, and not a Coordina∣tion,

or opposition; forasmuch as the speciall is subordinate to the generall or vniuersall. But subordinate causes can produce no other than subordinate eff••••ts. But here we see the effects or motions to bee quite opposite the one to the other; in asmuch as the motion of Descent in the Aire (which they ascribe to the v∣niuersall forme) is cleane opposite to the motion of Ascent, as∣cribed to the speciall nature. Thirdly, these Philosophers vrging the necessity of Nature to preserue the Vniuerse, are much de∣ceaued in the manner and meanes thereof. True it is that all Earthly and heauy bodies are directed and disposed to the con∣seruation of the earthly Globe. But euery such body (as wee haue shewed before) seekes first the safeguard and preseruation of it selfe, and secondarily by the safeguard of it selfe the preser∣uation of the whole. For how can any part, when it neglects its owne safety, endeauour the preseruation of the whole: sith the whole is but one compounded of many parts. And therefore can it not bee auoided, but that the disorders and disharmony of one part▪ should preiudice and destroy the whole frame. If they turne to the other part, and grant this vniuersall forme to bee Internall, many reasons stand opposite. For first I would de∣mand, whether this vniuersall forme bee simple or compounded. It cannot bee simple, because it would alwayes produce one sim∣ple and vniforme effect: but experience hath t••ught the contra∣ry; because wee shall not alwayes find the aire to descend, but sometimes to moue obliquely to the left or right hand, back∣ward and forward; as when it enters into the house by a doore or windowe. On the other side, it cannot well be called a com∣pound forme; because all formes the more vniuersall they are, the more simple they are to be accounted: because the speciall includes more composition than the generall. Moreouer, all compounded substance arise out of simples, which are to bee esteemed first in nature. Secondly, I would aske whether this vniuersall forme bee vna numero, the selfe same indiuiduall in all the parts and bodies; or diuerse, according to the diuersity of the said Bodies. It cannot bee one and the selfe same in all bo∣dies, because, according to the opinion of Aristotle, the whole vniuerse is not one continuate body composed of essentiall parts;

but rather a heape or masse collected and digested out of many bodies. Secondly, the forme being thus one indiuiduall, would bee singular or speciall, not vniuersall. If they affirme that this forme is diuerse according to the diuersity of the bodies, it can∣not bee the cause of this motion or descent in the Aire. For this motion (as they suppose) is destined and appointed to no other end, than to comfort Nature in her distresse, when shee stands in feare of rupture or dissolution. But how can this forme being bounded within the limits of the Aeriall superficies perceaue or feele this exigence of Nature in other Bodies? Whatsoeuer they can say in this, is altogether vncertaine, and not warranted by any sound demonstration. A second reason for the naturall des∣cent of the Aire, may bee drawne from a possible supposition; from which wee may enforce a true conclusion. Let vs suppose a portion of Aire by some violence to bee carried aboue his pro∣per orbe; as for example, to the space which by our common Philosophers is ascribed to the Element of Fire, neere the con∣caue superficies of the Moone, I would here demand whether this portion of Aire thus transposed would ascend higher, or descend lower, or rest still in the same place? It could not ascend higher; first because in this wise it should be moued farther out of his owne place, whereas according to the principles of Phi∣losophie, all bodies transposed from their proper places, haue an aptnesse or inclination to returne againe to their proper seats, and not to roue farther off. Secondly, this granted, the Aire should inuade the place of the fire and so the Elements should suffer a confusion; which Aristotle holds absurd. Thirdly, there cannot be imagined in that higher orbe any point or center, to which it should direct his motion; and therefore there is no such motion found; or it must bee very irregular. If on the other side it were granted, that such a portion of Aire so separated, should descend; I aske againe, whether they hold this motion naturall or violent: It cannot bee a violent motion, because it is directed to his owne naturall and proper place; and this motion in the Elements, is alwayes accounted naturall. Last of all, it cannot rest still in the same place, because all bodies forced out of their places (all obstacles being remoued) must

needs returne vnto their proper place. Wherefore no other star∣ting hole is here left to our opposites, but that they grant a na∣turall motion, and so consequently yeeld to our assertion. A third reason may here bee drawne from the condensation of the Aire. It is a receiued opinion amongst most Philosophers, that the thinne and subtile parts of the Aire will naturally mount vpward; but the thicker and condensated parts, pitch and set∣tle themselues downeward: Which obseruation, if it bee true, will yeeld vs this conclusion. That the Aire is by nature heauy, and therefore moueth downeward, toward the center of the Sphericall Globe of the Earth. Which I will demonstrate out of these Principles, 1 That that body, which by addition of parts or condensation, is made more heauy or ponderous, must needs haue some weight in it selfe. This may easily appeare, be∣cause the mixture of lightnesse with heauinesse will not intend and encrease the ponderosity, but slacke and diminish it. For the chiefest thing which remits or diminisheth any quality, is the mixture of his contrary, as wee see the quality of cold to be abated and weakened if it entertaine any mixture of heat: 2 The thickning or condensation of any body is made by addi∣tion and coaction of more parts into the same space or com∣passe. As if the Aire or any such like body were thickned, it would confine it selfe to a more narrow roome then before, and so consequenly the narrow roome would containe more parts then before. Out of which wee conclude, that forasmuch as ma∣ny parts pressed together in the same space, make the whole masse more ponderous; these parts so pressed together, must needes haue some waight in themselues. Which may further be illustrated; because the intention of the quality commonly fol∣lowes the condensation of the subiect: Which may easily ap∣peare in red-hot-iron, which burnes and scorcheth more than flame or coales; because euery part hath more degrees or heat. Now where more parts are closely pressed together, the heat must needs bee more feruent. I haue dwelt longer on this sub∣iect, because I would not seeme to broach a new opinion with∣out sufficient reason. To conclude all, and come as neere the re∣ceiued opinion as I can; I will say, that the Aire may bee consi∣dered

two wayes; first absolutely in it selfe; secondly in compa∣rison of heauier bodies, to wit, the Earth and Water. In the first sense I grant no absolute lightnesse in the Aire; because out of his naturall inclination, it tends as neere as it can to the center, as all other lower bodies. But if we consider it comparatiuely in respect of other heauier bodies, we may call it light, that is, lesse heauy or ponderous. So that by lightnesse we vnderstand no absolute lightnesse, but a priuation. The summe of all wee haue hitherto proued, is this; That all terrene bodies, as Earth, Water, Aire, and other mixt bodies which concurre to the composition of the Earthly Spheare, as neere as they can, settle and conforme themselues to the center of the Earth; which site or position of them to the center, is their true and naturall place, wherein they seeke their preseruation.

2 Of two heauy Bodies striuing for the same place, that alwaies preuaileth which is hea∣uiest.

3 Hence it comes to passe that the Earth enioyes the lowest place, the next the Water, and the last the Aire.

The increment or increase of any effect, must necessarily arise from the greater vigour or efficacy of the efficient cause, as both Reason and Philosophie well teach. Now (as wee haue shewed) all heauy bodyes naturally do descend downeward, out of a naturall inclination they haue to attaine the center: but where there is a greater weight or constipation of ponderous parts in the same masse, there must needs proceede a greater inclination: Supposing then the Earth, Water, and Aire, being three waighty bodies to incline and dispose themselues to their vttermost force to inclose and engirt the center of the Terrestri∣all Spheare; it must needes bee that the Earth beeing the most compact and ponderous, must obtaine the preheminence; next to which succeedes the Water, then the Aire, being of all other

the least ponderous. Yet wee deny not but the Water and Aire being setled in this wise, are in their naturall places; which to vnderstand, wee must repeate what we said before, that Nature hath a twofold intention; the one primary, the other secondary. Indeed if we consider Natures primary or speciall inclination in the bodies themselues, we shall finde them (as wee said) imme∣diatly directed to the center as neere as might bee: but the se∣condary intent of Nature was, that the bodies should so settle and conforme themselues, as that each of them should obtaine a place according to his degree of massinesse and waight. Out of this may bee answered a certaine obiection which some haue produced, to proue the Aire to bee absolutely light in his owne nature. Experience teacheth vs (say these men) that a bladder blowne vp with winde, or an empty barrell being by force kept vnder water▪ the force and obstacle omitted, will suddenly ascend to the top; and that a man ready to sinke in the Water, will not so easily sinke downe while hee can hold his breath: all which effects they ascribe to no other cause, than to inclination of the Aire to moue vpwards from the center. But indeed this motion, howbeit agreeable to the vniuersall nature and consi∣stency of the Spheare, is notwithstanding in respect of the Aire it selfe, vnnaturall and violent; because this ascent of it is not caused by the forme of the Aire, but the interposition of a hea∣uier body striuing for the same place, and so reuerberating it backe from the place, whereunto it tended. For here is to bee imagined, that the bladder or empty barrell drowned in the water, claimes and inioyes for the time that place or distance, which otherwise so much water should occupie; to wit, so ma∣ny inches of feete from one side to the other. No maruell then that obstacles remoued, the Water being most ponderous and waighty, receiues his owne right; and (as it were) shoulders out the Aire, and violently driues it off to his owne habitation. Whence many haue imagined that this motion is proper and naturall to the Aire, when of it selfe it is meerely violent, and enforced by the interiection of another body more waighty and ponderous than it selfe.

7 this conformity of the Terrestriall parts, two things are to bee obserued: 1 The center it selfe: 2 The parts which conforme them∣selues vnto it. The Center is an imaginary point in the midst of the Terrestriall Globe, to which all the parts are conformed.

The Fathers of the Mathematicall Sciences, haue laboured to deriue all their doctrine from a point, as the first and most simple principle whereon all the rest depend. Not that they imagine a point to bee any positiue entity in it selfe; but because it is the first bound of magnitude, whence all terminated quan∣tities take their originall. The first princ••••le wee may call it, not of naturall constitution, because a thousand points colle∣cted, could not be so compounded, as out of it should arise the least magnitude; for (as the Philosopher hath taught vs) con∣tinuate and diuisible things cannot bee made out of such things as are meerely discontinuate and indiuisible, but because it is the first Mathematicall principle or beginning of termination and figuration. This point, although it haue euery-where an vse in Geometrie, yet no-where more remarkeable then when it becomes the center of a circle: which center wee ought not to imagine a meere Geometricall conceit, but such as findes ground in the Naturall constitution of the Terrestriall Spheare. For see∣ing all terrene bodies are carried in a right line as by a Radius to one point, from euery part of the circumference; we may ob∣serue a center as it were designed and pointed out by Nature it selfe in the Globe: Some haue here distinguished betwixt a point Physicall, and a point Mathematicall, as allotting the former Latitude, and sensible existence; but making the other meerely Indiuisible. But if the matter bee rightly vnderstood, they are not two points, but all one, distinguished only by a di∣uers name of conceit or consideration. For wee consider first a point as it is existent in a sensible particular body, and so we call

it Physicall. Secondly wee abstract it from this or that body sen∣sible; but alwayes conceit it withall to bee in some body, and in this sort wee terme it Mathematicall: for the Mathematician abstracts not a Quantity or Quantitatiue signe from all subiects; for so being an accident, hee should conceiue it abstracted from its owne nature; but from this or that sensible body, as wood or stone. Such a point ought we to imagine the center of the Earth to be, not participating of any latitude or magnitude, albeit exi∣stent in some magnitude. I am not ignorant that some Writers haue taken a Physicall point for a small and insensible magni∣tude, in which sense the Globe of the Earth is called the center of all heauenly motions. But this sense is very improper; and besides in this example is to bee vnderstood a point Opticall, as such as carries no sensible or proportionable quantity in re∣gard of the sight. Taking then the center of the Earth to bee a point fixt in the middest of the Earthly Spheare, as we haue des∣cribed, wee will further describe the nature of it in two Theo∣remes.

1 The center of the Earth is not an Attractiue, but a meere Respectiue point.

An Attractiue point I terme that, which hath in it a vertue or power to draw and attract the Terrestriall parts or bodies, in such sort as the Loadstone hath a power to draw iron or steele. But a Respectiue point is that, which the Bodies in their motions doe respect and conforme themselues vnto, as the bound or center to which their course is directed. Which may bee illustrated by the directiue operations of the Load-stone (which wee shall hereafter handle) by which the Magneticall Indix or needle pointeth directly Northward: not that in the North is fixed any Attractiue vertue or operation, whic•• might cause that effect; but because the Magneticall Instrument is directed towards such a point or center. That the Center of the earth hath no Attractiue force, may bee proued, 1 Because it cannot in any probability bee thought that an Imaginary point hauing only a priuatiue Being and subsistence, should challenge to it selfe any such operation. For all positiue effects, proceed

out of positiue causes, neither can it be imagined that this At∣traction should grow out of a meere priuation. Secondly, should this be granted, that the motion of Earthly parts should be from the Attractiue vertue of the Center; it would follow necessa∣rily, that this motion should not bee Naturall, but violent: as proceeding from an externall cause, which all ancient and mo∣derne Philosophers deny.

2 The same point is the center of Magnitude and waight in the Terrestriall Spheare.

That the same point in the Terrene Globe, should make the center both of Magnitude and Waight, may seeme very plaine: 1 Because we are not to multiply things and Entities in our con∣ceit, without any necessary consequence drawne from Nature or Reason; enforcing vs thereunto. But what reason could euer perswade any man, that the Earth had two Centers, the one of Waight, the other of Magnitude, but only a bare Imagination, without proofe or demonstration. Secondly, if this were gran∣ted, that the Center of magnitude were remoued some distance from the other; then consequently would one part of the Earth ouer-poize the other in ponderosity, and so the whole Spheare would either be shaken out of its place, or dissolue it selfe into its first principles. Both of which being by experience contra∣dicted, our assertion will stand sure and vndoubted. In the meane space, we deny not but that some little difference may be admitted in regard of the vnequall parts of the Earth; but this must needs be so small and insensible as cannot bee cacullated, or cause any alteration.

8 The Terrene parts conforming themselues to this center, may bee considered two wayes: either Absolutely, or Comparatiuely. Absolutely, as euery part is considered in it selfe.

9 A terrestriall part considered in it selfe, vn∣dergoes

the respect either of a Point of Mag∣nitude; as a point, when any signe or point in it selfe is considered in regard of his con∣formity to the center.

A Point, albeit existing still in some magnitude (as we haue shewed) may notwithstanding bee abstracted from this or that body, as seruing for the center of any body, whose naturall in∣clination and conformity to the vniuersall center of the Earth, we may in the first place handle, as the Rule by which the mo∣tion and inclination of the whole magnitude ought to bee squared.

1 Euery point or center of waighty body, is moued toward the center of the Terrestriall Spheare by a right line.

A Right line is the measure and rule almost of all Naturall actions: which albeit it be familiar in almost euery operation; yet most of all in the motion of the Earthly bodies tending to the center of the Earth. Why Nature in this kind should chiefly affect a Right line, sundry reasons may bee alleaged: 1 From the End which Nature doth propose it selfe, which is to pro∣duce the worke which shee intends, the readiest and shortest way; as Aristotle testifies of her in the 5 of his Metaphisickes. Now it is manifest that a Right line drawne betwixt the same points, is alwayes shortest, as Euclide shewes in his Elements; where hee demonstrates that two sides of any triangle being counted together, are longer then the third. The better to vn∣derstand the working of Nature, wee shall obserue in the moti∣on of a heauy part to the center, a double scope or end; first, that the said part of a terrestriall body, should bee moued or se∣parated from the place to which it is by violence transposed. Secondly, that this body should bee restored home, and vnited to the Sphericall substance of the Earth, in which it must chiefly seeke its preseruation. That these two ends are best and soonest compassed by a right line is most manifest: For first a sepa∣paration

from the place to which it is moued, is more quicke & expedient by a right line; forasmuch as crooked and circular lines, turne backe as it were into themselues againe. Also the v∣nion and coniunction of a part with the Spheare of the Earth, is most indebted to a right motion, because (as wee haue declared) the way is shorter. Secondly, it may bee alleaged, that Nature is an vniforme and necessary Agent, restrained to one only bound or end, and therefore can neither strengthen, weaken, remit or suspend the action, but workes alwayes by the same meanes, the same effects; whence it is that she chuseth a right line, being but one betwixt two points; whereas crooked lines may bee drawne infinite, and the motion directed by crooked lines would proue various and opposite to the prescript of Nature▪ Moreouer should wee imagine that nature at any time wrought by a crooked or circular line, it might be demanded, from what Agent this obliquity should arise? not from Nature it selfe: be∣cause (as wee said) shee worketh alwayes to the vtmost of her strength, hauing no power to remit or suspend her actio••s. But a crooked motion ariseth from the remission or slacking of the Agents force, and turning it away from the intended end, which only findes place in Free and voluntary Agents. Neither comes this Deflexion from the medium, or Aire; because it can haue no such power to resist. Thirdly, if the motion were not performed in a right line, it could haue no opposite or contrary; because (as Aristotle teacheth) To a circular or crooked motion,* 1.4 no other motion can bee opposite or contrary in respect of the whole circle; but only in regard of the Diameter, which is alwayes a right line. By this it is plaine, that a waighty point considered in it selfe ab∣stractly, cannot but be carried to the center in a right line: which right line, really and Physically points out vnto vs a Radius or Beame drawne from the center to the circumference, to shew that the God of Nature in composing the earthly globe, both ob∣serued and taught vs the vse of Geometrie.

2 A point mouing toward the Center, will moue swifter in the end, then in the beginning.

This hath been plainely obserued by experience, that a stone

let fall from a towre or high place, will in motion grow swif∣ter and swifter, till it approach the ground or place whereon it falls. The reason may bee giuen from the Aire, which resist so much the lesse, by how much the body descendeth lower to∣ward the Earth or center; because when it is higher, the distance being greater, the parts of the Aire will make more Resistance. The reason rendred by Aristotle of this Resistance, is, because in the beginning of the motion, the stone or heauy body findes the Aire quiet and fixed: but being once set on motion, the higher parts of the Aire, successiuely moue those which are vnder, being driuen by the violence of the stone so falling, and prepare, as it were, the way for his comming. This reason may in some sort content an ingenious wit, till a better bee found out.

10 So much for the motion of a heauy point or center: it remaines that we treate next of the motions and conformity of Magnitudes to the center of the Earth: wherein we consider not only the Center or middle point, but the whole masse of the magnitude, whose motion and conformity shall bee expressed in this Theo∣reme;

1 The motion of a magnitude toward the center, is not meerely naturall, but mixt with a violent motion:

This may easily bee demonstrated; because no point of any magnitude is moued to the Center naturally, but the middle point or center of the magnitude: For although the Center bee moued in a perpendicular line, which makes right angles with the Horizon; yet the extreme parts are moued in lines parallell, which cannot possibly make right angles with the Horizon, or meet in the Center; which may bee showne in this Fi∣gure.

[illustration]

Let there bee a Circle as ABL. This done, wee will imagine a certaine magnitude hanging in the Aire, and ten∣ding to the Center C, which is signified by the line PEN. It is certaine that the Center of the mag∣nitude E, will moue and conforme it selfe downeward toward the center of the Earth by the line EC, which motion will bee naturall, as that which is deriued to a center from a circumfe∣rence by the direct Radius, which is the Rule of all naturall mo∣tions: But the other parts without the center of this magnitude, cannot moue but in so many lines, which shall bee parallell the one to the other: as for example, the point N must needs moue in the line NG, and the point P in the line PF, which being of equall distance, will neuer concurre in the Center, and therefore cannot bee esteemed naturall rayes of the circle; whence wee may collect, that the motion of these parts is not naturall, but violent: for if any should imagine the motion of these parts to be naturall, then should the point N moue to the center of the Earth by the line NC, and the point P. by the line PC; and so by how much the more any waighty body should approach the Center of the Earth, by so much it should bee diminished and curtailed in his quantity: so that in the Center it selfe, all the parts should concurre in an Indiuisible point, which is absurd & contradicts all reason.

11 Hitherto haue we spoken of the conformity of all Earthly and waighty bodies to the Ter∣rene center, as they are taken Absolutely. It

now remaines that we speake of these bodies as they are taken comparatiuely, being compared one with the other.

This discourse properly belongs to an art which is called Sta∣ticke and Mathematicall; whose office is to demonstrate the af∣fections of Heauinesse and Lightnesse of all Bodies out of their causes. The chiefe sensible Instrument whereon these proper∣ties are demonstrated and shewne, is the Bilanz or Ballance. But these specialties wee leaue to such as haue purposely writ∣ten of this subiect: amongst which the most ancient and chiefe is Archimedes, whose heauenly wit ouertooke all such as went before him, and out-went all such as followed. Enough it will seeme in this Treatise to insert a proposition or two Staticall, to shew the Conformity of two magnitudes, and their proper Center, mouing downeward toward the Globe of the Earth, and it's Center.

1 The lines wherein the centers of two heauy bo∣dies are moued downeward, being continued, will meet in the Center of the Earth.

A heauy point or Center (as wee haue demonstrated hereto∣fore in this Chapter) is moued toward the Center of the world in a right line, which is imagined to bee a Ray of the whole Spheare deriued from the circumference to the Center, & ther∣fore it is impossible they should bee parallell or Equidistant, but concurrent lines. But because the whole distance betwixt vs and the Center is very great; it must needs happen that in a small space the concurse of perpendicular lines is altogether insensible. For if two perpendicular or heauy points moued in a line, should be distant one from the other the space of 10, a 100 or more feet; because this distance is very little in respect of the semidiameter of the Earth: the angle of concurse must needs be very little, and by consequence those two rayes or lines, measu∣ring the descent of two heauy Bodies, will seeme altogether Equidistant. Yet that there is such a concurrence, Nature and

Reason will easily consent. Hence wee may detect a popular er∣rour beleeued of the vulgar, that the walls of houses standing vpright are parallell and of equall distance; when contrariwise it is plaine that such walls are erected by a perpendicular, and measured by perpendicular lines, which being drawne out in length will meet in the Center of the Earth. The like may we pronounce of a deep Well, whose sides or wall are erected per∣pendicularly; and therefore should it reach as farre as the Cen∣ter, it must needs follow that the sides growing neerer and nee∣rer as they approach the Center, would in the end close or shut vp into a Pyramide, whose Base should bee the mouth of the Well. Likewise if a Tower should bee erected to the Heauens, it would be strange to imagine, how great and broad the vpper part of it would bee in respect of the bottome. Hence againe it may be inferred, that any p••uement leuelled by a perpendicular is not an absolute plain, but rather the portion or Arch of a sphe∣ricall superficies, whose Center is the same with the Center of the whole E••rth. But this roundnesse in a small distance is no way sensible: but in a great pauement of foure or fiue hundred paces leuelled perpendicularly; it will make some shew of roundnesse: whence it must needs follow, that an extraordinary great pauement measured ouer by a right line, cannot be called leuell or equally poized, forasmuch as it is not euery where e∣qually distant from the Center of the Earthly Globe.

2 Two heauy bodies of the same figure and matter whether Equall or Vnequall, will in equall time moue an equall space.

This proposition being inuented by one Iohannes Baptist de Benedictis, is cited and confirmed by Iohn Dee, in his Mathema∣ticall Preface to Billing slie's Geometry; Which corrects a com∣mon errour of those men, which suppose the lighter bodies ge∣nerally not to moue so fast downeward to the Center as the hea∣uy. The demonstration of this Theoreme, being drawne from many Staticall principles, which we cannot here conueniently insert, wee are enforced to omit: as intending not the search of these matters any farther than they direct vnto the knowledge

of Geographie. Yet were it no hard matter to giue •• more po∣pular expression of this reason out of the proportion betwixt this weight of the heauy Body, and the Resistance of the Medi∣um. Because the Greater Body, as it is carryed down-ward by a greater force and violence; so on the other side it meets a grea∣ter impediment, being not able so soone to diuide the Aire, as the Lesser: Likewise the Lesser body falling with lesse force, yet is more apt to diuide it then the other. Whence both set the one against the other, there will be no disparity in the time and motion.

12 Of the primary conformity of the Terrestri∣all bodyes in the constitution of the Terrestri∣all Spheare, wee haue treated: It now seemes needfull that we descend to the secondary, which is the inclination of all the parts, to make a round Spheare or Globe.

1 The Terrestriall Globe is round and Sphericall.

This Proposition is of great vse, and one of the chief•••••• grounds in Geographie. The ground of the Sphericall figure of the Earth, is the right motion of heauy bodies to the center. For this right motion (as wee haue shewed) doth expresse one Beame of the circle, by whose circumuolution is pro••uced the circumference of i••, which we call Secundary conformity of the parts of the Earth; in so much as it growes Mathematically (as it were) out of the first. For this Sphericall figure of the Earth, sundry sound reasons are vrged by Geographers: First, that the Earth is round according to its Latitude, that is, from North to South▪ Secondly, according to its Longitude, that is, from East to West, and therefore must it needes bee abso••utely Sphericall▪ The first part is shewed, that it is round from N••rth to South; for if a man trauell from North to South, or contra∣riwise from South to North, hee shall perceiue n••w starres in the Heauens to appeare and shew themselues, which before h••e

could not see: which can be referred to no other cause then the Sphericall conuexity, or swelling of the Earth. As for example▪ The starre which is called Canopus, which is a notable starre in the ship; appeares not at Rhodes, or at least from high places. But if you trauell forth Southward from Italy into Egypt, to Alexandria, the same starre (Proclus obserues) will manifest it selfe to your sight the fourth part of a signe aboue the Horizon.* 1.5 From whence wee may draw a sound proofe, that there is a Sphericall and gibbous conuexitie, which interposeth it selfe betwixt Rhodes and Egypt. In which place, the people who inhabite that part of Egypt, which borders vpon Arabia, which are called Troglo••ites, of their dwelling in caues, cannot see any Starre of the Great Beare. Whence wee may conclu••e, that the Earth from the North to the South, is round and Sphericall. For if otherwise the Earth were plaine, all the Northerne starres would appeare to the inhabitants of the Southerne Regions; and on the other side, all the other Southerne constellations would bee seene of the Northerne inhabitants, which sense and reason altogether contradict. Secondly, that the Earth is round accor∣ding to its Longitude betwixt East and West, may bee proued by two reasons. The first is taken from the rising and setting of the Sunne, Moone, and other Starres, for as much as all they doe not arise or set with all Nations at the same houres. For with the inhabitants of the East, the Sun-rising is sooner; with the Westerne inhabitants later; and that in such proportion, that euery 15 degrees measured out by the Sunnes diurnall moti∣on, adds or subtracts one whole houre in the length of the day. This is found by experience and testimony of Cosmographers, that the Sunne riseth with the Persian, inhabiting toward the East, foure houres sooner then to the Spaniard in the West. Sundry other the like examples may bee alleaged; all which we must needes impute to the Sphericall roundnesse of the Earth, proportionally increasing betwixt East and West. The other reason to confirme this last point, is drawne from the Ecclipses of the Sunne and Moone, which would not appeare in diuers places, at diuers houres, if the Earth were plaine or square. We see plainly that Ecclipses of the Moone appeare sooner to the

Westerne people, but later to the Easterne. As (according to Ptolomie) in Arbela a towne of Assyria (where Alexander ouer∣came Darius the last King of the Persians) was there obser∣ued an Ecclipse at the fifth houre of the night,* 1.6 which selfe∣same Ecclipse was seene in Carthage at the second: which to a∣ny man appeares plainly in this figure here inserted. In like man∣ner an Ecclipse of the

[illustration]

Sunne at Campania which was obserued betwixt 8 and 9. was (as Pliny reports) seene in Armenia be∣twixt 10 and 11 of the clocke.* 1.7 Whence may be gathered that this difference of ap∣pearance arose from the roundnesse of the Earth, interposing it selfe betwixt these two places. Another reason to proue the Spericall figure of the Earth, is drawne from the Ecclipse of the Moone, wherein the obscured point is described by a Sphericall figure, which must needs argue, that the body which causeth the shadow, is also round. For as the Optickes teach vs, the shadow is wont to follow and imitate the opacous body whence it proceedes, and all men confesse that the Ecclipse of the Moone is made by the interposition of the Spheare of the Earth betwixt the Sun & Moone, intercepting the beames of the Sun, which should illu∣strate & lighten the Moone. The third reason may be taken from the absurdities which would follow, should we admit any other figure besides. For granting it to be plaine (as some of the Plato∣nists haue imagined) it would necessarily follow in reason; 1 That the Eleuation of the Pole would bee the same in all the parts of the Earth. 2 That there Would bee the same face and appearance of the Heauens in all places. 3 That the Sunne and Moone, with other starres, would in all places arise alike at the

same houres. 4 That all Ecclipses would appeare to all places at the same houres. 5 That the same quantity of dayes & nights would bee at all places. 6 That the shadowes would bee euery where alike; and one Region would not bee hotter or colder then another; all which would plainly stand opposite to reason and experience. As many or more would proue the absurdities of those, that ascribe to the Earth any other figure then Sphe∣ricall. Which I willingly passe ouer, as not willing to fight with shadowes, and faigne an opposition, where I scarce finde an ad∣uersary. These reasons are sufficient to proue, that the whole masse of the Earth is Sphericall. Diuers other popular argu∣ments may be drawne from the finall cause to countenance this Assertion. For no other figure can bee assigned to the Earth, which can more vphold the order of Nature, or speake the wis∣dome of the Omnipotent Creator. 1 Because such a Figure would best beseeme the Earth, the seate and dwelling-place of all liuing Creatures, which is most capable: because otherwise the God of Nature would seeme to doe something in vaine, and without cause: Forasmuch as the same capacity might bee con∣fined within stricter bounds. Now it is apparant to all Mathe∣maticians, that amongst all those figures which they call Isope∣r••••etrall, a Circle is the most capable, and amongst the rest, those which appro••ch neerest vnto a circle. And as wee esteeme of a circle described in a plaine surf••ce, so must we iudge in solides of a Spheare. Which profitable Geometry of Nature wee shall finde instilled into most liuing Creatures, who by a certaine Na∣turall Instinct, without the vse of Reason, make their Nests and resting-places of a Sphericall Figure, as most conuenient, and of greatest capacity; as experience shewes vs, in the Nests of Birds, and Bee-Hiues, wherein the cells are fashioned round & Sphe∣ricall. 2 We shall find the holy Scriptures consonant to this o∣pinion in diuers places; but that it might seeme impiety to vse those sacred helpes in a matter out of controuersie, and needing no such Demonstration.

2 The rugged and vnequall parts of the Earth, hinder not the Sphericall roundnesse of it.

It is thought by ignorant people, that the Earth is not round, because of the rugged and vneuen parts of the superfi∣cies of it: For some-where it swells with great and high moun∣taines, rocks, and hills; Other-where it seemes indented, and (as it were) trenched into valleyes, & concauities; all which seeme to detract from a true Sphericall superficies; because in such a one, euery line drawne from the Center to it, should bee equall one to the other. Indeed that the Globe of the Earth is not Abso∣lutely and Geometrically round, as an Artificiall Spheare, is con∣fessed by Eratosthenes, cited by Strabo in his 1 booke of Geogra∣phie▪ whence Pliny in his •• booke, cap. 21. saith,* 1.8 that the Earth & Water make one Globe, not so absolutely round as the Hea∣uens, but much different, 〈◊〉〈◊〉 also Strabo confirmes. This propo∣sition depending on these 3 reasons which follow, will shew that this Inequality, how great soeuer it seeme to the sight, is altogether insensible, and bearing no proportion with the huge vastnesse of the whole Earth. The first is taken from the per∣pendicular hight of the greatest and highest mountaine, which is seldome or neuer found to exceed 10 miles, (although few Mathematicians will grant so much) whereas the whole Dia∣meter of the Earth containes no lesse th••n 7200 English miles; so that these hils compared to the thicknes of the Earth are but ••s 10 to 7200: which indeed hath no sensible proportion. The se∣cond is taken from the Ecclipse of the Moone, which being caused by the shadow of the interposed Earth, is described by a Sphericall figure, without any vnequall or rugged parts, which no doubt, would appeare, if these parts challenge any due proportion▪ or sensible quantity, in respect of the whole Earth. Thirdly, some haue illustrated this by a round bowle, or ball, whose externall surface, although vnequall, and indented here & there with scotches, other-where swelling with knobs, will notwithstanding being interposed betwixt the Sun-beame and a wall, or such place, giue a round or Sphericall shadow in the same wall or plaine, in regard of the little quantity of these small parts in respect of the whole Body. In like sort must wee imagine the mountaines and vnequall parts in the face of the Earth, to bee no otherwise then as so many warts or pimples in

the face of man, which cannot alter his du•• proportion or sym∣metry of the parts.

3 The Water concurring with the Earth in the Globe is also Sphericall.

It is a proposition agreed on by Archimedes, and almost all the ancient Mathematicians of any note, that the superficies of the Water, or any other liquor, standing and subsisting quietly of it se••fe, is Sphericall; whose center will bee the same with the center of the whole Earth, which we are here to handle, be∣cause it appertaines to the making vp of the Terrestriall Globe; although wee shall haue occasion hereafter to speake specially concerning the Water in Hydrographie, in the second part of this Treatise. The reasons to confirme this assertion, beside those that in generall proue the Sphericity of the Terrene globe are diuers: 1 It is obserue that Passengers in a Ship, lanching out into the deepe from some Hauen, will first perceiue the Towers, Buildings, Castles, Promontories, and Trees standing on the land, in their perfect figure and greatnesse: sayling far∣ther off, they will obserue them on the lower part, little & little diminished, vntill such time as the tops only of the houses and trees will bee visible. In like sort they which tarry on the Land, will first espye the top and mas•• of a Ship approaching, which sight will bee perfected more and more, as the Ship drawes to∣ward the land, and at last all parts of it will shew themselues; which accident can bee cast vpon no other cause, then the Sphe∣ricall

[illustration]

roundnesse, and swelling of the water; which, if the di∣stance be great, interposeth it selfe betweene the station on the Land and the Ship where∣in Passengers are conueyed, which experiment is expressed in this Diagramme here anne∣xed. Certaine Platonicks, of which the chiefest is Patricius a late Writer, would ascribe

this experiment to the impediment of the sight, caused partly by the distance wich cannot perfectly represent the ob∣iect, partly by the interposed vapours arising in the Sea; part∣ly by the quiuering light which is spread by the refraction of the Sun-beames in the water. I deny not but these causes may somewhat hinder, and cause that the true and perfect species of a body cannot alwayes visit the sight. Yet will it bee euident that this is not all, but that the Sphericall roundnesse of the wa∣ter will proue a greater impediment where the distance is any thing greater. But for one of Patricius his shifts concerning va∣pour arising out of the Sea, (to which Clauius seemes also to consent in his Commentary vpon Iohannes de Sacrobosco) it makes more for our assertion then his. For that which is seene in a thicke medium, according to the doctrine of the Opticks, seemes greater in quantity, and by consequence neerer, and so higher then would otherwise appeare: as wee see by experience, that the Sunne sometimes is seene of vs before it ascend aboue the Horizon, because of a refraction of it's beames in a thicke matter. Wherefore it were rather to be imagined, that a tower seene at Sea, or a ship from the land, through these thicke and grosse va∣pours, should appeare higher, and seeme neerer then if it met not with such vapours. Secondly, what is vrged concerning the trembling light, caused by a refraction of the Sun-beames in the water, is of no force: For although such a light might cause an impediment or hinderance to the sight; yet would not this decrement or hinderance bee by degrees and in such pro∣portion as we find it to be correspondent, to wit, to the distance interposed. And much wonder it is that Patricius (as my learned Friend M^r R. Hues obserues) being, as it seemes very well read in the stories of Spanish nauigations, should not bee conuinced out of the Navigation of Magellane, who taking his iourney toward the Southwest parts, passed by the Magel∣lane straights, now called by his name, and so returned by the Cape of Good Hope into Spaine, to which wee way adde the voi∣ages of Drake, Candish, and many others. The second reason is vrged by Aristotle in his 2^d booke de coelo, and hath its ground in Archimedes lib. 1. de Aqua-vectis, which is formed in this

sort. The nature of the water is to affect and flow to the lower place, whence it must necessarily bee inferred that it must bee round, for otherwise it should not alwayes obtaine the lower place. The reason of the consequence shall bee expressed in this

[illustration]

figure; for if we ascribe to the wa∣ter a plaine superficies, let it for example bee ADB, and from the center of the earth C let there be described a circle, to wit, EGF, then let there be drawne CD, a perpendicular line to AB, and let AC and BC be ioyned together. Now because the right line CD is lesse then CA, or CB, as will appeare euidently by sense; it will be plaine that the point D will be in a lower place then the point A or B, because D is neerer to the Center; for as much as DC is but a part of a beame of the circle whereas AC and CB euidently exceed that quan∣tity or proportion. Another reason there is, commonly drawne from the roundnes of drops cast on the sand, as also from water in pots, whose superficies seemes to swell aboue the brimmes; but this reason, as we shall proue in place conuenient, is rather against this assertion then for it; because indeed, wee affirme the water to be round▪ but so as it claimes the same Center with the Center of the Terrene Globe; and therefore cannot be sensible in so little a portion, as a drop, or pot of water. This proposition being sufficiently proued by these two reasons; it is needfull in the second place that wee answer certaine obiections cast in by the said Patricius against our assertion. Euery surface of the water (quoth Patricius) is either only plaine, or only round, or both plaine and round, or neither plaine nor round: First that it is not both plaine and round, seemes very euident, for so it should admit of contrariety: Neither can one part be plaine and another round, because the water is an vniforme and homo∣geneall body, not consisting of such vnequall parts: that it should neither bee plaine nor round seemes more impossible, be∣cause f••w or none haue dreamt of any other figure. Lastly, that it is not round only, hee labours to confirme by sundry rea∣sons

and experiments. First, he testifies of himselfe, that sayling in the Sea, he plainely ••aw in the morning before Sun-rising, the Mountaines of Corsica; which afterward, assoone as the Sunne was risen, vanished out of his sight. Whence he concludes, that this proceeds not from the roundnesse of the Earth, but from some other cause. But this argumēt to iudicious men will seeme very weake, 1 Because it depends altogether on the authority and credit of Patricius, whose assertion I take to bee no better then another mans deniall. 2^ly were this argument euery where sound, yet would it proue no other thing, but that this effect were not to be imputed to the Sphericall swelling of the Earth. Whence cannot bee drawne any generall conclusion, that the Earth or Water is not Sphericall. Wee deny not in the meane time▪ that other causes sometimes concurre, which may hinder or take away the sight of obiects from those who saile on the Sea. The second experiment, Patricius describes in this manner. At a certaine Towne called Coma••lum (saith hee) there is a ve∣ry great poole; through which poole or lake some 3 yeares a∣goe, it was my chance to bee carried in a boat. The bottome of the water almost all the way in all the iourney appeared to bee lesse then 2 foot in depth from the top. The way increasing, at first the lower parts and foundations of houses, then the tops and princely pinnacles began to vanish from our sight: at last hauing scarce passed 6000 paces, a Tower 72 foot high began to appeare, as it were cut off by the middle, and from the middle part vpward appeared visible; but after 10000 paces it was taken out of sight: I would here aske the Geographers (quoth Patricius) whether in so short a distance, wherein the bottome for the whole space surpassed not two foot in depth, the water could ascend to 72 foot? Had it beene my chance to haue gone with Patricius ouer the lake, I might perhaps by obseruation of this experiment, haue giuen a more probable coniecture of the cause. Neuerthelesse being vnacquainted aswell with the place, as the truth of his obseruation, I may perhaps guesse somewhat at his errour. First then, whereas hee auerres, that passing along for the space of a 1000 paces, a Tower of 72 foot high, seemed cut off by the midst, which at 10000 vanished

out of sight. I confesse that in so short a space the swelling of the water inter-posed, could not be so great as to hinder the sight, and bee the cause of this effect: wherefore some other Acciden∣tall cause must bee sought out. For the finding out of which to come as neere as I can, I would make inquiry, whether this passage of the Boat was directly forward from the Tower on the Water, no land inter-posed: or Indirectly side-wise, in such sort, as the shoare might be placed betwixt their sight and the Tower mentioned: The former no wayes can be imagined; for∣as much as it not only contradicts the grounds of our receiued Philosophie; but also of Patricius himselfe: for giuing the Earth a plaine surface, or Angular, or any other forme, it were impos∣sible that in so short a distance, such an effect should happen out of the figurature of the water. If the passage were oblique or in∣direct, in such wise as the shoare might any way inter-pose it selfe betwixt the Boat and the Tower, it were easie to imagine how such an experiment should happen: for the land by which the Boat might bee carried, might haue an ascent by such De∣grees, as the Tower at 1000 paces might bee for the halfe of it obscured, and at last bee altogether taken out of sight. This rea∣son then of Patricius, seemes rather to bee ascribed to the Land then the Water. The third reason of Patricius is drawne from the Homogeneity of the Water. If the water (saith hee) haue a round superficies, the parts of it would challenge the like figure, because in homogeneall bodies, the same reason is to bee giuen of the whole, and of the parts: But the parts of the water are not Sphericall, as may bee proued by diuers instances: 1 Because water in the mouth of a pot, seemes not to haue any such Sphe∣ricall roundnesse: for although at the brinke it seeme to bee re∣strained aboue the pot, yet no such swelling appeares in the middle. 2^ly That riuers are kept in by their bankes, which o∣therwise would flow abroad. 3^ly That riuers, when by the mel∣ting of snow, they swell so great, as they can hardly bee contay∣ned within their bankes, doe not seeme higher in the middle, then in other places. 4^ly If any man from one side of the riuer to the other, leuels at any marke, he may surely hit it: which hee should not doe, if there were any Sphericall swelling in the

midst, which might hinder the sight. 5^ly and lastly it seemes so vnlikely, that the water should rise in the midst, that it is more probable it should be more hollow; in that we plainly obserue that all filth and rubbish carried from the bankes into the riuer, is wont to settle and swimme in the midst. Notwithstanding all these argumēts of Patricius, our ground is yet vnshaken; 1 Con∣cerning small drops, and water in the mouth of pots; it is found to be round and Sphericall, though not exactly: the reason wher∣of wee shall declare hereafter. This roundnesse, I confesse, serues not any way to the confirmation of this assertion, because the Sphericity and roundnes which wee auerre to be in Water, hath for its center, the center of the whole Earth: and therefore in so small an arch or section, as the bredth of a pot, or a drop of water, cannot possibly haue any sensible appearance or existence. And we must needs confesse, that this experiment was very fondly vrged to this purpose by some of our Geographers, and such as stands not with any demonstration. Which granted, sufficiently answers all the reasons last vrged by Patricius, except the last. For as much as he requires in the Water, a sensible appearance of this roundnesse in euery riuer or little parcell of water, which cannot bee admitted. Touching the last thing which hee vrgeth, that all the rubbish and filthy matter, is from the bankes carryed into the middle, whence he would inferre▪ the middle to be hol∣low and lowest; we can answer diuers wayes: 1 That this ex∣periment is not alwayes certaine, because euery man may often∣times see the contrary; to wit, that such filthy rubbish rather vseth to cleaue to the banks of the riuer, then to float into the midst. 2^ly That if any such thing happen, it is because of the tor∣rents which run violently from the banks into the midst, carry∣ing with it such things as are light, the steepnesse of the place being greater, the current wider or swifter. But nothing here can bee concluded to proue the water according to his naturall force, to be either plaine or hollow in the midst, which this Ad∣uersary vndertooke to demonstrate.

CHAP. III. Of the Partiall magneticall affections in the Spheare of the Earth.

1 HItherto haue we discoursed of such affe∣ctions of the Terrestriall Spheare as are Elementary, and knowne heretofore to ancient Philosophers: It followes in the next place that we treat of Magneticall affections, to wit, such as follow the magneticall nature of the Earth.

Of the vertue and propriety of the Load-stone▪ many haue written, but few sought out the true nature. The inuention of it is attributed to a certaine heards-man, who hauing his shooes shod with iron▪ and an iron-pike in his hand, resting himselfe on a quarry of Load-stone, could hardly remoue himselfe frō thence. But this seemes rather a pleasant Poeticall inuention, then a true History, hauing no good Author to auouch it. But to let passe the first Inuention, being a matter rather indebted to chance then industrie; no small difficulties haue discouered themselues in the inuention and finding out of the causes of Magneticall properties. Somewhat, I cōfesse, hath been written of such mag∣neticall affections as haue been most knowne; such as is the ver∣tue Attractiue, by which it drawes to it selfe iron, or steele; as also the vertue Directiue, by which a needle touched with the Magnet, directs and conformes it selfe North and South. The rest of Magneticall proprieties I find in ancient Writers, as little knowne as their causes; & if any matter herein were broached, it was merely coniecturall, and depending on no certain demō∣stration: neither had we any certaine or satisfactory knowledge

of this thing, vntill such time as it pleased God to raise vp one of our Countrymen D. Gilbert, who to his euerlasting praise hath troden out a new path to Philosophy, and on the Loadstone ere∣cted a large Trophie to commend him to posterity. This famous Doctor being as pregnan•• in witty apprehension, as diligent in curious search of naturall causes: after many experiments, and long inqui••y, found the causes of most magneticall motions and proprieties hid in the magneticall temper and constitution of the Earth, and that the Earth it selfe was a meere Magneticall body challenging all those proprieties, and more then haue expressed themselues in the Load-stone. Which opinion of his was no soo∣ner broached, then it was embraced and well-commed by ma∣ny prime wits, aswell English as Forraine. In so much that i•• hath of late taken large root, and gotten much ground of our vulgar Philosophie: Not that in the maine scope and drift of it▪ it contradicts or crosses all Peripateticall principles, or the most part of such grounds as haue hitherto borne the stampe aswell of Antiquity, as of Authority: But that it hath brought to light matters of no small moment, which neuer found any ground or footsteps in our ordinary Philosophie. This new Philosophie I dare not commend as euery-where perfect and absolute, being but of late yeeres inuented, and not yet brought to mature per∣fection: yet would it sauour of little ingenuity or iudgement in any man, peruersely to deny all such Magneticall affections in the Earth as are grounded on plaine experiments and obseruati∣on, sith no Philosophie was euery way so exact, but required experience dayly to correct it. I intend not here an absolute dis∣course of Magneticall Bobies and Motions, but leaue it to their search whose experimentall industrie is more suteable to such a subiect. Onely I will shew some generall grounds appertaining to the constitution of the Terrestriall Globe, which I hold ne∣cessary for a Geographer. Wherefore ere I curiously distinguish these Magneticall proprieties of the Earth into other seuerall kindes, I will set downe this Theoreme, as a ground or founda∣tion of that which followes.

1 The Terrestriall Spheare is of a Magneticall nature and disposition.

A Magneticall Body by some is defined to bee that which seated in the Aire, doth place it selfe in one place naturall, not alterable. This situation is supposed to agree to all the Starres▪ especially to the great Globes of Saturne, Iupiter, Mars, and the Sunne; as also to such as giue their attendance on them, late∣ly detected by the Trunk-spectacle; to wit, those two Starres which moue about Saturne, the foure which moue about Iupi∣ter, the two which circle about the Sunne, as Venus and Mer∣curie; and lastly the Moone, which encompasseth the Spheare of the Earth. But to let passe those other Globes, as farther off, and therefore lesse subiect to our search: our discourse shall only touch the Earth whereon wee liue, which wee shall proue to partake of a certaine Magneticall vertue or inclination: which to shew more openly, we must vnderstand, that all Magneticall Globes haue some parts of their bodies which bee also Magne∣ticall, which being diuorced from their proper Spheare, & mee∣ting no obstacle, will settle themselues to the naturall situation of their peculiar Orbes. Which wee may plainly perceiue in the Spheare of the Earth, wherein wee shall find two Magneticall minerals; whereof the one is the Load-stone, attracting iron or steele; the other the Iron or steele it selfe: either ofthese two▪ artificially hanged in the Aire, or placed in a little boat on the water, all incombrances being remoued, will conforme & settle their parts and Poles correspondent to the poles and parts of the Terrestriall Spheare, as North and South. This hath been found in all parts of the Earth by such as haue trauelled round about her, as Drake and Candish, whose Compasses were alwayes di∣rected Magnetically in all places which they passed: which we cannot ascribe to any other cause then the disponent faculty of the Earth's Magneticall Spheare, as shall appeare hereafter by demonstration. Moreouer it hath been obserued by such as saile Northerly and Southerly, that the Magneticall Inclinatory nee∣dle, in euery eleuation of the Pole is conformed and disposed to the Axell of the Earth, according to certaine angles answerable

to the latitude of the Region, as wee shall shew hereafter. This diuersity of conformity must necessarily arise, either from the Magneticall instrument in it selfe absolutely considered, or els from the Harmony and correspondency it hath with the Ter∣rene Globe. It cannot be the first; because it should bee the same in all places and Regions of the Earth, which is contrary to ex∣perience, and our supposition. Then must wee needes deriue it from the Magneticall disponent vertue of the whole Globe of the Earth, from which vertue the whole Earth may bee called Magneticall. Nay if we truely consider, these Magneticall affe∣ctions primarily agree to the Earth, as the mother of all Magne∣ticall bodies; but afterward secondarily are deriued into the parts; because (as Gilbert relates it) the cause of magneti∣call motions and affections is the magneticall forme of a Spheri∣call Globe; which forme first agrees to the whole Globe of the Earth, and so is deriued to all his homogeneall parts. These parts are called Homogeneall, not in regard of their Matter and quan∣tity, but in respect of their Magneticall nature, and communion, which in euery part is conspicuous. If any man should wonder why the Earth should bee called Magneticall in regard of this minerall, which seemes one of the least and scarcest substances whereof it consisteth; we may many wayes answer, First, that although the surface of the Earth seemes for the most part com∣posed of other materials, more conuenient for the vse of liuing Creatures which dwell therein: yet may infinite rocky mines of Magnets be couched lower toward the center, which streng∣then and consolidate the Earthly Globe▪ Secondly, wee must not imagine the Magneticall substance of the Earth, to bee all one kinde of stone, but various: for somewhere it is hard & so∣lide as the true magnet it selfe and the iron which is nothing els but a mettall decocted out of the Load-stone; (for iron O••••e differs little or nothing at all from the Load-stone it selfe) some∣where againe, this substance is more thinne and fuid, being lesse concocted as some kinde of clay, and certaine vapours ari∣sing out of the Earth, which bee magneticall: which being brought to a harder and more massie substance, will haue the same affections and motions with the Loadstone it selfe. This

assertion of the Earth's magneticall nature, wee shall confirme more euidently hereafter, where we shall proue both the Poles, the Meridian, Parallels, and other circles, to bee not bare Ima∣ginary lines, as some haue thought (but to bee Really grounded in the magneticall nature of the Earth, and are to be shewed in any round Loadstone, wrought and placed conueniently with instruments thereunto applied.

2 The Magneticall affection of the Earth is twofold, either Radicall or Deriued The Ra∣dicall disposition we call that which is the first root and ground of all other magneticall mo∣tions.

3 The Radicall vertue or inclination is a∣gaine twofold, either Motiue or Disponent. The Motiue is that by which all magneticall bodies are inclined and stirred vp to the mo∣tion.

In the Reasonable soule of a man, wee haue two faculties which shew themselues; a motiue, and a directiue or disponent power: whereof the one stirres vp the motion, the other regu∣lates, conformes, and directs it: The former is the Will, the later the Discourse and Iudgement. This distinction of faculties, how∣soeuer more euident in the soule, findes place in all Naturall a∣gents: in which a Philosopher ought to distinguish betwixt that which giues them a power to moue, and that which limits, determines, and (as the Schoolemen are wont to speake) mo∣dificates the action. Amongst others the magnet-stone seemes most to partake of these two powers, as that which amongst all naturall agents (in Gilberts opinion) seemes most to haue resemblance with the soule of a man: so that by an apt Trope it hath been called of many, the Magneticall soule of the Earth; for hence wee may well perceiue one vertue or inclination, which ••••useth the magneticall needle to moue out of its place; ano∣ther

by which it is apt to conforme it selfe North and South, as also to obserue certaine angles correspondent to the latitude of the place, as shall bee demonstrated in due place. Of the mo∣tiue power we will produce these Theoremes.

1 The Magneticall motion is excited in a small & vnperceiuable difference of time.

This proposition may be shewed out of euident experiment, wherein euery mans sight may be a witnes. For if an Iron-needle touched with the Loadstone, be placed within the Spheare of the magneticall vertue of the stone, it will presently moue it selfe, notwithstanding the interposition of solide bodies, which made Gilbert to imagine this motion to bee effected by a meere spirituall and immateriall effluxe, which may well be compared to the light, which neuerthelesse it surpasseth in subtility: for the light is moued from East to West so quickly, that many haue thought this motion to haue been in a moment or instant of time. But this quicknes of motion may much more be imagi∣ned in the Magneticall vertue, being of a more subtile and pier∣cing nature, as may bee gathered from this reason, to wit; That the light is alwayes hindered by the interposition of a thicke and opacous body; but the vertue Magneticall findes a passage through all solide bodies whatsoeuer; and meets with no im∣pediment.

2 This Motiue quality is Spherically spread through euery part of the Magneticall body.

Here againe may wee finde a great resemblance betwixt the magneticall vertue and the light; for as all light Bodies, as the Sunne, Moone, and Starres, cast their beames euery way into an orbicular forme: so this Magneticall vigour casts it selfe a∣broad not only from the center toward the superficies, but from the superficies outward into the Aire or Water, where this mag∣neticall body is placed, and so makes vp a Spheare; but yet with this difference, that if the body bee meere and perfectly Sphericall, the Orbe of the magneticall vertue will end in a perfect Spheare, as wee see the magnet G to confine his vertue

[illustration]

[illustration]

within the Circle BF. But if it be a square, or any other fi∣gure not Sphericall, it imitates a Spheare as neere as the body will suffer, in that it spreades it selfe euery-where from the cen∣ter by right lines; yet will it be confined in a square figure cor∣respondent to the body, whence it proceeds, as we see the vertue of the square magnet A, to cast his beames into the square figure LD.

3 The motiue quality of the Magneticall body is strongest of all in the Poles, in other parts by so much the stronger by how much these parts are situated neere the Poles.

Wee suppose out of the principles of Magneticall Philoso∣phie, that a Magnet hath two Poles, whose vse wee shall shew hereafter. These Poles are found by experiment to haue more force and vigour in them then other parts, and all other parts to enioy more or lesse force, by how much neerer or farther off they are situated to their Poles. The reason is ascribed by these Writers to the disposition of the Magneticall vigour in the bo∣dy of the Load stone, as shall appeare by this figure following in Gilbert, expressing the great Magneticall Body of the earth. Let the Sphericall superficies of it bee HQE, the Pole E, the Center M: HQ the plaine of the Equinoctiall; from euery point of this Equinoctiall plaine, the vigour Magneticall is conueyed and extended to CFNE; and to euery point from C to E the Pole: but not towards the point B, so neither from

G toward••

[illustration]

C. The vi∣gour is not strengthned in the part FHG, from that which is GMFE; but FGH doth in∣crease the vertue in H: so that there can arise no vigor so far from the pa∣rallels to the Axel—tree aboue the said parallels, but internally from the parallels to the Pole. So wee see that from euery point of the Equinoctiall plaine, the force is deriued to the Pole E. But the point F hath only the vigour from GH, and the point N from OH: but the Pole E is corroborated and strengthened from the whole plaine of the Equinoctiall HQ. Wherefore the vigour magneticall in this Pole is most eminent and remarkable, but in the middle spa∣ces; as for example in F, the magneticall quality is so far streng∣thened, as the portion of the Equinoctiall plaine H, can giue. But D^r Ridley in his late Magneticall Treatise, in the 6. Chapt. seemes to oppose this Demonstration. For although hee ac∣knowledgeth that the vigour is strongest of all in the Poles; yet (saith hee) if tryall bee made what the Pole will take per∣pendicularly; and also what the parts aboue 34 degrees will lift vp, it will appeare to bee halfe asmuch perpendicularly; so that the Pole doth not take vp as much, as this and the other part doth on the other side. But the decision of these differences I leaue to such as are more experimentall then my selfe, being

destitute of those helpes and instruments which they enioy.

4 It behoues vs in the second place to speake of the Disponent vigour of Magneticall bo∣dies▪ The Disponent force we call, that facul∣tie by which magneticall Bodies are dis∣posed or directed to a certaine site or position.

1 Magneticall bodies moue not vncertainly, but haue their motions directed and conformed to cer∣taine bounds.

This Proposition is confirmed by manifold experiments. For magneticall bodies are neuer found to moue vncertainly, and at all adventures, but conforme themselues to certaine Poles; and make certaine angles proportionall to the latitude, as we shall shew hereafter in particular. The reason of which experiment wee can draw from no other cause, then the first institution of Nature in all Naturall agents, which wee would haue directed to certaine ends, that nothing in her Common-wealth might seeme idle or vnnecessary; wherefore shee giues all agents not only a power to worke their ends; but also shewes them the way, squares and regulates the meanes which direct vnto the end. No-where is this directiue power more remarkable, then in magneticall bodies, especially in their Direction and Varia∣tion, motions treated of hereafter in place conuenient; to which for a further confirmation of the Theoreme, wee referre the Reader.

9 The Radicall facultie of the magneticall bo∣dy being somewhat spoken of, aswell in their motiue, as disponent vertues. Wee are in the next place to speake of the deriued motions, which arise out of these faculties.

6 These motions magneticall are either partiall, or totall. The partiall wee call that by which the parts of the Earth are magnetically moued and conformed as well one to the other, as to the whole terrestriall globe.

7 The magneticall partiall motions are Coition, Direction, Variation, and Declination. Magneti∣call Coition is that motion by which magne∣ticall bodies are ioyned and apply themselues one to the other.

For the knowledge of this magneticall motion, we need goe no farther then the Iron and Steele, which wee shall obserue to moue unto the Load-stone, and cleaue vnto it, if so be it bee pla∣ced within the Spheare of his vertue. This motion is commonly called Attraction, but improperly, as is obserued by D. Gil∣bert. 1 Because Attraction seemes to suppose an externall force or violence, by which one thing is carryed and moued vnto an∣other: but the Coition is meerely naturall, as proceeding from the internall forme of both the bodies. 2 Attraction supposeth the force of mouing to bee onely in the one party, and the other to bee meerely passiue, and not actiuely concurring to this mo∣tion; whereas in the magneticall coition, both parts are mutu∣ally inclined by nature to meet and ioyne themselues one to the other. Not that the force of motion in both parts is alwayes equall: because one magneticall body is greater and stronger then the other, and then the one part seemes to stand still and draw the other vnto it, although there bee in this part so resting an inclination to the other; which mutuall inclination of con∣iunction in magnets, we may easily see in two magnets of equall quantity and vertue, which being set at a conuenient distance, will so moue, that they will meet in the mid-way. Some haue gone about to parallel this Attractiue force of the Load-stone with the Attractiue force of Ieat or Amber, which wee see by a

naturall vertue to draw vnto it selfe little strawes, and other such like matter. But hee that truely vnderstands the nature of a magneticall body, shall finde a great disparity: First, because the Ieat or Amber which are comprised vnder the name of Ele∣ctricall bodies, drawes vnto it by reason of his Matter: where∣as otherwise the cause of the Magneticall Coition is to bee sought in the forme, as being too subtile a thing to spring from a materiall substance. Secondly, Electricall bodies draw and at∣tract not without rubbing and stirring vp of the matter first; and presently faile, if any vapour or thicke body should be interpo∣sed. But in a magneticall motion wee find no such matter, be∣cause it requires no such preparation or rubbing of the stone, nor is hindred by interposition of solid bodies, as wee proue in this place. Thirdly, the Load-stone moues and prouokes to mo∣tion nothing els but other magneticall bodies; but the Electri∣call will draw any little thing as straw, haire, dust, and such like. Fourthly, the Magnet will lift a great waight according to his vertue and quantity; but Ieat the smallest and lightest things. Lastly, the Electricall bodies, as Gilbert well confirmes by ex∣periments, draw other bodies vnto them by reason of a moist effluence of vapours, which hath a quality of ioyning bodies to∣gether: as wee see by the example of two stickes in water at a certaine distance, which will commonly moue till they meet to∣gether. But the magneticall coition cannot bee other then an act of the magneticall forme. Of the cause of it many Philosophers haue freely spent their vncertaine coniectures, rather out of a feare to bee esteemed ignorant, then of confidence to be accoun∣ted learned. Most run vpon the forme of the mixt body, which growes from the composition of the foure Elements; but this opinion is very feeble, and cannot goe without crouches: for sith all mixt formes grow out of the temperament and disposi∣tion; they adde nothing to the thing compounded, but diuersly modificate what was before in the simple Elements; it cannot bee imagined how such an affection as this should bee onely found in the magnet, and no other mixt body. Indeed we ascribe this affection to the forme as the immediate cause; but by this forme we vnderstand not the forme of the mixture, resulting out

of the mixture and temperature of the foure qualities; but the magneticall forme of all globous bodies, such as are the Sunne▪ Moone, Starres, and this Terrestriall Spheare whereon we liue, whose natures receiued the stampe in the first creation for the preseruation of this integrity. Hee that shall seeke for the origi∣nall of all formes of this kinde in the mixture and constitution of the foure Elements, shall labour much, and finde little, and nei∣ther at last be able to content himselfe, or instruct others; except wee suppose a man sufficiently taught when hee heares ordina∣ry matters expressed in exoticke and artificiall tearmes. For my owne part, I content my selfe with a rule of Biel the Schoole∣man; That when an immediate effect proceeds from an imme∣diate cause, wee ought not to search farther why such a cause should produce such an effect. Euey man being demanded why the fire is hot, is ready to flye to the forme of fire, and alleage this as the cause: but should hee inquire further, why the forme of fire should bee the cause of heat, hee might perhaps puzzell a whole Academie of Philosophers, and neuer proue himselfe the wiser. For the further illustration of this motion, these Theo∣remes will seeme necessary.

1 The Magnet communicates his vertue to iron or steele if it be touched with it.

Experience teacheth that any iron-instrument, touched with the Load-stone, receiues instantly the same vertue Attractiue. But the manner how this vertue should bee communicated on so sleight a touch, hath been controuerted. The common Philo∣sophers haue imagined, that certaine little parts of the Loadstone are separated from it in the touch, which cleauing to the iron or steele, cause this Attraction But that this vertue cannot be com∣municated by any corporall processe, or any such little parts cleauing to the iron, is not so easie to imagine: for first it seemes impossible, that with a bare touch, these parts should bee sepa∣rated from the magnet, or at least should bee so fast linked to the iron. Secondly, these parts being so little and insensible, can∣not haue so much vigour as wee see an Iron will haue at the touch of the Load-stone. Thirdly, the Loadstone can worke vpon

the iron notwithstanding any body interposed, which is an eui∣dent signe that the iron it selfe is of a magneticall temper. Wherefore to shew a reason of this effect, we say; That Iron is a mettall excocted out of the Load-stone; which albeit it retaine in it selfe the vertue of the Load-stone, yet by reason of the li∣quefaction, is altogether languishing, and as it were buried; but vpon touch of a Load-stone, is stirred vp to his former vigour: for the magnet insinuats his Incorporeall influence into the iron, and so rectifies and animates that force which was almost dead.

2 The magneticall Coiton is strongest of all in the Poles.

This may easily bee demonstrated by an experiment: for if the iron needle which is proposed to bee Attracted, and the Poles and Center be placed in the same right line; then this Coi∣tion

[illustration]

will be to a perpen∣dicular, as in A and B, to wit, the Poles in the Diagramme: but in the middle space they will obliquely respect and point: and by how much farther off from the Pole it is, by so much is this vertue weaker: but in the E∣quator it selfe it be∣comes meerely parallell without any inclination at all. To know in what proportion this force is increased or weakened, we must put another ground; That the force of this coition is increased proportionally as the chords of a circle: for by how much the least chorde in a circle differs from the Diameter, so much the forces Attractiue differ from themselues. For sith the Attra∣ction is a Coition of one body with another, and magneticall bodies are carried by a conuertible nature: it comes to passe that a line drawne from one Pole to another in the diameter, direct∣ly

meetes with the body, but in other places lesse, so that the lesse it is conuerted to the body, the lesse and weaker will bee the coition.

3 So much bee spoken of the magneticall Coiti∣on: It followes that wee speake of Magneticall Direction, which is a naturall conuersion and conformity of the magneticall bodies to the Poles of the Earth.

It is manifest that a magneticall body so seated, that it can moue without any impediment, will turne it selfe in such wise, that the one Pole of it will respect the North Pole of the Earth, the other the South, which motion wee call Direction. This we may plainely see in a Marriners compasse, whose Lilly alwayes respects the North point. If a compasse bee wanting, the same may bee shewed in a little corken-boate, which being put in the water with a load-stone in it, will so turne and conuert it selfe, that the Poles of the Load-stone will at length point out the Poles of the Terrestriall Globe. The manner how, shall be dis∣closed in these Theoremes.

1 The South part of the Load-stone turnes to the North, and the North part to the South.

To confirme this assertion, some haue produced this experi∣ment. Let there bee cut out of a rocke of Load-stone, a Mag∣net of reasonable quantity. Let the two poles both North and South bee marked out in the Load-stone, the manner of which, wee shall perhaps teach hereafter: then let it be put in a corken little boat on the water, so that it may freely float hither & thi∣ther: It will be euident that that part which in the rocke or Mine pointed Northward, will respect the South, and contrarywise the South part will respect the North; as wee may see in this figure: Let the Magnet as it is

[illustration]

continuated with the Mine or Globe of the Earth be AB, so that A shall be in the North

[illustration]

pole, B the South-Pole. Let this Load-stone be cut out of this rocke or Mine▪ & placed on the water in a little timber boat, which shall be CD: we shall find that this little dish or boat will turne it selfe so long, vntill the Northpart A, be turned to the Southpart B: and on the other part, the Southpart B, be conuerted to the Northpart A: and this cōformity would the whole rock of Load-stone claime, if it were diui∣ded and separated from the Globe of the Earth. The reason why the magnet in the boat on the water, turneth, windeth, and seateth it selfe to a contra∣ry motion to that it primarily receiued, whiles it was ioyned to the bowels of the Earth, and vnited to the body of the great Magnet, is; because euery part of a Load-stone being separated from the whole, whereof it is a part, becomes of it selfe a per∣fect, compleat, magneticall body, (as we may say) a little Earth, hauing all the properties of the great Globe, as Poles, Meridi∣ans, Aequators, &c. And therefore according to the nature of magneticall vnion, spoken of in our next Theoreme, will in no wise endure to settle it selfe as it did before; but deemes it a thing more naturall, and of more perfection, to turne his aspect a contrary way, to that which he inioyed at his first constituti∣on. Here may we note a great errour of Gemma Frisius, who in his corollary vpon the 15 Chap. of his Cosmographicall Com∣ment▪ on P. Appian, affirmes; that the Needle magnetically effected, would on this side the Aequator, respect the North∣pole; but being past the Line, would straight-way turne about, and point to the Southpole: An errour (as M^r Hues saith) vnworthy so great a Mathematician. But Gemma Frisius in some

••ort, may be excused; for as much as the grounds of magneticall Philosophy, were in his time either not discouered, or most vn∣perfectly knowne, and the vncertaine relations of Nauigators were reputed the best Arguments: and how easie a matter it is for a Trauailer in this sort to deceiue a Scholler, who out of his reading and experience can shew nothing to the contrary, let e∣uery man iudge.

2 This contrary motion here spoken of, is the iust confluxe and conformity of such bodies to mag∣neticall vnion.

This is demonstrated by Gilbert in this manner. Let the whole magneticall body be CD, then C will turne to the North of the Earth B, and D vnto the South part A. Let this magnet bee cut

[illustration]

in twaine by the middle line or Aequator, and the point E will tend to A, and the part F, will direct it selfe to B: for as in the whole, so in the parts diuided, nature de∣sires the vnion of these bodies. The end E willingly accords with F; but E will not willingly ioyne it selfe with D, nor F with C, for then it would haue C, against its nature, to moue to∣ward A the South, or D in B▪ which is the South. Separate the stone in the place of diuision, and turne C to D, and they will conueniently agree and accord; For D will turne it selfe to the South as before, and C to the North; and E and F ioynt parts in the minerall or rocke, will now bee most sundred. For these magneticall parts concurre and meet together not by any affini∣ty of matter, but receiue all their motion and inclination from the forme; so that the limits, whether ioynt or diuided, are dire∣cted magnetically to the Poles of the Earth, in the same manner, as in the diuided body.

3 If any part Southward of the magneticall body bee torne away or diminished, so much shall bee also diminished of the North-part; and contra∣riwise if any part bee taken away in the North-part, so much shall the vertue of the South-part be diminished.

The reason is, because the Magnet hauing eminently in it the circles which are in the Earth, is separated or diuided by a mid∣dle line or Aequator, from which middle space the vertues are conueyed toward either Pole, as we haue before shewed. Now any part being taken away from the North or South part, this Aequator or middle line is remoued from his former place into the midst of the portion which is left, and so consequently both parts are lesse then before: For although these two ends seeme opposite, yet is one comforted and increased by the other.

9 Of the motions of Coition and Direction wee haue handled. It followes that we speake of the motions of the second order, to wit, Variation, and Declination.

10 Variation is the deuiation or turning aside of the directory Magneticall needle from the true point of North, or the true Meridian tow∣ards East or West.

In the discourse immediatly going before, hauing treated of the magneticall body, wee haue imagined it to bee true, and pointing out the true North and South points of the Terrestriall Globe; which certainely would bee so, if the substance of the Earthly Globe were in all parts and places alike, equally parta∣king the Magneticall vertue, as some round Load-stone; nei∣ther should wee find any variation or deuiation at all from the true Meridian of the Earth: But because the Terrestriall Globe

is found by Nauigatours to bee vnequally mixed with many materialls, which differ from the magneticall substance, as fur∣nished with rockie hills, or large valleyes, continents, & Ilands, some places adorned with store of iron Mimes, rocks of Load-stone, some altogether naked and destitute of these implements; it must needs fall out, that the magneticall needle and compasse directed and conformed by the Magneticall nature of the E••rth, cannot alwayes set themselues vpon the true Meridian, that passeth right along to the Poles of the Terrestriall Globe; but is forced and diuerted toward some eminent and vigorous mag∣neticall part; whereby the Meridian pointed out by the mag∣net, must needes varie and decline from the true Meridian of the Earth, certaine parts or degrees in the Horizontall circle; which diuersion wee call the Variation of the compasse: so tha•• variation, so far as it is obserued by the compasse, is defined to bee an Arch of the Horizon, intercepted betwixt the common intersection with the true Meridian, and his deuiation. This effect proceeding from the Inequality of magneticall vertue scattered in the Earth, some haue ascribed to certaine Rockes or mountaines of Loadstone, distant some degrees from the true Pole of the World; which rockes they haue termed the Pole of the Loadstone, as that whereunto the magnet should dispose and conforme it selfe: which conceite long agoe inuen∣ted, was afterward inlarged and trimmed ouer by Fracastorius. But this opinion is a meere coniecture, without ground: for what Nauigatours could hee euer produce that were eye-wit∣nesses of this mysterie? or how can he induce any iudicious man to beleeue that, which himselfe, nor any to his knowledge euer saw? The relation that the Frier of Noruegia makes of the Frier of Oxfords discouery, recorded by Iames Cnoien in the booke of his Trauels, where he speaks of these matters, is com∣monly reiected as fabulous and ridiculous; for had there beene any such matter, it is likely he would haue left some monuments of it in the records of his owne Vniuersity, rather then to haue communicated it to a friend as farre off as Noruegia. Moreouer the disproportion in the degrees of variation in places of equall distance, will easily correct this errour, as we shall shew in due

place. More vaine and friuolous are all the opinions of others concerning this magneticall variation: as that of Cortesius, of a certaine motiue vertue or power without the Heauen; that of Marsilius Fici••us of a starre in the Beare; that of Petrus Pere∣grinus, of the Pole of the world; that of Cardan, of the rising of a starre in the taile of the Beare; that of Bestardus Gallus, of the Pole of the Zodiacke; that of Liuius Sanutus, of a certaine magneticall Meridian; of Francis Maurolycus, of a magneticall Iland; of Scaliger, of the he••uen and mountaines; of Robert Norman, of a respectiue point or place: All which Writers seeking the cause of this variation, haue found it no further off then their owne fancies. More probable by farre, and conso∣nant to experience, shall wee finde their opinion, which would haue the cause of this variation be in the Inequality of the mag∣neticall Eminencies scattered in the Earth. This Inequality may bee perceiued to bee twofold. 1 in that some parts of the Earth haue the magneticall minerals more then other parts; for as much as the Superficies of some parts is solid Earth, as in great Continents: 2, Because although the whole Globe of the Earth is supposed to be magneticall, especially in the Inter∣nall and profound parts: yet the magneticall vertue belonging to those parts, is not alwayes so vigorous and eminent as in some other parts: as wee see one Load-stone to be stronger or weaker then another in vertue and power: but of those two, the former is more remarkable, which may bee shewed by experience of such as haue sailed along many seacoa-stes: for if a sea-iourney bee made from the shore of Guinea by Cape Verde by the Cana∣rie Ilands, the bounds of the Kingdome of Morocco, from thence by the confines of Spaine, France, England, Belgia, Ger∣many, Denmarke, Noruegia: we shall find toward the East, great and ample Continents; but contrarywise in the West a huge & vast Ocean: which is a reason that the magneticall needle will vary from the true point of the North, and inclines rather to the East; because it is more probable that these Continents and Lands should partake more of this magneticall minerall, then the parts couered with the Sea, in which these magneticall bo∣dies may bee scarcer, or at the least deeper buried, and not so

forceable. On the contrary part, if wee saile by the American coasts, we shall rather find the variation to be Westward: as for example, if a voyage be made from the confines of Terra Flori∣da, by Virginia, Norumbega, and so Northward, because the land butteth on the West: but in the middle spaces, neere the Canary Ilands, the directory needle respects the true Poles of the Terrestriall Globe, or at least shewes very little variation. Not for the agreement of the Magneticall Meridian of that place with the true by reason of the Rocke of Load-stone, as some haue imagined: because in the same Meridian passing by Brasile, it fals out farre otherwise: but rather because of the Terrestriall Continents on both sides, which almost diuide the Magneticall vigour, so that the Magneticall needle is not forced one way more then another; the manner whereof wee shall finde in D. Gilbert expressed in an apt figure, to whom for further satisfacti∣on I referre the Reader.

1 The Magneticall variation hath no certaine Poles in the Terrestriall Globe.

It is but a common receiued errour (as we haue mentioned) that there is a certaine Rocke or Pole of Load-stone, some de∣grees distant from the true Pole of the world, which the Mag∣neticall needle in it's variation should respect. This Pole they haue imagined to be in the same Meridian with that which pas∣seth by the Azores,

[illustration]

whence they haue la∣boured to shew the rea∣son why the Compasse should not vary in that place: which they ex∣plaine by this Figure. Let there be a circle de∣scribing the Spheare, E AF, the Horizon EF, the Articke Pole A, the Antarticke ••. The Pole or Rocke of Loadstone

placed out of the Pole of the Earth B. Let there bee placed a magneticall directory needle in H; it will (according to their assertion) tend to the point B, by the magneticall Meridi∣an H B; which because it concurres with the true Meridian B A, or H A, there will be no variation at all, but a true direction to the North Pole of the Earth. But let this magneticall needle be placed in the point D, it is certaine, according to this opini∣on, that it will tend to the Pole of the Loadstone B, by the mag∣neticall Meridian D B. Wherefore it will not point out the Pole of the Earth A, but rather the point C; because these two Me∣ridians come not into one and the selfe-same. Hence they haue laboured with more hope then successe, ••o find out the longi∣tude of any part of the Earth, without any obseruation of the Heauens: which I confesse might easily be effected, if this con∣iecture might stand with true obseruation. But how farre this conceit swarues from the experience of Nauigatours, one or two instances will serue to demonstrate. For if the variation had any such certaine poles as they imagine, then would the Arch of variation bee increased or diminished proportionally according to the distance of the places. As for example; If in the compasse of an hundred miles, the Compasse were varied one degree, then in the next hundred miles it would vary another degree, which would make two degrees. But this hath often been proued otherwise by diuerse experiments of Nauigations, mentioned by Gilbert, and F. Wright. I will only produce one or two. If a ship saile from the Sorlinges to New-found-land, they haue obserued, that when they come so farre as to finde the Compasse to point directly North, without any variation at all; then passing onward, there will bee a variation toward the North-East, but obscure and little: then afterward will the Arch of this variation increase with like space in a greater pro∣portion, vntill they approach neere the ••ontinent, where they shall find a very great variation. Yet before they come a shoare, this variation will decrease againe. From which one instance, if there were no other, we might conclude; That the Arch of vari∣ation is not alwaies proportionable to the distance: which granted, quite ouerthrowes that conceit of the Poles of variation. Be∣side

this, if there were two such magneticall Poles, there can be but one common Meridian, passing by them and the Poles of the Earthly Globe. But by many obseruations collected and ob∣serued by Ed. Wright and others, there should be many magneti∣call Meridians passing by the Poles of the world: as in the Me∣ridian about Trinidado, and Barmudas; the Meridian about the Westermost of the Azores: lastly, the Meridian running amongst the East Indian Ilands, a little beyond Iaua Maior, the magne∣ticall and true Meridian must needs agree in one. Now for as much as all these magneticall Meridians passe by the Poles of the earth, there can no cause be assigned why the magneticall Poles should bee said to bee in one rather then another; and if in any, then in all. Whence it must needes follow, that as many magne∣ticall Meridians as you haue to passe by the true Poles of the world▪ so many paire of magneticall Poles must you haue, which will be opposite to all reason and experience.

1 The point of Variation, as of Direction, is on∣ly Respectiue, not Attractiue.

It was supposed by the Ancients, that the Direction and Variation of the Loadstone was caused by an Attractiue point, which drew and enforced the lilly of the Compasse that way: which errour tooke place from another common-recei∣ued opinion, that all the other motions of the magnet were re∣duced to the Attractiue operation: but the errour was corre∣cted by one Robert Norman, an English-man, who found this point to bee Respectiue, and no way Attractiue. Whose reason or demonstration is not disapproued by D^r Gilbert, although in other matters hee sharply taxeth

[illustration]

him. His experiment is thus. Let there be a round vessell, as we haue described, ful of water; in the midle of this water-place an iron-wier, in a conuenient round corke, or boat, that it may swimme vpon the wa∣ter, euen poyzed: let this iron-wire be first touched with the load-stone, that it may more strongly shew

the point of variation; let this point of variation be D, let this iron-wire rest vpon the water in the corke for a certaine time; It is certainly true that this iron-wire in the cork, will not moue it selfe to the margent or brinke of the vessell D, which certain∣ly it would doe, if the point D were an attractiue point.

3 The variation of euery place is constant and not variable.

This hath beene ratified by the experience of Nauigatours, which in the selfe-same Regions haue neuer missed the true va∣riation which they haue assigned them before. If any difference bee assigned in variation to the same Region, wee may impute it to their errour which obserued it, arising either from want of skill, or conuenient instruments. Neither can this euer be chan∣ged, except some great deluge or dissolution happen of a great part of land, as Plato records of his Atlanticke Ilands.

4 The variation is greater in places neere the poles of the Earth.

This proportion is not to be taken vniuersally, but commonly for the most part; yet would it haue truth in all places, if all o∣ther things were correspondent. It is obserued that the varia∣tion is greater on the coasts of Norway, and the Low-countries▪ then at Morocco, or Guinea. For at Guinea the magneticall needle inclines to the East, a third part of one Rumbe of the Compasse: In the Ilands of Cape-Verde, halfe; in the coasts of Morocco, two third parts: In England at the mouth of Thames, according to the obseruation of D. Gilbert, and Ed. Wright, though some de∣ny it, one whole Rumbe; in London the chiefe city of it, eleuen degrees and more, which we also find, or thereabout, in Oxford. The reason is, because the magneticall motiue vertue is stronger in the greater latitude increasing towards the pole: and the large Regions of land lying toward the Pole, preuaile more then those which are situate farther off.

12 Thus much for the Variation. The Declination is a magneticall motion, whereby the magne∣ticall

needle conuerts it selfe vnder the Hori∣zontall plaine, toward the Axis of the Earth.

What wee haue hitherto spoken of Direction and Variation magneticall, was such as might be expressed and shewed in the plaine of the Horizon, by the Directory needle equally poy∣zed, when it is set in any point of the Horizon. But this Decli∣nation whereof wee are now to speake, is the motion of an iron-wire or needle, first equilibrated, and then stirred vp by the loadstone, vpon his owne Axis, from that point of the Hori∣zon, the other end of it tending toward the center of the Earth: where wee may, for the better expressing of the motion, note two things: 1 That the magneticall wier, set in a conuenient instrument, if it bee carried from the Aequator to the Pole, or from one Pole to another: will by little and little turne it selfe round, and make a circumuolution about his owne Axell. 2 That by this conuersion and circumuolution about his axell, it will according to diuers places and latitudes, make diuers An∣gles in diuers places; both which are included in this moti∣on of Declination, and are warranted by experience made by an Inclinatory needle applyed to a Terrella, or round Load∣stone; as also by the experience of Nauigations on the great Spheare of the Earth. To explaine which motion, there are cu∣rious instruments formed and inuented by D^r Gilbert, and D^r Ridley, which the curious in this kinde, to their greater satisfa∣ction may peruse. In the meane time wee will here content our selues with one figure following, borrowed from their more copious inuention; wherein we shall find enough to expresse the manner of this motion. In this Figure let ABCD be the Terrella or round magnet representing the Spheare of the Earth: A the North-pole, B the South, A••B the Axell, CED the Aequator: AKB, and ALB the Meridian circles meeting in the Pole. AC, and BD the Meridian or right Horizon, hauing in it the two Poles: FG and HI two parallels. The Loadstone being thus designed in his outward Poles, as it is according to his na∣turall eminency stored inwardly▪ Let the Needles bee placed (being before touched) on the Limbe ouer-against the Poles,

[illustration]

AB, and we shall obserue them to res∣pect them di∣rectly, cōcur∣ring in one straight line with the A∣xell of the Earth: Then set the same Needles in the Limbe ouer—against the Aequa∣tor CD, and they will dis∣pose & settle themselues in a parallell site to the Axell of the Earth, and in∣cline neither to one Pole or other: Hence may bee collected by plaine consequence, that there is a semi-circle betwixt each of these foure needles. Now to finde the quadrants of these, apply Needles in the Limbeat 33 degrees distant from the Aequator on each side of him, and they will make right angles with the axell of the same, where these eight needles haue 8 quadrants between them, that is, foure semi-circles which will make two whole circles, one on each side of the Aequator. But if you place the needles in the midst betweene the Aequator and the Poles, they will respect the axell but obliquely as in all other parts, ex∣cept in the eight places before-mentioned. From hence may we learne what we proposed: first that the Declination is a conuer∣sion of the magneticall wire or needle vpon its owne axell: se∣condly, that this wire by this motion so excited, if it bee moued on any Meridian North or South, will apply and conforme it selfe according to certaine angles, to the Axell of the Earth. Thirdly, there will arise this corollary, that the magneticall nee∣dle about the round Magnet, maketh two circles. Concerning

this declination wee will insert two especiall Theoremes.

1 The Declination is answerable to the lati∣tude not in Equality of degrees, but in proportion.

It is manifest out of that which wee haue spoken, that this motion of Declination supposeth two motions; The one of Conuersion, whereby the needle is turned round on his owne Axis: The other a Progressiue motion, whereby the center it selfe of the Inclinatory Needle is carryed forward vpon a Meri∣dian from North to South, or contrarywise. These two moti∣ons supposed to proceed and beginne together, cannot possibly meet in such Equality, as that the degrees of Declination directly answer in Equality to the degrees of latitude, which is demonstrated by this Figure

[illustration]

here inserted. Let the magne∣ticall body bee A, this body while it shall bee moued aboue the Earth from GD the Equi∣noctiall toward the Pole B, will bee turned vpon his owne Center, and in the middle of the progresse of the center from the Equator to the Pole B, it will be directed to the Equator D in the middle betweene the two Poles. Therefore the middle must needes turne faster on his owne center, then the center it selfe turned forward; that by this conuersion it should directly respect the point D: wherefore this motion will bee swifter in the first degrees, to wit, from A to L, but in the latter it will be slower from L to B, in respect of the Aequator from D to C. Now if the Declination were equall to the latitude, then the magneticall wier should obserue and follow the facultie and peculiar vertue of the center of an operatiue and attractiue point. But reason & experience teacheth, that it obserueth the whole body and masse, with all the externall limits of the Earth and Load-stone; the whole vertues and forces of both concurring,

aswell of the conuertible wier, as of the whole Earth: Neuer∣thelesse from this experiment the skilfull in Magneticall Philo∣sophie, haue found out a proportion whereby the latitude of places may instrumentally bee found out by the degrees of De∣clination.

2 The Magneticall Declination is caused not of the Attractiue, but of the Disponent and Conuersiue vertue of the Earth.

There is nothing more admirable in Nature, then the order and situation of all bodies in their places, most conuenient for each ones conseruation. For the obtaining of which harmony, (as wee haue taught in our second Chapter) it is endowed with a proper motion conuenient, to place and seat it selfe, both for the preseruation of it selfe, and the whole Vniuerse. This na∣turall Inclination is no-where more eminent and cospicuous, then in the harmony of magneticall bodies, which are (as it were) the sinewes of the Terrestriall Globe. These motions some haue imputed to the Attractiue force, but very erroneously, as wee haue proued already of Direction and Variation, and shall here demonstrate concerning the Magneticall Declination: for first, if it were caused by any Attractiue force approching it would follow of necessity, that a Terrella or round Spheare; made of a solide or perfect loadstone, would more turne and wrest the magneticall needle, then if it were made of a weaker and more imperfect substance: also that a needle touched with a stronger stone, should shew a greater Declination then that touched with a weaker. But experience hath found the contrary, because the Declination will bee all one, bee the stone stronger or wea∣ker. Moreouer a Loadstone armed with an Iron-Nose (as they tearme it) put vpon the Meridian in any latitude, will not lift vp a piece of iron more perpendicularly, then if it were naked and vncouered, although it will lift vp much greater and heauier waights; which experiments are sufficient to confirme our as∣sertion, that this Declination is caused only by the disponent and conuersiue vertue of this Terrestriall Globe.

3 The magneticall Declination hath a variation.

That in the magneticall Direction there is found an Irregu∣larity or variation, hath beene sufficiently warranted by Artifi∣cers Instruments. The like Irregularity is in the motion of De∣clination, which makes magneticall Instruments and experi∣ments more subiect to errour and imperfection. The variation of Declination is defined to bee an Arch of the Magneticall me∣ridian betwixt the true and apparent Declination. The cause hereof is onely to bee sought in the vnequall temper of magne∣ticall parts in the Earth. For as in the Direction, magneticall bodies are drawne and wrested from the true meridian, by the eminent and more vigorous force of the Earth, one side ouer∣ruling the other: so the magneticall needle (the conuersion somewhat increased) declines sometimes beyond his naturall site and conformity. This may cause an errour, but not of any great moment: sometimes when there is no variation or Dire∣ction at all in the Horizon, there may bee a Variation or Decli∣nation; to wit, either when the more eminent and stronger parts of the Earth are placed iust vnder the Meridian; or when these parts are more impotent then the generall nature requi∣reth; or els when the Magneticall vigour is too much increased on one side, and diminished on the other as wee may behold in the vast Ocean.

CHAP. IIII. Of the Totall motions Magneticall.

1 HAuing passed the Partiall motions magneticall, wee are next to speake of the Totall motions, which more neerely agree to the whole Earth, such as are the

Verticitie and Reuolution.

2 The Verticity is that whereby the Poles of the earthly Spheare, conforme and settle them∣selues vnto the Poles of the Heauen.

1 The Spheare of the Earth by her Magneticall vigour, is most firmely seated on her Axell; whose Ends or Poles respect alwayes the same points in the Heauens, without Alteration.

That which in a little Magnet or Load-stone is called Dire∣ction, in the vast Globe of the Earth is called Verticity. To vn∣derstand which, wee must conceite, that the Earth hath natural∣ly two Poles, vnto which the meridionall parts doe direct not only magneticall bodies neere the Earth, but her owne massie situation and firmenesse; and settles her selfe so strongly by her magneticall vertue passing through the Meridionall parts to the Poles, as if shee were tied by many strong cables to two Herculean pillars, not subiect to alteration: And if it should happen by any supernaturall power, that the situation could bee changed: shee would (no doubt) by her magneticall vigour and verticity, returne and restore her selfe to her former position, as all magneticall needles will doe to their proper site and conformity Of this Verticity needes no more to bee spo∣ken, then hath been already said in the point of Direction; be∣cause the former is a representation of the latter, and depends on the same demonstration. Out of which ground wee may eui∣dently conclude, that the Axell of the Terrestriall Globe re∣maynes alwayes inuariable: By which we may refute the opi∣nion of Dominicus Maria, who was Master to Copernicu••; who out of certaine vnperfect obseruations, was induced to beleeue that the Poles of the World were changed from their true and naturall situation: I haue obserued (saith hee) looking on Pto∣lomies Geographie, that the eleuation of the Pole Articke al∣most in all Regions, as it is put downe in Ptolomie, differs and failes in one degree and ten minutes from that which wee finde

in our time: which cannot bee ascribed to the errour of the ta∣ble, because it is not probable that the whole series should bee depraued according to this equality of number. Wherefore it must follow of necessity, that the North pole should bee mo∣ued toward the verticall circle: which mystery not knowne of the Ancients for want of former obseruations, hath shewed it selfe to our times, being inriched not only with their, but our owne experiments. According to this opinion of Dominicus Maria, the North pole should bee eleuated higher then it was, and the Latitudes of Regions should bee greater then they were. But to this opinion we will oppose the opinion of Sta∣dius, which holdeth that the latitudes of Regions haue beene decreased and diminished from that they haue had in Ptolomie, without any such regular Increment or Decrement; which hee labours to confirme by many obseruations: as for example, the latitude of Rome as it is set downe by Ptolomie is 41 de∣grees ⅔ parts: but by newer obseruation it is found to be 41 de∣grees, ½ parts: out of which wee may well coniecture, that Ptolomies obseruations were not alwayes exactly true, being for a great part such as hee had receaued from Hipparchus, and not examined himselfe: as may bee seene in the latitude of ma∣ny Citties in Europe, where hee missed sometimes 2, some∣times 3 degrees. Wherefore no iudicious Geographer would vpon such imperfect obseruations and vncertaine coniectures bring in a new motion of the earth to ouerthrow that magne∣ticall. Harmony and consistency corroborated with so many and sure demon••trations. This may serue to answer a certaine Ten••nt of Vasquez the Iesuite, and some others; who imagine the Center, and by consequence▪ the Pole of the Earth, to bee moued vp and downe by a certaine motion of Liberation. The argument on which they would ground their assertion, is taken from the Center of Grauity, in this manner. The whole masse of the earth (say they) is so setled about the Center, that it is equally poized: that is as much as to say, that the parts are in∣dowed with an equall waight. Now such Bodies as are so e∣qually poized by the addition or diminution of any part on either ••ide▪ will bee straight-way t••rned from that ••i••e▪ which

they had before in Aequîlibrio: as is dayly confirmed by expe∣rience of a Ballance, and other such mechanicke instruments. Wherefore in the Terrestriall spheare, the Center and Poles should in this wise bee changed and altered, and the whole suffer a kinde of starting or Libration. For it is manifest by dayly obseruation, that some things in the superficies of the earth are fallen off, and carried into another place: as Men, Beasts, and Birds, which moue from one place vnto another. Nothing is here of more moment then the motion of the Sea, by which the parts of the water by continuall ebbing and flow∣ing, suffer such a sensible change of Addition and Diminution, that no man can imagine how the parts of the Earth about the Center should alwayes bee equally counterpoyzed, but the waight on one side should bee predominant vnto the other, and so driue the Center from his former place. This Argument Blancanus,* 1.9 another late Iesuite, leaues altogether vnanswered; either imagining it too strong, or out of a combined faction of their owne society, vnwilling to contradict his fellow. And in∣deed should wee consider the spheare of the earth, no otherwise then according to his Elementary constitution: this reason would hardly admit of a solid answer: For howsoeuer in the vast frame of the Earth, the addition or subtraction of some parts would make but an insensible difference: yet can it not bee denied, but the least waight whatsoeuer added or subtra∣cted, would turne it from its Equall-poyze: Neuerthelesse, this I hold too absurd for a Christian to beleeue, for as much as it contradicts the sense of holy Scriptures,* 1.10 which auerre the earth to bee so setled on her foundation, that shee should not at any time bee remoued, or shaken: which motion (as shall bee pro∣ued in the second Theoreme) I take to bee vnderstood of such a Trepidation of the Center and the Poles, which by a meta∣phor are tearmed the foundation of the earth, and not of the circular motion, as some haue laboured to wrest it. Wherefore nothing is here left vs to satisfie this doubt: but to haue re∣course to his magneticall verticity, whereby the poles of the Earth endowed with a magneticall vigor, and ouerswaying the elementary ponderosity of the earthly parts, are (as it were)

so fast bound to respect the same points or poles in the Hea∣uens, that the Center can no wayes bee shaken, or moued out of his place.

3 The Magneticall Reuolution is a motion by which the whole globe of the Earth is moued round.

Aristotle in his 1 booke de coelo makes 3 kindes of simple motions, out of which hee labours to deduce the number of simple bodies. The first is the motion from the center, such as is of Fire and Ayre, and all light bodies: the second to the cen∣ter, such as is of Earth and Water; the third is round about the center or middle, which hee ascribes to the Heauens: so that if this ground were true, the Earth could challenge to it selfe no other then the right motion; whereby the parts of it being se∣parated from the whole, returne to it againe. But this opinion although popular and plausible, hath beene contradicted, as well by ancient Philosophers as moderne: for by long experi∣ence and diligent obseruation, they haue found the earth to bee endowed with a star-like vigour, whereby shee may, hauing all her parts vnited together by reason of her grauity vnto the Center, and her place made sure by her magneticall poles, moue naturally vpon her owne poles, at least if so bee shee claime no other motion. This opinion first blosomed (as farre as I can gather) in the Schoole of Pythagoras, was cherished by Hera∣clides Ponticus, and Ecphantus, two famous Pythagoreans: to which afterward ioyned themselues Nicetus Syracusanus, and Aristarchus Samius; all which haue vndertaken to defend that the Earth moues circularly, and that this circumgyration of the Earth causeth the rising and setting of the Sunne, as well as of other starres, although in the manner they haue not expres∣sed themselues alike, hauing inioyed as yet scarce the first dawn of knowledge. But all this while Philosophie contented her selfe with the acquaintance of a few choice friends, not daring to prostitute her treasures to popularity. But when it hapned in after times that shee was taught the language of the vulgar, and spake to the vnderstanding of each mechanicke, shee soone

contracted some staines, and squared her selfe rather to please the most then the best. Thus the multitude as a vast torrent pre∣uailed against the learned, and cast into exile the inuentions of the Ancients, which their ignorance was readier to censure then vnderstand. Yet were not the seeds of this Philosophy quite ex∣tinct, but as forgotten for a time; vntill there arose Copernicus, a man of incomparable wit, who quickned and reuiued it, to his euerlasting prayse and our profit: I would not here be mistaken, as though I strongly apprehend these grounds, and reiect all the principles of our Peripateticke Philosophie: I only inueigh a∣gainst their preiudicate ignorance, which ready to licke vp the dust vnder Aristotles feet with a supercilious looke contemne all other learning, as though no flowers of science could grow in another garden. I confesse this opinion of the Earths circular motion to bee subiect to many and great exceptions, and oppo∣sed by strong and waighty arguments drawn probably from the booke of God, the touch-stone of sincere verity; yet I hold it too strongly fortified to be inuaded by popular arguments drawn from seeming sense, and bolstered vp with names and authori∣ties. For mine owne part, I confesse not absolute subscription to this opinion; yet could I not conueniently leaue it out, because hauing vndertaken to insert this Magneticall Tract; I would not willingly mangle it in any part, but shew it whole and intire to the view of the iudicious; who herein may vse their Philoso∣phicall liberty, to imbrace or reiect what they please. If these grounds seeme true, they will finde acceptance; if otherwise, it cannot indamage Truth to know her aduersary. Wherefore I thinke no man will take it amisse that I insert this following Theoreme.

1 It is probable that the terrestriall Globe hath a circular motion.

Copernicus ascribes three motions to the spheare of the Earth, whereof the first is in the space of 24 houres about her owne axell; making the day and night, and is therefore called the Diurnall: The second is yeerely, wherein the Center it selfe of the Earth is moued from West to East, describing the circle

of the Signes. The third is a motion of Declination performed in an annuall reuolution; reflecting against the motion of the Center; for the Axis of the Earth is supposed to haue a conuer∣tible nature, whereas if it should remaine fixt, there would ap∣peare no inequality of day and night, Spring, Autumne, Sum∣mer, or Winter: I will not here curiously distinguish the diffe∣rences; limits, and periods of these three motions, but leaue it to the skilfull Astronomer, to whom properly it appertaines: it is enough for mee to shew it probable that the Earth should challenge to it selfe a circular motion, in prosecution of which I shall labour chiefly to establish that first motion which is of the Terrestriall globe about her owne axis, which is the easiest both to beleeue and vnderstand. That I may the better expresse the grounds of this opinion, I will labour to proue these two points. 1 That this opinion is consonant to reason. 2 That it no way contradicts the sense of the Holy Scripture. The for∣mer assertion wee will againe diuide into 3 articles. 1 That the motion which wee seeke to establish in the Earth cannot with∣out much absurdity bee granted to the heauens. Secondly that it no way contradicts to nature of the Earth it selfe. Thirdly, that the arguments produced against this opinion, are not so strong, but may bee answered with probability. First therefore finding the dayly rising and setting of the Sunne, Moone, and other Starres to arise from some motion, wee are to seeke out the true subiect of this motion. It is agreed vpon by all that this subiect must bee the Heauens, which are carryed in 24 houres from East to West, or the Earth which must moue in the same time from West to East. For the first wee must take a•• granted of those which defend the opposite opinion these two grounds 1 That the subiect of this motion (if it bee a heauenly body) is the first moueable and supreame spheare of all the celestiall ma∣chine; because all the rest haue assigned them their seuerall motions. 2 That of two bodies circularly mouing vpon the same Center, in the same space of time, that which is greater in quantity must needs haue the swifter motion; as wee see the spokes of a wheele to moue faster neere the circumference, but slower in those parts which are ioyned to the Center. This

granted, wee shall find the greatest of the first and supremest orbs to bee so incomparably vast in proportion to the Earth, and the motion of it according to this magnitude to bee increa∣sed to such a swiftnesse, as must needes transcend all fiction and imagination. For besides the two Elements placed by the Peripa∣••etickes betwixt the Earth and the Celestiall bodies, to wit, Aire and Fire, which challenge no meane distance betwixt their concaue and conuexe superficies: who knowes not how many distinct and strange concamerations of Orbes and circles are placed and signed ou•• betwixt the Moone and the first Moueable? Aristotle hath reduced all the Orbes to eight. whereof seuen were allotted to the seuen Planets, but the eight to the fixt Starres, which hee supposed to bee fastned as so ma∣ny nailes in the same wheele. But Ptolomie perceiuing this number to bee insufficient to satisfie his obseruations, was infor∣ced to adde a ninth to encrease the number. Yet this contented not Alphonsus, but hee must make vp tenne. And although this opinion preuailed a long time in the Schooles of Philosophers, as most exact and absolute; yet came it farre short to satisfie the search of two latter Astronomers, Clauius, and Maginus; who to adde something to Antiquity, haue found out another orbe, and so the whole tale is become eleuen: and much it is to bee feared that the big-swolne belly of this learned Ignorance, will beget more children to help the Mother, because all the former haue proued lame and impotent: God send her a safe deliuery. To returne to my purpose; all these orbs thus ranged and conca∣merated in order, cannot but haue each of them a great and ex∣traordinary thicknesse and profundity: being to carry in them such huge and vast bodyes, as the Sunne and Starres, which are of themselues mighty Globes, for the most part greater then the Earth, as Philosophers haue found out by diuers Mathe∣maticall instruments, and expressed in Tables. Also because a∣mongst the Planetary Orbes wee shall finde them clouen into many partiall and lesser Orbes, as Epicycles and Excentrickes, the first of which must in reason surpasse the thicknesse of the Diameter of the Planet. The profundity of all these Orbes is measured by their Diameters, which wee shall find to surmount

each other in extraordinary proportion. For the Diameter of the Earth is 1718 German miles. The greatest distance or e∣longation of the Moone being new, 65 semi-diameters of the Earth; the least is 55 semi-diameters. The greater elongation of the Moone in the middle space is 68; the least 52 semi-dia∣meters of the Earth. Notwithstanding it is very probable, that the Orbe of the Moone is yet of more thicknesse and profun∣dity. To passe ouer Venus and Mercurie, and come to the Sunne, wee shall find his distances from the Earth in his greatest Excentricity to bee 1142 semi-diameters of the Earth. Mars, Iupiter, and Saturne, are yet farther off from the Earth, and their Orbes endowed with a greater treasure of thicknesse. The distance of the Firmament wherein are placed the fixt Starres, is by the best Mathematicians thought incomprehensible, and not measurable by mans industrie: in so much that Aristotle holds the Earth no other then as a point, if it bee compared with the eighth Spheare, which hee supposed to bee the highest and first Moueable. To let passe the ninth Spheare; the tenth, which was vulgarly thought the first Moueable, if it bee valued according to the proportion of the rest, would haue his conuexe superfi∣cies moued so fast in one houre, that it would ouercome so much space as 3000 greater circles of the Terrestriall Globe; for as much as in the conuexe superficies of the starry Firma∣ment, it would containe more then 1800. And who can bee so sharpe sighted to see the profundity and thicknes of this orbe▪ containing in it starres innumerable; whereof some are appa∣rent to each mans eyes, others lying hid by reason of the distance, whereof many haue lately beene discouered, by reason of the Trunk-spectacle lately found out: so that it may bee a pro∣bable coniecture, that all these starres are not placed in the same Orbe, or at least that this Orbe is farre greater and dee∣per then the ordinary current of Astronomers haue imagined it to bee. To these eight Orbes here deciphered, should wee adde the Caelum Chrystallinum, the Primum Mobile, the Idol of our common Astrologers; and another, which Clauius and Ma∣ginus haue inuented; what bound should wee set to the greatne•• of the Heauens, or the swiftnesse of their motions? how farre

beyond all rouing imagination or Poeticall fictions should it transcend, as thatwhich neither Nature could euer suffer, or the wit of man vnderstand? a motion a thousand-fold swifter then the flight of a bullet from a peece of ordinance, I had al∣most said, then thought it selfe: For if a man cast his imagina∣tion on some marke or degree in the Sunnes parallell on theTer∣restriall Globe, and so instantly transferre it to another, and so to a third, passing ouer at each time the distance of 100 miles; hee would find the Sunne to bee farre swifter in his moti∣on, and to haue ouer-passed him incomparably in his course: were the Sunne placed in the superficies of the Earth, and his course no greater then one of the greater circles of the Terrene Globe, hee should by their owne computation, finish his course in 24 houres; and so runne 21600 miles in that time, which maketh 900 miles in one houre. And if this motion seeme so swift, that it could hardly haue credit among ordinary capaci∣ties; what should wee thinke of this motion, which is imagi∣ned infinitely swifter? If Ptolomie feared lest the Globe of the Earth should be dissolued and shattered in pieces by a far slower motion; of what should wee imagine the heauens to be made, which can suffer so portentous and incogitable a whirling? Here the common Philosopher stands astonished, and rather then hee will be thought to know nothing, hee will say any thing: why (saith he) should wee not beleeue it? sith the Heauens in their motion find no Resistance, whereas all other bodies are slacked by the medium or Aire by which they are to moue. If in the Hea∣uens were any such let or hinderance, it would bee either in the Agent or Mouer; or in the Patient or body moued: Not in the mouer, because (as Aristotle hath taught) the Heauens are mo∣ued or turned round by an Angell, or Intelligence, fixed to his Orbe, of a spirituall and immateriall substance, which in a body meetes no opposition. Not in the body moued: because of it's owne Nature it is prone and inclinable to this motion. But this reason is like a reed that hurts his hand that leanes on it: for first, what indigence or necessity in Nature is obserued so great, to bee the father of such Intelligences? What serious iudgment can euer imagine the Angels to bee like gally-slaues chained fast

to their gallies, or turne-spit-dogs labouring in their wheeles? To what vse shall they serue? not to stirre vp and beginne the motion; for why should we debarre the Heauens from the pri∣uiledge ofall other Bodies farre lesse excellent, whose motions challenge no other cause or beginning then their owne forme and nature: Not to Regulate and confine this motion; for Na∣ture which beginnes any action or motion, is able of her selfe to set limits and bounds vnto it, without the helpe of any ex∣ternall agent. Finally not to continue this motion; for as wee are taught in our Philosophie, Euery Naturall Agent, if it bee not hindered, still acts to the vttermost of his power, and there∣fore needes no externall coadiutor to continue his action: for o∣therwise we might suppose the Heauens to grow weary and faint in their intended course. Secondly, whereas they say there can bee no Resistence in the body moued, they contradict their owne grounds: for it is agreed by all, that the higher Orbs doe turne and wrest about the lower: I would willingly aske, by what kinde of action, either by a vertuall influence or emana∣tion, or els by a corporall touch and application: The former is improbable, and (as farre as I can gather) not auuouched by any; and were it so, it would seeme ridiculous; for why should wee rather ascribe this effect to an vnknowne in∣fluence of an externall body, then to the vigour of his owne forme and nature. For if one orbe in this sort can moue another, why could it not moue it selfe, being more present to it selfe then any other; If they say by a corporall application of bodies and their parts. I see not how they can auoid this Renitencie and reaction, which alwayes doth suppose some resistence: for how can one solide and hard body bee imagined to heaue and push another forward without some reluctancy in the pati∣ent? because the inferiour Orbe hauing of it selfe a proper mo∣tion, this must needes be violent, as supposing a forcing & wre∣sting of Nature from her proper course, whereof it is not hard to shew a sensible demonstration; because the Orbe naturally directed one way, is turned and directed another way at the same time: which both motions concurring in the same body, must needes offer violence one to the other. Moreouer the im∣munity

from corruptible qualities granted to the Heauens, which is the ground of this opinion; hath beene muh talked of a∣mongst the Aristoteleans▪ but neuer warranted by any certaine demonstration: wee see (say these Philosophers) the Heauens to haue remained since the beginning of the World, without a∣ny sensible alteration and change: and therefore must all the E∣lementary and corruptible qualities bee excluded. To disproue this, I need goe no farther then the last Comet, which Mathema∣ticians by the parallax found to bee in the heauens. And where∣as otherwise they seeke a sensible alteration in other parts, they deceiue themselues: for as in the earth whereon wee dwell, howeuer the parts interchangeably corrupt and ingender dayly, yet the whole Globe will apparantly remaine the same, keeping it's integrity: so may it happen to many of the superiour Globes, whose parts dayly corrupted and renewed againe (although, for the great distance, to vs insensible) the whole Globe remai∣neth still perfect in his perfect Sphericity. I cease any further to inuade anothers Prouince, and therefore descend to a second argument, to proue this extraordinary, violent, and swift mo∣tion in the heauens to bee improbable. It is ordinarily obserued in other Orbes of the heauens, that the higher the Orbe is pla∣ced, the motion is slower; as for example, the Spheare of the Moone, which is next the Earth, is carried about in 27 dayes. Mercury and Venus are slow enough in their course, as the for∣mer in 80 dayes, the latter in 9 moneths: the Sunne in a yeere; Mars in 2 yeeres; Iupiter in 12; Saturne in 30. Also those A∣stronomers which giue the fixt starres a motion, would haue them to finish their course, according to Ptolomie, in 36000: but if wee will beleeue Copernicus, in 25816 yeeres: so that the higher and greater the circles be, so much slower will be the motion: what iniury were it then to the concord and harmony of Nature, to impose vpon the highest Orbe of all, such an vn∣measurable strange motion, which might strike the most S••ra∣phick•• Angell into admiration? To these may bee added other Arguments in Copernicus, which albeit they be not demonstra∣tiue, will make the matter more probable. First, that Nature in all things is a compendious and short worker, and vseth not

many helpes for such thinges as may bee performed by fewer: and therefore need wee not to vse the helpe of so many Orbes and concamerations to square our obseruations, which will find more steady footing in this one ground once granted, of the Earth's circular motion: Secondly it will seeme more conso∣nant and agreeable to Nature, that the highest and vttermost Spheare of all, which bounds and engirts in all the World be∣sides, should rest quiet and vnmoueable, then to suffer such an intollerable motion, as might endanger the whole Fabricke. Lastly, I may adde this one, that this diurnall motion, granted to the first Moueable, can in my iudgement hardly stand with the regularity of heauenly Bodies, if wee expresse it no o∣therwise then the ordinary sort of Astronomers. For a regular motion is defined, to bee that whereby in equall times a body is moued through equall places. But this Diurnall motion re∣ceiued from the first Moueable, concurring with the Sunnes an∣nuall motion, will exclude this equality. For first it is granted, that the Sunne in his motion from the Aequator, to the Tro∣picke, according to sense, runnes ••uery day in a distinct parallell: for although euery minute hee declines somewhat from the Aequator toward the Tropicke, yet the difference is not sen∣sible: so that wee may well euery day assigne a parallelll-in•• to the Sun's motion. Secondly, they must grant that these pa∣rallells are diminished, and grow lesse and lesse toward the Tropicke, from the Aequator. Thirdly, that (as wee haue fore∣shewed) of two bodies mouing in the same time on the same center, that should moue faster, which is greater: so one body mouing in diuerse vnequall circles, in equall time, it must of necessity follow that it must needes moue faster, in that which is greater: here wee may conclude, he moues faster in the Ae∣quator, then in the Tropicke, because in the one hee is carryed in a greater parallell, in the other a lesse, and yet in the same pe∣riod of time, as wee may see in this Figure following. Let the Sunne bee in the point of the Eclipticke A, it is manifest that he will sensibly moue for that day in the parallell AP. Then let him bee moued by his periodicke motion, into the point of the Eclipticke B, it will for that moment moue in the

[illustration]

[illustration]

parallell IBO. Last of all, let it bee in the point of the Aequator C. his pa∣rallell will bee HCL. It is manifest out of our for∣mer grounds, that he will be moued slowest in AP. Faster in IO. Fastest of all in HCL. Which swiftnesse and slownesse in the Suns motion makes it irregular. Some haue thought to salue this by saying that this motion is Regular because in equall time, the Sunne goes proportionall, not equall spaces, which Aguillonius holds in his Opti••ks. But this shift is friuolous; because it takes not away the obiection, why the Sunne should moue faster and slower▪ For the Heauens being a naturall, not a voluntary agent; and according to these grounds finding no hinderance or impe∣diment; must alwayes worke to his vtmost power, and so can∣not slacke or increase his action, or motion, that it should moue faster or slower. Hitherto haue wee shewed that this Diurnall motion cannot without some absurdity bee granted to the hea∣uens: in the next place we are to shew, that it no way can crosse the Naturall disposition of the Earth it selfe, which wee shall demonstrate in this manner. If this circular motion should crosse the disposition of the Earthly Globe, it would happen either immediatly in respect of the meere Nature, which the Logicians call à priore; or els in regard of certaine properties, which follow necessarily the Nature of it, which they terme à posteriori. If they say it happens à priori in regard of the meere Nature▪ they must necessarily haue recourse to the proprieties and accidents for a demonstration: For the Internall formes of all things being in themselues insensible, cannot be discouered vn∣to vs but by their externall proprieties▪ But if probable conie∣cture may here find any place, I see no reason why the earth be∣ing found to bee of a magneticall temper, should not challenge

the same which other magneticall Globes farre greater then the Earth, possesse; to wit, a circular reuolution about her owne Poles; which Kepler and Galileus haue obserued aswell in the Sunne, as Iupiter▪ and in like matters to iudge alike, seemes more warrantable, then to faigne a dispa••ity, which Nature ne∣uer grounded, or obseruation found. But this, as a matter of small note, I easily passe ouer, following the foot-steps of our Aduersaries, which seeke to demonstrate the Earth's stability out of the externall effects and proprieties. If then this Reuolu∣tion contradict any proprietie▪ it must bee of necessity either in regard of the Quantity and Magnitude; or els in respect of the figure and quality, or of some Motion, or of the si••e and positi∣on; for I find no other propriety of any moment which can enter into this consideration: First, that the Quanti••y can no way thwart this circular Reuolution, is manifest, because it would happen either in that it were too Great, or too Little. It cannot be by reason of the greatnes; because the great globes of the Sunne and Iupiter, manifold greater then the Globe of the Earth; are by late experiments of the Trunk-spectacle, found to moue about their owne▪ Axell in a small portion of time: the like haue others deli••ered of the Mo••n•• and Venus▪ It is not then the Masse or quantity which can hinder it in the Earth; neither on the other side can it bee the smalnesse: for bodies smaller are found as apt, or rather apter to receiue a circular motion, which they will not deny mee; and therefore cannot this be preiudici∣all to the motion of the Earth. In the next place the figure of the Earthly Globe cannot hinder this motion, because by all sound Philosophers, being acknowledged to bee Sphericall, it cannot but bee deemed most apt to receiue Reuolution; in so much as some haue hence laboured to draw an argument for the Earths circular motion, as deeming this Figure to bee giuen to the Earth for no other end or vse. Thirdly, no Quality in the Earth can resist this circular motion; for this quality (by the consent of all) would bee the naturall heauines or waight of the Earth: But this heauines takes not away the naturall Reuo∣lution: 1 Because Grauity or heauinesse is nothing els but the inclination of the parts of the Earth, returning to their na∣turall

place, hauing beene sequestred from it: but these parts hauing once regained their proper places, moue no farther, nor are in those places esteemed heauy, or waighty: whence it is commonly said amongst the Peripatetickes, Nihil grauitat in suo loco, nothing is heauy in his owne place, which may easily bee demonstrated out of Staticke principles, whereby we finde heauinesse and lightnesse to bee giuen to the bodies according to the medium, and their massinesse and solidity in respect of one to the other. 2 If this heauinesse bee opposed to the circular motion then either immediatly by it selfe, or secondarily by some concomitant accident. It cannot bee the first, because grauity is a quality; but motion; an action; which for ought my Philoso∣phy hath taught mee, are not opposite▪ If by reason of some ac∣cident; then (no question) because it is contrary to lightnesse or leuity, which seemes requisite to such a motion: We willingly yeeld this naturall grauity of the parts of the Earth to stand op∣posite to the motion of Ascent or mouing vpward from the Center; but neuerthelesse it is not any way contrary to the cir∣cular motion: 1 Because contraries are alwayes supposed to be in eodem genere, in the same kind: but the motion of heauy bo∣dies to the Center, and of the Earth about the Center, are not in the same kinde, the one being a right motion, the other circu∣lar; neither can the waight of the Terrestriall masse adde or diminish any thing in regard of the circular motion, because a Sphericall and a right motion cannot either directly concurre, or directly oppose one the other. 2 Wee may vrge out of the 4 Chap. of Aristotles 1 booke De Calo, That no ci••cular motion can admit of contrariety: which hee confirmes by a demonstra∣tion, which wee forbeare here to insert, being loath to roue too farre from our present matter. At length wee will proue that this orbicular motion giuen vnto the Earth, cannot ouerthrow or thwart any other motion of the Earth: for if this were so, it would happen for one of these two respects; Either because the Earth hath some motion or other contrary to this; or els because diuers motions cannot bee in the Earth. The first cannot be true, for that wee haue spoken before; because the right mo∣tion they finde in the Earth, cannot bee iudged contrary to the

Sphericall; neither can the later bee admitted as an vndoubted truth; for howsoeuer Aristotle sets it downe for an Axiome, that one simple body hath but one simple motion, yet being abso∣lutely vnderstood without any limitation, will bee found by ex∣perience false: for it is manifest out of the experiment of the new Perspicils, that the Bodies of the Sunne and Iupiter, simple in nature, (if wee beleeue Aristoteleans) haue at least a double motion, the one vpon their owne Poles lesse then Diurnall, the other of their Centers, which are moued from the West vnto the East, vpon other Poles familiarly knowne vnto Astrono∣mers. The Peripatetickes heere seeke an euasion, by distingui∣shing the motions of the Planets into a proper or naturall, and Accidentall or mutuaticious: but this answer comes not home to this present question. First, because these two motions of the Sunne and Iupiter will easily bee proued to bee naturall and without violence, or restraint: Secondly, because in this ans∣wer they suppose the Heauens to bee cut and diuided into di∣uerse Orbes, Sections, and Con••amerations, which later Astro∣nomers vpon better experience haue derided, or at least omit∣ted as Hypotheses or suppositions, to settle Imagination, rather then reall, or true grounds. If they would vnderstand this Prin∣ciple of Aristotle, to wit▪ That one simple body should challenge one simple motion: of a motion of the same kinde it might per∣haps obtaine some credit. But the right motion of the parts ioyning to the whole, and the Circular motion: also the Cir∣cular motion of a Planet about his owne Axell, and the Circu∣lar motion it selfe about the Earth, are found to bee diuerse kindes, and therefore no way incompatible in the same subiect. Moreouer what infallible argument can perswade vs, that the Globe of the Earth is a meere simple Body, such as Aristotle describes vnto vs in his Philosophie? Either this imaginary simplicitie must bee sought in the Reall Existence of the Earth, or els in our mentall Abstraction. The former they cannot a∣uerre, because not only the Elements themselues, by their owne confession, are impure and corrupted: But the whole Globe of the Earth seemes to consist of diuerse mixtures, and Hetero∣geneall bodies, which apparantly exclude such simplicity If

they would haue it rather to consist in the Abstraction or se∣paration of the minde, which may diuide and distinguish be∣tweene the true nature of the Earth, and his Accidentall Na∣tures; I shall not contradict: although it seeme ••ather grounded on imaginary coniecture, then experience: That the Earth of it selfe distinguished from the waters, should haue any such simple Nature. If wee follow reason and experience as our Guides, wee shall obserue in the Terrestriall Globe a twofold constitu••ion; The one Elementary from the parts whereof it consists, out of which it cannot challenge any motion, but the right, which is of the parts separated from the whole, agreeing to the Earth▪ Water, and all other heauy bodies thereof consi∣sting. The other magneticall, wherein all other bodies are vni∣ted in one Magneticall forme of the Earth. In which sort the whole Globe of the Earth may bee termed a Homogeneall sub∣stance; for howsoeuer the matter and the Elements whereof it consists▪ seeme Heterogeneall and diuerse one from the other; yet since in this Magneticall Nature, there is a Harmony and Communion, well wee may call it a Homogenity of the Forme and Nature; not of the Matter and Quantity, as common Phi∣losophers commonly vse the word: So that euery part or Ele∣ment whereof this Terrestriall Spheare is compounded, may claime his owne motion, and properly; yet all conspiring in one vniuersall forme of a Sphericall Body, may notwithstanding be turned round with a Sphericall motion. In the last place wee are to proue that this Circular motion granted vnto the Earth, can no way oppose or indanger the naturall site or position of the Earth: If the situation or position were feared to bee chan∣ged, it must needes happen one of these wayes; either that the Center of the Earth should bee moued out of his place: or that the parts should bee separated & distracted one from the other; or that the Poles should be changed and altered: The first can∣not touch our assertion; because in this place wee affirme not, that the center of the Globe is moued out of his place; but that the whole Earth in the same place is turned round vpon her owne Center. For the opinion of Copernicus, which holdes the Center of the Earth to moue round about the earth, wee shall

censure in our next Chapter▪ In the second place, the parts of the Earth by this motion cannot bee separated or disunited one from the other: first, because all the parts are vnited to the whole by their naturall grauity; that if by chance they should bee separated, they would naturally returne backe vnto their owne place. Secondly, this motion is supposed Naturall & not violent, which in so great and massie a Body, can make no sen∣sible Alteration. Lastly, the Poles of the Earth by this meanes, cannot bee moued out of their places; because by a certaine Magneticall verticity (as wee haue formerly shewed) the same Poles of the Earth alwayes naturally respect the same points of the Heauens, as if they were bound vnto two firme Pillars indissoluble. Hitherto hauing proued the Circular mo∣tion of the Earth; neither to bee giuen to the Heauens without some absurdity, and yet no way to contradict or oppose the Nature of the Terrestriall Globe; wee are in the third place to examine the reasons vsually vrged against this Assertion. The first reason is drawne from sense. If there were any such Spheri∣call motion (say they) how comes it to passe, that it cannot of vs bee perceiued? an Argument worthy such Philosophers, as measure all rather by seeming sense, then Demonstratiue reason; who cannot obserue on the sea in a calme, that the ship wherein hee is carried will seeme to rest, or at least to moue slowly▪ and the clifts and shores to moue vnto the opposite part? What then should wee thinke of the motion of the whole Terrestriall Globe? which hath lesse cause to bee percei∣ued, then that of a ship? The Bulke of a ship in respect of the Earth is small and of no quantity; the other being huge and massie: The motion of the ship meerely violent, inforced by the windes; of the Earth naturall and vniforme, stirred vp of his proper and naturall inclination, so that if any such motion be in the earth, it were impossible to bee perceiued by sense: Se∣condly, they vrge against vs, that in Homogeneall Bodies, there is the same motion of the whole, and all the parts: But euery part of the Earth (as experience teacheth) is moued downe∣ward toward the Center, and therefore the whole can haue no other motion: To this obiection wee haue partly answered be∣fore;

yet to giue further satisfaction, wee will adde something more: It is one thing to speake of the whole Terrestriall Globe and Spheare; another of the seuerall parts and Elements where∣of it consists: If the whole Spheare bee vnderstood, wee ascribe vnto it no other motion but the circular, which wee here labor to establish. The parts, whereof this Terrestriall Spheare consists, may bee considered two wayes; either as they are vnited in the whole by a Magneticall forme, or disioyned and taken by them∣selues: In the former the parts of the Earth are supposed to moue in the same motion, by which the whole Spheare of the Earth is moued; because the whole and all the parts taken together, are the same, and subiect to the same circular reuolution. Not∣withstanding this, any part seuerall and disioyned from the whole, hath a right motion downeward toward the Center, by which it returnes to its true naturall vnion. This inclination of the parts agrees not with the whole Earth, neither vnto any part vnited and conglobated to the whole; but onely to a part separated from his place; so that the whole, may notwithstan∣ding in his place inioy a circular motion. Now to come more neerely home vnto their Arguments drawne from the Homo∣geneity of the Earth, wee answer as before, that there is a two∣fold Homogeneity: The one of the matter and quantity; the o∣ther of the Magneticall forme and Nature of the former: wee may conclude out of the right motion of all the parts, the dis∣position of the whole, so wee vnderstand it in a good sense: first that euery part is here to bee vnderstood, not in, but out of his proper place: Secondly, that by the whole, wee ought not to vnderstand the whole Globe with all his parts, conformed in one Sphericall frame; but all the parts indefinitely taken; for if wee should vnderstand of the whole Globe, their Argument will in no way hold true: If according to the later, wee might well grant them their Conclusion, yet can it not oppugne our Assertion: Because it will follow out of the Naturall inclinati∣on of euery part, that all the parts seuerally taken, haue such a disposition of returning to the Earth, being separated there from: Yet will not this by any necessary inference bee proued to agree to the whole Globe of the Earth; but rather will it

follow contrarywise, that the whole Spheare of the Earth is moued circularly, and therefore euery part with, and in it, is moued with the whole in the same motion. A third argument which is thought greater then all the other, is drawne from two experiments: The first is, that a stone or Bullet let fall from a higher place to the ground, will perpendicularly descend to the point of the Earth right vnder: Secondly, that two Bullets imagined to bee of equall weight and matter, being dischar∣ged from equall pieces of ordinance, with the like quantity of powder, the one towards the East, the other towards the West, will reach an equall distance in the Earth; both which would seeme impossible if wee grant this supposition of the Earths circular reuolution. For in the former case, the Earth sliding away swiftly during the fall of the stone, would change the point marked out for another: And in the second, for the like cause, the Bullet shot towards the East, being preuented by the swiftnesse of the Earth's motion, carrying along with it the Ordinance out of which it proceeded, should returne backe ouer the shooters-head; and contrarywise that Bullet shot to∣wards the West, besides his owne motion, by the motion of the Earth the other way, should bee carryed so much farther, as the Earth is remoued from the place where it was first dis∣charged: Both which experiments seeme to crosse this cir∣cumgyration of the Terrestriall Globe, which our magneticall Cosmographers labour to confirme: But with them to giue an answer to these and the like experiments, wee must distin∣guish the parts of the Earth into three sorts; some are hard and solide parts, adioyned to the Globe, as stones, mineralls, & what else in the bowels of the Earth is vnited to it, or at least necessa∣rily adherent to the outward face of it. Some other parts there are of a thinne and fluid substance, as the Aire and other va∣pours in it, deriued from the Earth; A third sort there are of such parts as being in themselues solide, are notwithstanding by some violence separated from the solide globe, as stones cast into the Aire; Arrowes, Bullets, and such like, discharged from the hand or Engine: For the two former wee may easily ima∣gine them carried with the same circular motion, which we as∣signe

vnto the whole, being no other then the parts of it depen∣ding from the whole masse: For the third sort (whereof con∣sists the difficulty) wee cannot imagine them so moued round, as if they were wholly separated from the Communion of the Earthly Spheare; for howsoeuer there seemes a separation ac∣cording to matter and quantity, yet retaine they the same mag∣neticall inclination to the whole masse, as if they were vnited to it; and therefore such solide parts are moued with the same vniforme and naturall motion wherewith the Earth it selfe is turned; so that in solide bodyes so separated from the superfi∣cies of the Earth, of an Arrow or Bullets shot, wee must ima∣gine a twofold motion: The one Naturall & vniforme, where∣by they are moued as homogeneall parts according to the reuo∣lution of the whole Spheare: The other violent by force im∣pressed from the Agent: The right motion proceeding from the strength of the shooter, cannot crosse or hinder the Naturall, be∣cause the one being right, and the other circular, admit no such proportion, as that one should hinder or further the other: Nei∣ther can these motions well be tearmed contrary or opposite, which are in diuers kindes: To explaine this matter farther, we

[illustration]

will adde this Diagramme; L••t the whole orbe of the earth bee imagined to bee LQM; whose center is A, the thicknesse of the Aire ascending from the Earth O Q. Now as the orbe of this fluid substance of the aire ascēding vni∣formely is moued round with the

Globe of the earth, so must wee imagine the part of it marked out by the right line OQ to bee carried round with an vnal∣terable Reuolution. Wherefore if any heauy body should bee placed in the Line OQ; as for example P, it will fall downe toward the center by the shortest way in the same line OQ: which motion downewards towards the center, can neither bee hindered by the circular motion of the Earth, nor yet Mixt or compounded with it: It cannot bee hindred: because (as wee haue shewed) a Right motion and a circular being not in the same kind, cannot properly bee reputed contrary: Neither for the same cause can they bee mixt or compounded: Wherefore this motion will be no other then one simple and Right motion, neuer varying from the Line OQ: which being once vnder∣stood, it is no hard thing to imagine a Bullet or stone forced by equall strength from Q towards L, and from Q. to∣wards the point M, to obserue alwayes a like distance notwith∣standing the Earth's cir••ular Reuolution. Hauing hitherto shew∣ed this Sphericall motion of the Earth to bee possible, and no way to contradict Nature, wee are in the next place to shew it to bee no way opposite to the sense of holy Scripture. This opinion of the Earth's circular motion, hath suffered much wrong by a certaine perswasion of some men, that it contra∣dicts the Text of Holy Scripture. Some precise men▪ mor•• ready to vrge, then vnderstand what they alleage, will condemne without examination, and sticke to the plaine l••tter, notwith∣standing all absurdities, denying the conclusion in despight of the premisses. To these haue associated themselues another sort, more to bee regarded, as more learned; the Critickes (I meane) of our Age, who like Popes or Dictatours, haue taken vpon them an Vniuersall authority to censure all which they neuer vnder∣stood. Had these men contained thēselues in their own bounds, they might questionlesse haue done good seruice to the Com∣monwealth of Learning▪ But when the seruant presumes to controle the Mistrisse, the house seemes much out of order. To seeke for a determination of a Cosmographicall doubt in the Grammaticall resolution of two or three Hebrew wordes, (which some haue gone about) were to neglect the kernell, and

make a banquet on the shells. But howsoeuer, we hope to make it appeare, that the Scripture vnderstood as it ought to bee, is so farre from fauouring their opinion, that the words them∣selues can hardly admit of such a sense, as they would fasten on them. But ere wee descend to the examination of particular places of holy Scriptures alleaged in their behalfe, wee will shew this opinion to bee much different from that of Coperni∣cus, as somewhat more moderate, and able to suffer an easier re∣concilement with the holy Text. For the places alleaged of sa∣cred Scripture, which seeme to oppose our Assertion, either seeme to proue the circular motion of the Heauens, or the rest, and stability of the Earth. But this opinion holding a Mediocri∣ty betwixt both, neither takes away the motion from the Heauens, neither oppugnes such a Rest or quietnesse in the Earth, as the Scriptures vnderstand. For first, albeit wee take away from the Heauens the diurnall motion, and giue it to the Earth: yet we grant to the heauenly Orbes their seuerall mo∣tions, allowing no part of it to bee absolutely voide of motion, Secondly, wee must vnderstand this in a fourefold sense; as op∣posed to foure kindes of Motions. First to the progressiue Mo∣tion of the Center of the Terrestriall globe from place to place. Secondly, to the separation or dissolution of the parts one from the other, by which the Globe may loose his integrity. Thirdly to the Translocation of the Poles, whereby the Poles inclining to one side or another, may bee imagined to change their posi∣tion. Fourthly, to the Diurnall Motion. In the first sense wee giue a Rest and stability to the Earth, because the Earth, how∣soeuer moueable, wee place in the Center of the world, as wee shall proue in the next Chapter. In the second sense we also grant it; because all the parts of the Earth being of a heauy nature, fall naturally downewards▪ and vnite themselues vnto the whole, to decline such a dissolution: In the third acception wee likewise allow such a stability: because the Poles of the Earth (as wee haue shewed) by their magneticall inclination, alwayes respect the same points in the heauens, and can from thence by no meanes remooue themselues. Only in the fourth and last sense wee exclude a Rest, allowing onely a diurnall Re∣uolution from West to East in twenty foure houres. The

first argument alleaged against vs is taken out of the 1 Chap∣ter of Ecclesiastes: Vna generatio (saith Salomon) abit, & al∣tera aduenit, quamuis. Terna in saeculum permaneat. Wherein by the word 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 which some interpret (Stat▪) they would inferre a perpetuall stability of the Earth. A childish conse∣quence, which a graue Diuine might well bee ashamed to vrge: euery man of common vnderstanding may plainely perceiue that Salomons scope in this Chapter was, to shew the vanity & vncertainty of all things vnder the Sunne: which as a speciall ar∣gument amongst others hee amplifies from the success••ie muta∣tion and changes of men liuing on the Earth: in that one gene∣ration goeth away, and another commeth, but the Earth keeps her integrity, and remaines in the same state. This Constancy then, or remaining of the earth, we can in no wise oppose to a∣ny circular motion, but to the changes and vncertainty of men in their generations; in which sense our most learned Linguists vnderstand it. Would not this seeme to any man a ridiculous argumentation, if any man should thus dispu••e: One Miller comes, and another goes, but the Mill remaines still: Ergo the Mill hath in it no motion? Or in a Riuer, one generation of Fishes is produced, and another is decayed; but the Riuer re∣maines the same, Ergo the Riuer remaines still vnmoued? Let any man goe no farther then the plaine wordes whereon these Grammarians stand, hee will easily find out another interpreta∣tion. For the word 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 deriued from 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 signifies as much as to persist, subsist, or to endure, being opposite to 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 which signifies as much as to stagger or start aside from his place, or position: so that nothing from hence can bee inferred to contradict the Sphericall Reuolution of the Earth in her proper place, vpon her owne Poles, which we only maintaine. A second reason they draw from the Psalme 104,* 1.11 out of these words, 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 wherein, (as one would perswade) no lesse then three argu∣ments are couched in three bare termes: But these arguments will (I feare) proue as little as the former. For first the word 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 signifying as much naturally as to found or seat in a place or frame, is not altogether, without a Metaphor giuen to the

Earth, because Almighty God hath so placed it vpon her owne center Poles and Axell, that shee cannot bee moued out of it: Likewise 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 implyes no other then a seat or place, being deriued from the word 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 which signifies no more then to per∣fect, establish, or make ready: The third is 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 from the word 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 which can signifie no other then to incline, to nod, slide, fall, or turne aside out of his place: All which can suffer no other paraphrase or Interpretation then this, That Almigh∣ty God hath set the Globe of the Earth so strongly fixed in her proper frame, that no power can bee so strong to dissolue this Fabricke, or turne her out of her appointed place: which expo∣sition of this place of Scripture, Copernicus himselfe would ea∣sily grant, as no way opposite to the triple motion hee la∣bours to establish▪ Here are these three arguments drawne from three words, suddenly shrunke into nothing. Another reason which I take to bee stronger then the former, some haue taken out of the 19 Psalme; where speaking of the Sunne, hee vses these words. In them hath hee set a Tabernacle for the Sunne. 5 Which is as a bridegroome comming out of his chamber▪ and re∣ioyceth as a giant to runne his course: 6 His going forth is from the end of the Heauens; and his circuite vnto the ends of it: and there is nothing hid from the heat thereof. Out of which words the Heauens should seeme to challenge the motion, which wee haue giuen vnto the Earth. To this we answer two wayes: First, that although this may oppugne Copernicus his opinion, that the Sunne standeth still in the middest as the center of the World; yet may it well stand with our Assertion, who allow the Sunne his seuerall motion in the Eclipticke: whether those words of the Psalme bee to bee vnderstood of the Sunnes Diur∣nall or Periodicke Motion, is not so soone decided: the Scripture not specifying expressely either. 2 we may answer with the Co∣pernicâns; That the Holy Ghost in these or the like places speakes 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉: being willing to descend to the weakest of mens capacity, and not to trouble mens conceits with such matters as to vulgar iudgements might seeme vnlikely or improbable. The like Analogie of speech may wee finde in the first of Genesis, where the Moone is called one of the greater

lights in regard of her appearance, being notwithstanding one of the least. These may suffice to shew the opinion of the earths circular motion to bee probable: I promised no more, & I hope I haue performed no lesse. I neuer held it an article of my faith, to defend the one, or oppugne the other; and therefore leaue e∣uery man to his owne free iudgement, to embrace or reiect what he please.

CHAP. V. Of the Site, Stability, and Proportion of the Earth.

1 OF Terrestriall affections which agree in respect of the Earth it selfe, wee haue hitherto spoken: We are now to treate of such as agree to it in respect of the Hea∣uens. These are chiefly three; 1 The Site, 2 The Stability. 3 The Proportion.

2 The Site is the locall position of the Earth in respect of the Celestiall Bodyes.

It might seeme a hard and almost impossible taske for any man to reconcile that which hath beene spoken in the former Chapter concerning the Earths circular Reuolution, with the grounds of common Geographers, which hold the Terrestriall Globe to bee setled and fixed in the Center of the world. The reason is; because such as hold the circular motion of the Earth, (whereof the chiefe is Copernicus) would haue the Sun to stand still, as the fixt Center of the Vniuerse, and the Earth to moue round about him betwixt Mars and Venus, which seemes cleane opposite to the former opinion. I must confesse that Copernicus

his opinion entirely taken and vnderstood, standeth altogether opposite to these our grounds: yet may that motion of the Earth which we haue established in the former Chapter (for ought I yet know) bee well reconciled with their opinion, which hold the Earth to bee the Center of the world. For the circular Re∣uolution wee gaue to the Terrestriall Globe, was not a motion of the Center of it, from one place to another, as that of the Starres which moue round about the Earth; but rather a turning of it selfe in its owne place, vpon her owne Poles and Axell-tree, in such sort as the wheele of a mill, or such a like engin fixt in one place is turned vpon his owne Axell: So that the motion wee there vnderstood was only the Diurnall motion of 24 houres, making the Day and Night. The other two motions mentioned by Copernicus, may be found out in the Heauens, and left to A∣stronomers. The reasons why I entirely embrace not Copernicus his opinion, are chiefely two. First, because it seemes too harsh and dissonant in nature, to make one and the selfe-same body subiect to so many motions, especially such as by common Phi∣losophers is denied all motion. Secondly, because the other mo∣tions granted to the Earth must needs suppose it to bee placed out of the Center of the world; the contrary of which we shall in this Chapter, God willing, sufficiently demonstrate. The mo∣tion therefore most called in question, and most likely to bee found in the Earth rather then in the Heauen, is the Diurnall Reuolution performed in 24 houres from the West to East: which (as we haue proued) being giuen to the Heauens would be farre swifter then nature can well suffer: wherefore with more probability may this motion bee taken from the heauens, and giuen vnto the Earth: The other without any absurdity at all may be granted in the Heauens: Sith no repugnancy is found in nature, but that euery heauenly body may be furnished with some motion: and therefore Copernicus might haue granted the Sun and fixed Starres their seuerall motions as well as the rest, which would haue seemed farre more probable then to haue en∣dowed the Earth with a Triplicity of motion. These things be∣ing thus opened, I will set downe their Theoremes.

1 The Terrestriall Globe is the Center of the whole world.

To vnderstand aright this proposition, wee must consider that a Center may be taken two manner of wayes: either Geometri∣cally, or Optically: In Geometry it is taken for an imaginary point, conceiued in a magnitude deuoyde of all quantity, yet bounding and termining all Magnitudes: Optically it is vsually taken for a small and insensible Magnitude; because to the fight it may seeme no other then a Point; In which last sense we may call the Earth the Center: For although the Earthly Spheare is en∣dowed with a great and massie substance, yet (as we shall here∣after demonstrate) in respect of the Firmament this greatnesse would vanish into nothing. For if a man standing in the Firma∣ment should behold it, it would seeme no other then as a small point. This being declared, wee will produce these reasons to proue the Earth to be the Center of the Vniuerse. The Center, I say, not of all heauenly motions (for some Starres are moued vp∣on their own Center) but of the whole heauenly machine being collectiuely taken as one Body The first argument is of Aristotle, taken from the grauity or naturall inclination of all heauy bo∣dies to the Center. The Earth (saith he) being a heauy & massie body, must needs seeke the lowest place, which is farthest off from the Heauens. But this can be no other then the Center or middest point of the whole world. Which argument by others is more subtily vrged in this manner. Suppose the whole masse of the Earth were cut and diuided into many parts, equall the one to the other, of the same waight and figure: which parts so diuided were placed in diuers places vnder the concaue Super∣ficies of the Moone, that they might be freely left to themselues to moue according to their naturall inclinations: It is most cer∣taine that all their parts being of the same nature, waight, quan∣tity, and figure, would descend with the same motion, & in the same equall time, to the same place; which could in no wise hap∣pen, except they should concurre in the Center of the world. But this reason, for ought I vnderstand, is only probable, and not backt with any necessary demonstration. For it proues not

thing else but the Earth to bee the Center of all earthie and hea∣uy bodies, and not to bee absolutely placed in the exact middle of the world. Another reason not much vnlike the former, is drawne by some from a finall cause, and the naturall harmony of the parts of the world, one with the other: The Earth (say they) is of all other bodyes, the most vile, and sordid: There∣fore it is agreeable to nature, that it should be placed in the mid∣dle, equally distant from each part of the Heauens, that one part might not seeme to complaine of this vnpleasing vicinity more then another: But this reason takes as granted to matters, as yet not decided. First, that the Earth, amongst all other bo∣dyes, is most vile and sordid, depending on the ground of Peri∣pateticks, that the heauenly bodies suffer no corruption, a thing sooner spoken then proued. Secondly that pure and impure bodies, the most excellent and most vile in nature, are alwayes most distant, as in nature, so in place: which is a peremptory as∣sertion without ground. A third reason more probable then the former, is drawne from the apparences of Starres aboue the Horizon: It is manifest that the Starres aboue the Horizon appeare alwayes to bee of one, and the selfe-same magnitude, and quantity, whether in the verticall point, or in the East, or the West, or any other place: whence we may collect that they differ equally in distance from the Earth, and by consequence the Earth is seated in the middle of the world: for if it were otherwise, that the Starres in some place should bee neerer, in other farther of••, they would some-where seeme greater, other∣where lesser, according to the grounds of the Opticks. This reason, howsoeuer popular, seemes to admit a two-fold ex∣ception. First, because it implies that a man standing on the su∣perficies of the Earth is equally distant from all places and parts of the Heauens, whereas the heauens in the Horizon are farther distant, by reason of a whole semidiameter of the earth inter∣posed. Secondly, all Starres arising in the East, or setting in the West, ordinarily seeme greater then in the Verticall point, by reason of vapours ascending and interposed. Whence wee can∣not well gather the Earth to bee seated in the middest from the like apparence of the Starres when experience teacheth the cō∣trary,

that they seeme not alwayes of the like magnitude. Con∣cerning the first, we answer that the Semidiameter of the earth interposed betwixt the Superficies and Center, is in it selfe greater. But this (as wee shall proue) in respect of the Heauens is so little, that the sense cannot gather any difference in obser∣uation of the Starres, but that they should alwayes appeare of the like magnitude. Concerning the second, wee must needs ac∣knowledge that vapours ascending about the Horizon by an Opticall Refraction, make the Starres seeme greater then other wise they would doe. But the reason may bee vnderstood in this sort: that whether a ••an be placed in the same Horizon where the Sunne is when hee riseth, or vnder that Horizon where the Sunne is now, vnder his Meridian, or vnder that horizon where hee is setting, hee will appeare to bee of one and the selfe-same greatnesse without any sensible difference. Whereas therefore they speake of the appearance of Starres, they would haue them taken as abstracted from all impediments of sight or interposed vapours, and so the reason may obtaine her force. The fourth reason why the earth should bee seated in the midst, alleaged by Ptolomie, and others, is this: wheresoeuer any man stands on the Surface of the Earth, six signes of the Zodiacke will shew themselues, and the other six signes will lye hid; and by conse∣quence halfe the heauens will appeare, the other halfe will bee vnder; which is an euident reason that the Earth is in the midst, for otherwise it could not so happen. The former is confirmed by Ptolomie, Alphraganus, and the best Astronomers: the conse∣quence may bee inferred out of naturall reason. This argument will sufficiently hold vpon this supposition mentioned before, and to bee proued hereafter: That the Earth hauing no sensible magnitude in respect of the Firmament, no sensible difference can shew it selfe betwixt the Sensible, and the Rationall Hori∣zon. Besides these reasons, which make the matter more then probable: others are produced by Ptolomie demonstratiue, ••ot admitting any euident or probable exception or euasion. The first is this; If the Earth bee placed out of the Center of the world, it must haue of necessity one of these three Sites or positions: Either it must be in the plaine of the Equinoctiall: or

at least it must bee placed, not onely without the plaine of the Equinoctiall, but without the Axell-tree: That is, to expresse it plainer; It must either bee placed beside the Axell-tree, yet e∣qually distant from both the Poles; or else it must bee on the Axell-tree, and so consequently neerer to one Pole then the o∣ther: or thirdly, it must needs be beside the Axell-tree, yet nee∣rer to one Pole then another. If the first position were admit∣ted, these absurdities would of necessity follow. First, that in a right Spheare there would happen no Equinoctiall, but onely in that Horizon which passeth by the Center of the world: for example sake; ••et there be imagined a Spheare, BDCE, whose

[illustration]

Center is A: let the Equa∣tor bee DE: the Axel-tree of the world BC: and let the Earth bee in F, the right Horizon HG not passing by the Center of the world A: which shall bee parallell to the Axis BC: since the Equator cuts the Horizon in right angles; It is most manifest that not only the equa∣tour, but other parallells of the same will bee vnequally di∣uided of the Horizon: for as much as it passeth not by the Cen∣ter or the Poles of the world: wherefore it must needs follow, that the dayes must continually be vnequall to the nights: which contradicts all experience; because in a right Spheare the dayes are alwayes found to bee equall to the nights. Secondly, out of this position it would follow, that no man in a right Spheare

should behold the halfe or hemispheare of the heauens, but ei∣ther a greater or lesser part, as may be demonstrated out of the same Diagramme, whereas sense can testifie that six signes of the Zodiacke are alwayes conspicuous aboue our Horizon, and the other six alwayes hid: only excepting that Hor••zon which passeth by the Center of the Earth, wherein the Mediety of Heauen is conspicuous. Thirdly, the same Starres in a cleere aire should not alwaies seeme of the same magnitude; for if the earth be placed in the Equinoctiall plaine, and beside the Axis of the world toward the Zenith or Meridian; the Starres which are in the Meridian will appeare greater then in the East or West, because they are neerer. But if it bee placed neere the Nadir or midnight point, they will appeare greater in the East or West, then in the Meridian: if it should bee placed towards the East or West, the Starres would either seeme greater in the East then in the West, or contrarywise, greater in the West then the East: all which plainely contradicts experience. Moreouer it would hence follow out of this last, that the fore-noone would not be equall to the after-noone, for as much as the Meridian circle passeth by our verticall point, which in this case cannot bee in the middle of the hemispheare, but will decline more, either to the East or the West. Fourthly, it must needs follow that in an oblique Spheare, either there will bee no Equinoctiall at all, or at least, if there were any, it would not be in the midst betwixt the two Solstices of Summer and Winter; which is against all common experience. To explaine which assertion, let there be a Spheare ABCD, whose Center shall bee E: wherein wee will conceiue the equatour to be BD: the two Tropicks IL, and XH: the Axell-tree of the world AC: Now if the Earth should be placed in the plaine of the equatour, out of the Axis of the world, as in F let there first be an oblique Horizon ZFY, cut∣ting all the parallells into vnequall parts, and the Axis in those parallells which are without: it is manifest that in the said Ho∣rizon there will bee no Equinoctiall; because the Horizon e∣qually diuides in two halfes only that parallell which is descri∣bed by P, which neuerthelesse the Sunne neuer comes vnto, as neuer going beyond the Tropicke XH: Let there bee another

[illustration]

[illustration]

oblique Hori∣zon OFM cut∣ting the Axell AC within the said paral∣lels in N: It is manifest by reason, that there will hap¦pen an equi∣noctiall in the said Horizon when the Sun shall describe the parallell by N: because this parallell is by the Horizon diuided into two equall partes. But this can in no wise happen in a middle space and time betwixt the two Solstices, for as much as the Equator only is equally distant and remoued from either Solstice. It is also manifest▪ that the Sunne residing in BD the equator, there can bee no equi∣noctiall, but either after or before: which is absurd and oppo∣site to obseruation. Fiftly, it will bee inferred out of these grounds, that no Horizon shall diuide the Heauens into two equall parts besides that which concurres with the equino∣ctiall circle, as BD, and such as are drawne by BD. Wherefore all people should not behold the one halfe of the heauens. Sixt∣ly, out of this opinion would necessarily bee concluded, that the excesse of the greatest and longest day aboue the equinoctiall day, should not bee equalized by the defect of the shortest day, by how much it is exceeded by the equinoctiall day: which is against all common experience; the consequence shall appeare by demonstration. Suppose A to be the Articke Pole: then will PG bee the excesse of the longest day XP aboue XG the E∣quinoctiall day. But KQ is the defect wherein the shortest day

IQ, is exceeded of the Equinoctiall day IK. All these absurdi∣ties are auoided, if wee put the Earth in the Center E. for so in euery oblique Horizon, as in SR, will bee an Equinoctiall, the Sunne risiding in the Aequator. 2 The Heauens will bee diuided into two equall halfes, and PG the excesse of the longest day, will bee equall to KV, the defect of the shortest day: whence wee may conclude the first part of this argument, that the Earth is not besides the Axis in the plaine of the Equinoctiall. Concer∣ning the second position: if wee should place the earth in the Axis of the world out of the plaine of the Equinoctiall, as many, or more absurdities would of necessitie follow: for example sake, let it be imagined in P: First then no Horizon beside a right would cut the Heauen into two equall parts or halfes, and con∣sequently the Zodiack. But this is proued false by experience (as we haue shewed) because six signes of the Zodiacke are alwayes aboue and conspicuous, and the other six vnder. Secondly onely vnder a right Horizon would there bee an Equinoctiall, because only such an Horizon equally diuides the Equatour into two halfes, as may bee seene in the former figure, in which the Equa∣tour is conceaued to bee BD: the right Horizon AC. the ob∣lique YZ, cutting the Equator in F into two vnequall parts: Now if it should happen that in any oblique Horizon, there should bee an equinoxe, it could no wise bee in the middle time betwixt the two Solstices, but would be much neerer to the one then to the other; as if the Earth w••re placed in N, betwixt the Tropicke XH, and the Equatour BD, there would bee an equi∣noxe when the Sunne passeth in the parallell by N. which pa∣rallell is farre neerer to the Summer Solstice, then the Winter Solstice. But if the Earth were in G, there would happen an e∣quinoxe iust in the day of the Summer Solstice; all which are most absurd, and most repugnant to common sense. Thirdly, this granted, the whole order and proportion of increase and de∣crease of dayes and nights, would bee confused and troubled. It is agreed on by consent of all Cosmographers, that euery where without the right Horizon, there is such an order and proporti∣on of the increase & decrease of the dayes and nights, that twice in a yeere the dayes are equall to the nights▪ to wit, in the meane,

or middle betwixt the longest and the shortest day, that the lon∣gest day is equall to the longest night, and the shortest day to the shortest night. That the excesse of the longest day aboue the Equinoctiall day, is so much as is the defect of the shortest day in regard of the said Equinoctiall day. All which and many more such Apparences would bee interrupted, were the Earth placed any where else then in the Center E; as will appeare by the Scheme. For the Earth being placed in E, euery oblique Ho∣rizon, as SR, will diuide the Equatour BD, into two equall he∣micircles, so that so much shall appeare aboue as lies couched vnder, and so that day will bee equall to the night. In like sort the Tropicks HX and IL will bee diuided into two vnequall parts, yet so as the Alternate segments shall bee equall, to wit, PX and VL, also TH and VI, as it is demonstrated by Theodo∣sius, lib. 2. prop. 16. Whence it comes to passe that the longest day XP is equall to the longest night LV, and the shortest day IV is equall to the shortest night HP. Finally, PG, the excesse of the longest day XP aboue the Equinoctiall day XG, is equall to KV the defect of the shortest day vnder the Equinoctiall day IK, which is shewed out of the similitude and equality of the Triangles TEG, and VEK. Now of the contrary parts, if the Earth should be placed in the Axis without the Center E, as in P, beyond all the parallells, no equinoxe can bee in an oblique Spheare (as wee haue shewed) but alwayes the dayes will bee longer or shorter then the nights. But if the earth bee placed in the point G, by which passeth the last of the parallells, there will be one only equinoxe, & that in the Solstice in an oblique spheare in all other parts of the yeere the dayes would either be longer, or else shorter then the nights. But if the Globe of the Earth bee seated within the parallells in the point N, there would be two Equinoxes in a yeere, wherein the spaces of dayes and nights should increase and decrease. Neuerthelesse these increments & decrements should neither in number nor in greatnesse be equal to the increments and decrements of the nights, as may be ga∣thered very easily by sense, comparing the two Triangles, DNG, and QNK, because that more and greater segments of parallels are comprehended in the Triangle LNK, then in the Triangle

PNG. Fourthly, if the Earth should vnequally respect the Poles, and were not placed in the Center, the shadowes of Gno∣mons erected which make right angles with the Horizon, should not bee cast directly forward in one right line in the time of the Equinoxes: the Sunne exactly placed in the East or West: as for example: let the earth be A, seated in the plaine of the E∣quinoctiall circle BC

[illustration]

and let there bee a Gnomon erected on the plaine of the Ho∣rizon, which is repre∣sented by the circle BC: It is manifest to sense that the sun set∣ting in C, the shad∣dowes will be cast in the opposite part to∣wards B. Likewise the Sunne rising in B will cast his shadow towards C. But AC and AB, concurre in one right line, which plainely demonstrats vnto vs, that the earth is seated in the plaine of the Equinoctiall. But if it were placed out of it towards either side, as in E, if a Gnomon be set vp on the Horizon as EF, wee shall see that the Sunne rising in B in the time of the Equinoctiall, the shaddow will bee directed by the line EG, likewise the Sun setting in C, the shaddow will make the right line EH: But these two right lines being produced, will cut one the other in the point E, and therefore cannot concurre in the same right line, whereof ordi∣nary experience witnesseth the contrary. Fifthly, if the Earth were thus placed, it would follow by necessary consequence, that two signes of the Zodiacke diametrally opposite, should not be seene by a Dioptricke instrument: which is against experience which witnesseth that the rising and setting of the Sunne, may be seene by one right line: also the rising in the Summer Solstice and the setting in the Winter Solstice, to answer to each other in one right line in euery Horizon: which could not bee perfor∣med vnlesse the Earth were in the Equinoctiall plaine and the

[illustration]

[illustration]

Center. Let there bee a•• Horizon BDCE, the E∣quator BC, the Axel-tree of the world DE, the Tro∣picke of Cancer FG, of Capricorne HI. Let the Earth first bee placed in the Center A: here may plainely bee perceaued that the Equinoctiall East B, and the Equinoctiall West C, answer and con∣curre in the right line BC: also that the East point of the Summer Solstice F, and the West of the Winter Solstice I, to concurre in the same right line FI▪ also the Winter East point H, and the Summer Westerne point G, to answer mutually one to the other by the same line GH. Which Apparence is confirmed of all Astronomers. Now let the Earth be set in the Axis out of the Equatour in K: It is ma∣nifest to sense that the contrary will alwayes happen: For the Winter point of the Sunne setting I, by a right line drawn from the Earth will not directly answer to the Summer point of ri∣sing F, but to the point L. Likewise the Winter point of Sunne∣setting G, will answer to the point M, and not to the Winter rising H. Whence wee haue sufficiently demonstrated this se∣cond position of the Earth beside the Center of the World to be inconuenient, and no wayes to bee defended. For the third po∣sition that the earth should be so remoued out of the Center, as that it should neither be in the Equinoctiall plaine, nor yet in the Axell-tree. Wee need produce no other confutation, then what wee haue said before of the other two positions. Because out of this, the same or greater absurdities would follow, then of the other, as any man may easily vnderstand out of these demonstra∣tions wee haue before recited. The second demonstratiue rea∣son, wherewith Ptolomy would confirme the Earth to be in the Center is drawne from the Ecclipse of the Moone in this man∣ner. If the Earth were not in the Center of the World, there

would not alwayes happen Eclipses of the Moone, when the two greater lights are diametrally opposed, but sometime they would happen when these great lights are not residing in oppo∣site places of the Zodiack; which is false, and against experience; for all Astronomers haue witnessed, that eclipses of the Moone then only are seene, when the Sunne & the Moone stand direct∣ly

[illustration]

opposite the one to the other: because then is the earth direct∣ly interposed. Now let the Center of the world be A, in which if the Earth bee placed, it is manifest that it then happens when the Sunne and the Moone are exactly opposed, and the earth in∣terposed directly, which in this case cannot otherwise happen: But if the Earth bee placed beside the Center of the world, as in B. These things may fall out, that the two Luminaries may re∣side in two opposite points of the Zodiack, and yet cause no e∣clipse; because the Earth is not in the same Diameter by the which they ••••e opposed. Also the Moone will sometimes suffer

an Eclipse, when shee is lesse distant from the Sunne then a semi∣circle. In a word, this eclypse is in places opposite. A semicircle will then only be seene when the Diameter of opposition shall passe by the Center of the Earth, and the world; all which are manifestly repugnant to experience and obseruation. Out of this demonstration of Ptolomy, Clauius, a later Astronomer in this sort drawes the like conclusion. Let there be obserued two

[illustration]

diuers eclip∣ses of the Moon in di∣uerse places of the Zo∣diack: Now because each Eclipse ha∣pened when the Sun and the Moone were oppo∣sed the one to the other, in one Dia∣meter (as Experience & Astrono∣micall sup∣putations warrant) it must necessarily bee concluded that the earth should bee in each of those Diameters, and so by conse∣quence in the common section of them both: Sith then all the Diameters of the world concurre, and cut one the other in the Center: it must needs follow that the Earth should bee in the Center and midst of the World. Diuerse reasons there may bee drawne to proue this assertion. But these demonstrations of Pto∣lomy, as I haue set them downe enlarged, and explained by our later writers, may seeme sufficient, especially in a matter of few called in question.

2 The Position of the Earth in the Center of the World may be reconciled as well with the Diurnall motion of the Earth forementioned, as the Appa∣rences of the Heauens.

That this proposition may the better bee vnderstood, wee are first to set downe in a Scheme, or Diagram, both the number and order of all the heauenly Orbs, conceiued according to our grounds. Secondly, we must shew in particular, how this ran∣ging of the heauenly bodies is capable of all the motions, and apt to satisfy the apparences. In which parts I wil not too nicely descend to Astronomicall curiosities, being too many and subtile for a Geographer to discusse. Only I will giue a tast, to satisfie such as suppose no middle way can bee troden out betwixt Pto∣lomies stability of the Earth, and Copernicus his three Moti∣ons. I might seeme perhaps presumptuous beyond my know∣ledge, to reiect and passe by the draughts and delineations of Pto∣lomy, Alphonsus, and their followers, which are commonly de∣fended and in vse: or that other of Copernicus, supported with the authority and credit of so great an Astronomer: or that of Tichobrahe more corrected then either, and to preferre my own, being an Embrion, or halfe fashioned. To this I answer. First, that I only expose this Scheme following to the view of the iu∣dicious, iustifying it no farther then will stand with Astronomi∣call obseruation. Secondly, I herein arrogate little or nothing to my selfe; for as much as I haue digested, and compounded it out of the obseruations and experiments of late Astronomers, and only collected together what they scattered; The Scheme it selfe is expressed in this manner; wherein to beginne from the lowest: The Center is the Globe of the Earth, to which wee haue giuen a Diurnall motion from the West to the East vpon her owne Poles, whose Reuolution is made in 24 houres: About the Earth as the Center of the whole world, the Moone is car∣ried in her circle, which amongst all the Planets, is found more neerely to respect the Earth, as well in place as nature. Next succeeds the Sunne, as the leader of all the Planets, which car∣ried

[illustration]

[illustration]

round a∣bout the earth in an Annuall circuit, des∣cribes the E∣cliptick circle: about the Sun as the proper Center, are all the Planets moued except the Moon. The two immedi∣ate cōpanions of the Sun are Venus, & Mer∣curie, which so cōpasse him about, that the Earth neuer comes betwixt them and the Sunne. The other three Planets, as Mars, Iupiter, and Saturne, howsoeuer they enuiron the Sunne as their proper Center, yet so as within their circles, they comprehend the body of the Earth: The Planet Mars, because hee is found by Astrono∣mers, to moue sometimes aboue, sometimes vnder the Sunne, is vnderstood to moue in such a circle, which on the opposite side shall cut the circle of the Sunne: yet so as Mars and the Sunne can neuer meet in one point: Forasmuch as Mars, as well as the other Planets, is supposed to be carryed in an Epicycle about the Sunne, and to keepe an equall distance from him howsoeuer moued: Neither is he euer found vnder the Sunne, but about the time of the opposition, as Astronomers obserue: whence a cause hath beene giuen, why Mars should appeare greatest at the time of Opposition. These fiue Planets, to wit, Saturne, Iupiter, Mars, Venus, and Mercury, may bee considered according to a double motion: The one is proper and naturall, wherein they are moued about the Sunne, as their proper Center: The other Accidentall, and as it were by a consequence of Nature, where∣by

in their circuit mouing about the Sunne as their Center, they must of necessity, by a consequent site of the place, be carryed a∣bout the Earth. For the Sunne placed in his Eclipticke line, so compasseth round the Earth, that with him hee is supposed to carry the Epicy••les, wherein these Planets are moued round a-about him. Whence wee finde the motion of these Planets about the Sunne, as their owne Center, to bee regular, but about the Earth irregular: which proceeds from their Excentricity in res∣pect of the Earth. Aboue all the Planets wee place the Firma∣ment, or Starry Heauen, hauing a very slow motion, not to bee finished in many thousand yeeres, and this motion is on other Poles then the Poles of the world, to bee sought out in or neere the Poles of the Eclipticke. This Heauen would Aristotle haue to bee the first moueable, and therefore gaue it a very swift motion, which is the same which wee call Diurnall, and haue gi∣uen to the Earth. But it seemes more consonant to nature, that the slower motions should agree to the higher bodies: and the swifter to the lower, that there might be a proportion, betwixt the time and the space of motion: It remaines that wee proba∣bly shew that out of their suppositions, the Celestiall Appa∣rences may bee as well or better salued then by the ordinary grounds. The Apparences which are most called in question, concerne either the Motion, or the Places, and Positions. All the rest are either of lesse moment, or at least are thereunto redu∣ced. Euery motion which is found or thought to bee found in the Heauens, is either the Diurnall, or Periodicke. The Diurnall Motion (as wee haue already shewed) belongs to the Earth, which according to our grounds is supposed to moue from the West vnto the East in 24 houres, Which may answer to the Motion of the first moueable Spheare; which according to Aristotle, is the Starry Firmament, and thought to moue from the East to the West. The Periodicke Motion, is either a slower Motion, to be finished not vnder many thousand yeeres, or else a swifter Reuolution of the Planets. This slow motion the com∣mon Astronomers would haue towfold: The one from the West to the East on the Poles of the Eclipticke: the other a Motion (as they call it) of Trepidation, from the South point to the North

and backward againe: but one slow Motion of the sixt Starres vpon the Poles of the Eclipticke, granted to the Firmament, will (for ought I see) satisfy both. The reason why they put two distinct Motions, is, 1▪ Because they haue obserued the Starres of Aries, Taurus, and the rest of the Zodiacke, not to be seated in the same place wherein they were anciently found; but to be moued certaine degrees from the West towards the East. Whence they would conclude a Motion to bee from the West vnto the East. 2. It will stand with no lesse experience, that the foresaid Starres of the Firmament haue moued themselues from the South towards the North. To passe ouer the r••st, the Pole∣star, which in Hipparchus time was distant from the Pole about 12 Degrees, is now obserued to approach almost three degrees. These two Motions, should they bee esteemed in the account of Astronomers might seeme deficient. Notwithstanding wee may probably coniecture this to bee no other then one, and the selfe∣same Motion vpon the Poles of the Eclipticke: Whence it may come to passe, that the fixt Starres are not only carryed from West to East, but also by reason of the obliquity of the Eclip∣ticke line, encline more and more dayly to the Pole of the World whence they may againe returne. For this motion from the West to the East, is of the primary intent of nature, wherein the Starres moue in circles parallell to the Eclipticke: But from the North to the South, as by the necessary consequence of the po∣sition and obliquity of the Zodiacke: because it cannot bee auoi∣ded, but that it should either incline to, or decline from the Pole. If they should obiect (as many doe) that this progresse is not proportionall in respect of the time according to the calculati∣on of the Astronomers. Wee answer. 1. That this difference is so small, that it should rather seeme to bee imputed to the ne∣gligence or ignorance of such as tooke these obseruations, then to any diuersity of motion. For who knowes not in these dayes of ours, wherein this art is arriued at a farre greater perfection, di∣uerse Astronomers in obseruing the same Star at the same time, to differ much the one from the other: Whose knowledge not∣withstanding, is fortified with the experience of the Ancients, and inuention of new Instruments. What then shall wee thinke

of those, which distant so many ages in time, and vsing diuerse & vnlike Instruments in their obseruations, haue differed in mat∣ters of so small moment: chiefly in seeking out the period of this long and slow motion, which by reason of his slownes, since the time it was known to man, hath not ranne the fifteenth part of his circle. For my part, I shall rather ascribe it to the errour of their obseruations, then multiply Orbs without a greater cause. First, because (as wee haue said) the difference is so small, and almost insensible 2. Because wee haue beene taught by our Astronomicall histories, what kinde of Instruments were then in vse, which to later Astronomers haue beene thought too rude and vnfit to make such subtile obseruations. Lastly, concerning the Site and Position, no lesse reason may bee giuen out of our Hypothesis, then the common way. For by placing the fiue Pla∣nets to runne in their Epicycles about the Sunne, may we giue a reason of the inequality of their distance from the Earth, where∣in an ingenious minde in our common grounds can hardly giue himselfe sufficient satisfaction.

3 The stability is an affection whereby the Ter∣restriall Spheare is firmely setled in his pro∣per place.

The Stability, or firmenesse of the Earth which we here vn∣derstand, 1. No way denyes or contradicts the motion of the parts of the Earth, whereby being separated, they returne to their proper place. 2. Neither the circular Reuolution of it on her owne Poles and Axell, whereof wee haue formerly spoken. But either such a motion whereby the parts of it may bee seue∣red one from the other, and so the whole Masse dissolued; or whereby the Center of the Earth may be moued out of his pro∣per place; or at least such as might mooue the Poles of the earth from their true verticity, whereby they should not respect al∣wayes in the Heauens the same points or poles. Which kinde of stability from motion we will establish in this Theoreme.

1 The Earth is firmely seated and setled in her pro∣per place.

This Theoreme may bee proued as well by reason, as authority of holy Scripture: From reason it is demonstrated in this manner. If the Earth should not be setled in her proper place, this would of necessity happen; either by dissolution and separation of the parts one from the other: or by remouing the poles out of their fixt places: or else by motion of the Center from one place to the other. The first cannot be admitted; because (as we haue be∣fore taught in the second Chapter of this booke) All Terrestriall Bodies are endowed with an inclination or ponderosity to ap∣proach as neere as they can to the center of the Earth; so that by this coherency and conformity, the whole earth is ransom'd from any such mutability. Neither can the whole Spheare bee dissolued without an especiall miracle: And if so it should hap∣pen, the parts would returne againe, and conforme themselues to compose the same Spheare. Likewise the second way; The earth cannot loose her stability, because (as wee haue shewne in our former Chapter) the earth hath her two Poles magneticall made fast vnto the Poles of the world, as if they were bound firmely to two great pillers, neuer to bee shaken. Finally, The Center of the Earth cannot be moued out of his place any wise, because, as we haue demonstrated in the Chapter before, with∣out the disturbance and inuersion of the whole frame of Nature the Earth can haue no other place then the Center or middest of the whole world. Some haue alleaged as an argument that prin∣ciple of Aristotle: That one simple Body can haue but one simple Motion: and therefore the earth challenging to it selfe a right motion to the Center, cannot also haue a circular or round mo∣tion, and so of necessity must rest vnmoued in her proper place. But this reason, as I haue shewed, is weake to proue this asserti∣on. First, because this principle of Aristotle is not grounded on certainty, but contradicts experience, as I haue elsewhere shew∣ed. 2. This right motion to the Center is not to bee ascribed to the whole, as the immediate subiect, but to the parts of it sepa∣rated from the whole; so that nothing will hinder, but that the whole Globe may haue a motion proper to it selfe on his owne Poles. But to let this reason passe as weake; all those argu∣ments alleaged by the common Astronomers, and Philosophers

against the circular motion of the Earth proue indeed no other matter then this stability which we establish: but if racked any farther come short to satisfie. For authority of Scripture, many places are vrged to proue this stability; whereof wee haue a pregnant place in 104 Psalme, wherein Dauid magnifying the Creator, saith That hee laid the foundation of the Earth so sure, that it should not be moued at any time: To which may be added many other Texts, but that I hold this one sufficient in a matter which few men call in question. Wee are in the third place to treate of the proportion of the Earth, with the heauenly bodies.

4 The Proportion is that wherein the quantity of the Terrestriall Globe is compared with the quantity of the Heauens.

We must here remember a distinction before touched, that the Globe of the Earth may bee considered two wayes; either Abso∣lutely in it selfe, or Comparatiuely in respect of the heauenly Bo∣dyes. If we consider it absolutely in it selfe, wee shall finde that the Earth hath a vast and huge magnitude, and not any wayes to bee compared to a point; because it is a body, and therefore subiect to diuision, whereas a point is conceaued as an indiui∣sible signeadmitting no parts at all. S••condly, because the mag∣nitude of the Earth many times taken, will measure the great∣nesse of the Heauens, as wee may obserue by Astronomers who measure the magnitude of the greatest Stars by Diameters and Semidiameters of the Earth: whereas a point of it being a thousand times multiplied, will neuer beget a magnitude or measure of the quantity of any Body. Thirdly, the Starres are not as meere points in respect of their Orbs, because they sensi∣bly are seene, as parts of these Orbs. But the Earth is greater then some of the lower Starres, as the Moone: Whence we may with good grounds auerre, that if a man were placed in the Moone, hee might behold the Earth far greater then the Moone being obserued by vs in the Earth. Wherefore no man can de∣ny but the Earth in it selfe hath a great vastnesse. But if wee con∣sider this greatnesse in respect of the Heauens, we shall find this vast greatnesse to shrinke almost into nothing, and become as a

meere point without sensible magnitude. But this is not altoge∣ther generall without limitation; because the heauenly bodies are distinguished into the higher and greater, such as are the Fir∣mament with the foure higher Planets, such as are Saturne, Iu∣piter, Mars, and the Sunne: or the lower and lesser, such as are Venus, Mercurius, and the Moone, which difference in place and greatnesse admits a great diuersity in this proportion, as wee shall shew in these two Theoremes.

1. The Earthly Globe compared in quantity with the Firmament and superiour Orbes of the pla∣nets, hath no sensible magnitude.

This Proposition is supported not only by the authority of many and graue Authors, as Aristotle, Ptolomy, Pliny, Alphra∣gan, and others: but by diuers strong reasons drawne from ex∣perience and obseruation of Astronomers. The first argument shall be this which is most popular. The Sunne and many other Starres in the Firmament, are found out by Astronomicall In∣struments to bee manifold greater then the Globe of the Earth: yet appeare they in respect of the heauens but as a little point or portion. Then must the Earth, being in comparison far les∣ser, be deuoyd of all sensible magnitude or proportion. Second∣ly, if the Earth had any notable quantity in respect of the Hea∣uen, then must the Diameter of the earth haue as great a quan∣tity in respect of the Diameter of the Sky; for there is the same proportion of the Diameters which the circumferences haue one to the other, as is demonstrated in Geometry. Now if the Diameter of the Earth hath any notable magnitude in cōparison of the Diameter of the Skye, then the Starres which be ouer our heads, be neerer vnto vs by a notable quantity, then when they bee either in the East or West. For it must needs follow that the Starres placed in the verticall point, are neerer by the Semidia∣meter of the Earth, then when they are either in the Easterne or Westerne point, as we see in ••his figure here set downe ACDB, wherein I make E to be the Center of the Earth, AEB the true Horizon, and EF the Semidiameter of the earth. Now if the Semidiameter FE haue any sensible proportion, then must G

the verticall point

[illustration]

be neerer to F. then either A or B. sup∣posed to bee the East & west points; because EA, or EB, are the whole Semidiameter of the Celestiall cir∣cle, whereof FG is only a part. But contrarywise there is no such diuersi∣ty perceiued in the magnitude of the Starres, but that they appeare still to bee of one and the same greatnesse, except by accidentall interposition of vapours and grosse bodies: wherefore it must of necessity follow, that their distance is all one in all parts of the Skye, and by consequence the Semidiameter of the earth hath no sensible diuersity in di∣stance. Thirdly, hence would arise another reason no lesse for∣cible then this; that if the Semidiameter of the Earth had any comparison or proportion to the Semidiameter of the Skye, the Horizon that we haue on the vpper part of the earth, should not diuide the Skye into two equall parts; for as much as the part which is couched vnder the Horizon, would alwayes be greater, and the other lesser, as in our former Diagramme: if EF haue a notable quantity in compa••ison of EA: then will the line CFD, being the Horizon on the top of the earth, differ notably from the line AEB, being the Diameter of the World, and the Horizon to the Center of the Earth: and so shall not the Horizon CFD, diuide the world into two equall parts, but the vpper part shall alwayes be lesser then the lower, which crosses ordinary experience: for we may see in long winter nights, that those Starres which are in the East Horizon, in the beginning of the night, will be in the West at the end of twelue houres: and contrarywise, those Stars which did set in the West, when those

others did rise in the East, shall rise agayne when the other shall set. Fourthly if the earth had any sensible greatnesse in respect of the Heauens, then were it vnpossible for any Sunne Diall to bee regular and obserue due proportion. For we see the shaddowes to moue as duely and orderly about the Center of Dials and such instruments, as if their Center were the very Center of the world: which could neuer happen if these two Centers should differ notably in respect of the Spheare of the Sunne: to expresse it the better we will set this Figure, which represents the three notable circles in a Diall, which are described by the course of the Sunne in three notable places of the Zodiacke, to wit, the two Tropicks, and the Equinoctiall. Herein the vttermost arch

[illustration]

BLC represents the Tro∣picke of Capricorne, and is described no greater then the quarter of a circle, be∣cause the Sun placed in the Signe, shines vnto vs but six houres. The Equinocti∣all is set as halfe a circle, because the Sun being in it, appeares vnto vs 12 houres, & is here noted out by EIF. The Tropicke of Cancer containes 3 quar∣ters of a Circle, because when the Sun is in it, there are eighteen houres from Sun-rising to Sun-set: and that circle is GHK. The Center of the Diall is A, and the Style which giues the shadow DA, whose top being D, doth describe those portions of circles with such exactnesse, as if the Diall were set in the very Center of the Earth, and the distinction of the houres shewes it selfe no otherwise then if the Center of the Diall were the same with the Center of the world. To these arguments I may adde, that if there should bee a sensible greatnesse of the earth in respect of these superiour Orbes, either all or most of these absurdities would arise which follow their opinions, who place the Earth out of the Cēter of the World, which we haue before treated of.

2 The Terrestriall Globe compared with the in∣feriour Orbs hath a sensible magnitude.

Although the whole Earth compared with the Firmament and superiour Orbs of the Planets, seeme no otherwise then a point: yet from this wee must except the Orbes of the lower Planets Venus, Mercury, but especially the Moone: Who are found by obseruations of diuerse skilfull Astronomers to haue a sensible and notable greatnesse in respect of the earth, where∣of a manifest argument may bee drawne from the Parallax or variation of the sight: wherein our obseruations of the same Starre at diuerse places are not the same, though at the same time: neither will such a Starre to both places seeme in the same point of the Heauens; which could not possibly bee, except we admit a sensible difference betwixt the Rationall and Sensible Horizon; and so grant the Earth, in respect of such Orbs, some quantity and greatnesse. This diuersity of Aspect, which they call the Parallax may be seene in this Figure: let A be the Cen∣ter of the Earth, L the Moone, or other Starre to bee obserued,

[illustration]

EGD, the Firmament or Orbe of the fixt Starres: suppose then the eye to be in the fixt point M of the sensible Horizon XMY the said Planet will appeare in the point of the Firmament S, according to Opticall principles, whereby all things are sayd to be seene in the place directly opposite. Supposing againe the Eye to be in the point P of another sensible Horizon RPQ, the Starre L will no doubt appeare in the opposite point T. Nei∣ther of which meets with the Starre in the right place. For ima∣gining the Eye to bee placed in the Center A, the place of the Starre would bee V, which is his true place. These differences of sight could finde no place if the Earth were as a meere point and challenged no sensible Magnitude, in respect of these inferi∣our Planets: and yet experience of Astronomers hath sufficiently confirmed it. But this being a point very curious, and appertai∣ning to Astronomy, I leaue it to their farther industrie, whose profession it vndergoes.

CHAP. VI. Of the Circles of the Terrestriall Spheare.

1 ALL the properties which agree by Nature to the Terrestriall Globe, we haue handled. Here wee are in the next place to treat of such, as agree by vertue of our vnderstanding: Of this sort are all the Circles conceaued to be in the Terrestriall Globe.

2 A Terrestriall Circle is a round line conceiued in the face of the Terrestriall Globe, diuiding it into two parts.

A Circle is considered two manner of wayes: either abstra∣cted from this or that sensible matter, in which sort it is suppo∣sed to bee taught in Geometry; to which properly appertaines the knowledge of the Fabricke and Measure of all Magnitudes, especially of this, being amongst all, the most perfect and exact: Or else a circle is considered so far forth as it hath some ground in the Nature of the Earth, at least by application of the Celesti∣all Globe, and so it comes into the consideration of Geography. For conclusions demonstrated and proued in Geometry, are here to be admitted as principles supposed not demonstrated a new: which Logicke, if Clauius, Blancanus, and other such writers had well learned, they would not haue stuffed out their worke with such Heterogeneall mixtures, but haue reduced euery thing to his proper seat and science. A circle as well by the Geogra∣pher as Astronomer is diuided into foure quadrants, each qua∣drant into 90 degrees, all which make vp 360. So that a degree is the 360 part of a Circle, which I only mention as being of chiefest vse with vs, yet supposed to bee handled and taught in a higher science.

1 A circle though imaginary in it selfe, hath his ground in the Nature of the Earthly Spheare.

As in Logicke men haue inuented certaine Intentionall No∣tions, seruing as so many instruments to direct and regulate our vnderstanding in the apprehension of things: So in Cosmogra∣phie can there not be wanting such imaginary signes and circles to confirme and ayde our phantasie. And as in Logicke such No∣tions in themselues are meerely imaginary and intentionall, yet may be tearmed reall, so farre forth as they are grounded in the things themselues; so may we speake of these circles conceiued in the face of the Terrene Globe: which wee are not to con∣ceiue to bee fictious and imaginary, as if they had no ground at all in nature. For although there bee no such circles painted on the face of the Earth, as wee finde in an artificiall Spheare: yet must wee of necessity conceaue such reall respects to bee in the Earth it selfe: as when a Ship sayles ouer the Ocean, it can∣not bee said to leaue behind any visible marke or Character in

the surface of the water; yet in regard it made a reall passage, it will leaue a line conceiuable, signing out vnto vs the true pas∣sage. It is a matter which hath not a little troubled Cosmogra∣phers, to finde out the immediate and true subiect or ground of these circles; whether they should be immediatly taken from the earth, or else in the Heauens. The ancient Cosmographers haue acknowledged no other ground of these Circles; then the congruity and application of the celestiall Globe, and his parts with the parts of the Earth: but our Magneticall Philosophers more neerely searching into the nature of the Earthly Spheare haue found these Circles all (except the Horizon) to wit, the Meridians, and Parallells, to bee immediatly grounded in the Earth it selfe: whose opinion we cannot reiect, as being suppor∣ted by experimentall demonstration, as wee shall shew in par∣ticular.

2 The distinction of a circle into any certaine Number of parts, hath no certaine ground in the Nature of the earthly Spheare, but only inconueniency; leauing our iudgements free, to take such a Number as may best serue our purpose.

Some Astronomers more curious then wise, haue gone about to seeke a ground of this distinction of a circle into 360 parts out of the Sunnes course in the Zodiacke, a Circle (say they) by the opening of the Compasse, being described in a plaine, is di∣uided into six equall parts. Now because the Sunne being the rule and measure of all perfect motions, passeth through one sixt part in 60 dayes, the whole Circle was diuided into 360, for 60 multiplied by 6, will produce that number. But this reason seemes to infer nothing concerning any naturall ground, that this distinction shall finde in the Earth, though it may serue as an argument of Conueniency, the number 360 being fittest for that calculation. Another reason very like the former, is drawne from the coniunction of the Sunne with the Moone,

which happens 12 times in a yeere: and because from each con∣iunction to that which followeth are spent 30 dayes; Hence it is that the Zodiacke is first diuided into 12 parts, which multi∣plied by 30 will produce 360. This reason likewise proues only thus much, that it is the fittest number to calculate the Motion of the Sun in his Eclipticke: Not that this diuision hath any ground in Nature more then other▪ because being a continuate quanti∣ty, according to Philosophy, it may suffer infinite diuisions: for it was in the beginning left free to Cosmographers, to choose what number they pleased to expresse the parts or sections of a Circle: which they tooke (as it seemeth) not meerely from the motion of the Sunne, but from their conueniency, and commo∣dity, finding this number most commodious for the distinction of euery Circle. The reason was, because no number could bee found, which suffered more parts and diuisions then this. For as much as in 60, whereof 360 by multiplication is produced, hath exactly these parts 1.2.3.4.5.6.10.12.15.20.30. Likewise 360 hath exactly 1.2.3.4.5.6.8.9.10.12.15.18.20.24.30.36.40.46.60.72.90.120.180. Of all which parts there is so great vse in Astronomy and many times in Geography, that without it there would be small exactnesse. For as we see a yard measure would little steed the Mercer or Clothier, except it were againe diuided into smaller parts: so fals it out in the ac∣count of the Cosmographer.

3▪ Of the Terrestriall Circles, some are Absolute, some Relatiue: the Absolute are such as are assigned without any respect to our sight; of which sort are the Meridians and Parallells.

4. The Meridian is a circle drawne by the Poles of the world and the verticall point of the place.

The Meridian Circle is so called of Astronomers; because when the Sun (according to their suppositions) by the motion of the

first moueable comes into this Circle, it makes mid-day: and then hath been running his course from his rising to arriue there iust so long as he shall be mouing from thence to the place of his set∣ting. In this Meridian are placed the two Poles of the Equator, which are the same with the Poles of the world; in this also are the verticall point and the point opposite vnto it, tearmed the Poles of the Horizon, whereof we shall speake hereafter. So that so many Meridians are imagined to be in the Earth, as there are vertical points: for howsoeuer we see not many Meridians pain∣ted on the face of the artificiall Globe, yet must there be so many imagined in the reall Earth as Zenithes and Horizons: so that it is impossible for a man to moue neuer so little from East to West, without changing his Meridian: yet for more order sake haue the Cosmographers reduced the number of Meridians to halfe the number of the degrees in a Circle, to wit, to 180, that eue∣ry Meridian cutting the Equator, and other Parallels in two op∣posite places, should answer to two degrees in the same Circle. By which it appeares, that euery Meridian diuides the Terrene Globe in two halfes, whereof the one is respectiuely tearmed of the East, the other of the West. But to auoid all ambiguity of speech, we ought to consider that a Meridian is twofold; either the true Meridian, or Magneticall Meridian. The true Meridian, ordinarily so called, is that which directly passeth by the Poles of the World; of which wee here treat, which indeed (as wee shall shew) is the onely true magneticall Meridian. But that which some haue falsly called the Magneticall Meridian, is that which runneth by the Poles of the Magneticall Variation, and much differs from the true; because (as we haue taught) the va∣riation is diuerse according to the diuersity of place, & there∣fore cannot answer in any certaine proportion to the Poles of the Terrene Globe. The true Meridian Circle, as it hath mani∣fold vse in Astronomy, namely to distinguish mid-day, and mid∣night, to measure the rising and setting of the Starres, &c. mat∣ters not to bee neglected of Geographers; so hath it a more spe∣ciall vse in Geography: to designe the longitudes and latitudes of the places, with their distances, with many other matters trea∣ted of hereafter.

5▪ Concerning the Meridian circle wee are to know two things. The Inuention of it, and the Distinction: The inuention is whereby wee are taught to find out the true Meridian in any place assigned.

6▪ The Inuention of the Meridian is againe two∣fold: the one more Accurate, which is either Astronomicall or Magneticall, the other Po∣pular; the Astronomicall way is performed by obseruing the celestiall motion.

The Meridian may bee found out the Astronomicall way in di∣uerse manners by Instruments deuised for this purpose by in∣genious Artificers, whereof some are described by Gemma Fri∣sius in his Cosmographie. But to auoid the cost of curious Instru∣ments, I will set downe our way, depending on this Theoreme.

1 If two seuerall Sunne-shadowes bee obserued, the one in the fore-noone, the other in the after∣noone of the same day exactly to touch with their ends, the Circumference of the same circle descri∣bed in a Plaine, Parallell to the plaine of the Horizon: The line from the Center equally diui∣ding the Arch of that Circle betwixt the two shad∣dowes, will bee the true Meridian circle for that place.

This Theoreme, howsoeuer consisting of many parts, is not∣withstanding easie enough to bee vnderstood, being explayned by an ocular demonstration. Let there bee gotten a platforme of wood or metall, and placed euenly that it may lye parallell

[illustration]

[illustration]

with the plaine of the Horizon: In this plaine let there bee des∣cribed diuerse circles from the same Center E. In this Center let there bee raysed a Gnomon EF to right angles, so that the top of this Gnomon F, shall euery where bee equally distant from the circumference of each circle described in the plaine, which may easily bee knowne, because if it bee equally distant from any three points of any circles Circumference, it will also bee equally distant from all the rest alike, as Clauius hath taught in the 4 of his Gnomonicks. This platforme being thus ordered let the shaddow of the Gnomon bee obserued sometimes be∣fore Noone, vntill such time as it exactly shall touch the circum∣ference of one of those circles, as in EG. Againe in the After∣noone, let the shaddow bee obserued, till with his end it meet the circumference of the same circle, as in EH, which will hap∣pen so many houres afternoone, as the other before Noone. These two points G and H, being diligently obserued, let the Arch of the Circle GH bee diuided into two halfes with a

line drawne from the Center E, which shall bee ED. This line ED will bee the true Meridian for that place, on which when the shadow of the gnomon shall happen to fall, wee may assure our selues that it is full Noone.

7 The Magneticall Inuention is performed by the Magneticall Directory Needle.

This way is subiect to much errour, and not so certaine as the former, because (as wee haue shewed before) there are found very few places which admit not some of Variation: yet because it may bee profitable to such, who haue not the Com∣mand alwayes of the Sunne, or sight of the Starres, I will in∣sert this Theoreme.

1 The Line wherein the Directory needle is di∣rected from North to South, is the Meridian for the place.

This may bee shewed in any Marriners Compasse, or 〈◊〉〈◊〉 Sunne-Dyall, whose needle is magnetically touched. For b••••ing set euenly parallell to the playne of the Horizon, it will shew by the needle, the Miridian for that place in euery verticall point on the earth. For example in the Sea-Compasse in the next page, experience will witnesse in euery Region of the Earth, that the one point signed out by the Lilly, will alwayes turne to the North; the other opposite part, will turne it selfe to the South; which two parts being ioyned together by a right Line will shew the Meridian fo•• ••••at place: The Meridian (I say) not alwayes the true; for this Inuention taken from the Magnet is not so exact as the Astronomicall: for as much as few or no places are found, wherein the Magneticall Needle admits not a Variation from the true points of North and South: Neuerthelesse, this way is very necessary to bee knowne: for as much as the Sunne and Starres are not alwayes to bee seene; at least in such place and manner as may fauour exact∣nesse of obseruation: Hence may bee demonstrated in particu∣lars, what wee obserued before in generall in our Magneticall

[illustration]

[illustration]

Treatise that the Circles of the Globe are not meere Imaginary Fictions, or bare Respects, growing out of the Application of Celestiall bodies (as some haue thought them) but grounded on the Magneticall Disposition of the Terrestriall Globe.

8 Beside the Astronomicall and Magneticall In∣uention of the Meridian, there is another way more popular, but lesse exact, which is without any obseruation of the Heauens, or the Magnets operation.

Of the Inuention of the Meridian circle, the true and exact

knowledge (as wee haue shewed) is endebted to heauenly ob∣seruation, or Magneticall experiment. Neuerthelesse Nature is not so barren, but she hath pointed out to an industrious obser∣uation, some markes and foote-steps in other inferiour bodies, for the finding out of this profitable circle. Which wayes, how∣soeuer of lesse Account then the other, and therefore of lesse vse, are notwithstanding pleasant to vnderstand: because nothing delights more an ingenious minde, then the contemplation of Gods working, in and by his creatures, which men vsually terme Nature. To make a particular search into all Planets, Stones, Met∣tals, and other such Bodies, were to goe too far out of my way, without a Guide. I will giue one only Instance of Trees, where∣of I will insert this Probleme.

1 By the Incision of a Tree, to find out the Meridian.

To performe this Probleme, let there bee chosen out some Tree in an open free field, farre from walles or other obstacles; in such

[illustration]

a place as it hath beene on either side freely en∣lightned and hea∣ted by the Sunne∣beames: let the Trunke of this Tree bee very right and sound: let this Trunke bee cut off by the middest, in such sort that the secti∣on be Parallell to the Horizon, and the vnder-part of the Trunke bee left to stand in his former Naturall situation: Now the Section on the top of it being well plained,

will as in a plaine discouer diuers circles, which are Excentricke and not drawne from the same Center, but on the one side nee∣rer together; on the other further off: That part then which shewes the circles thicker and neerer together, points out the North: The other wherein the circles are wider and further off, the one from the other, designes out the South-point: betwixt both which if a right line bee drawne, it will bee the Meridian for that place. Which experiment Blan••anus (as hee writes) tryed in a Plume-Tree, but giues no reason for it. The cause I take to be no other then the extension and diffusion of the sappe or moisture, by the heate of the Sunne: which is more on the South-side then the North-side: for as much as the Sunne in our clime respects vs on the South, neuer on the North. Hence is it, that the circles which are nothing else but the excrescences of the moisture, being more rarified on the South-side, and there∣fore requiring a greater place, are found to bee greater.

9 Hauing shewed the Inuention, wee are in the next place to treat of the Distinction of these Meridian circles: A Meridian therefore is termed either First or Common.

The distinction of Meridians into First and Common, hath no foot-steps in Nature, but is a meere arbitrary Imposition of antient Cosmographers. For no reason besides Conueniency can be shewne, why one Meridian should be called First rather then another: yet cannot this Distinction bee wanting to a Geogra∣pher, for as much as some setled bound must be set, from which to begin our accompt of Longitudes.

10 The first Meridian is that from which wee begin to number the Longitude of the Earth, from West to the East. In respect of which all the rest may bee called common or lesse notable.

The ancient Cosmographers, amongst whom Ptolomy was the chiefe, haue set the first Meridian in the Fortunate Ilands, from whence they began their accompt, passing Eastward through Europe and Africa, and so through Asia, to the vtter∣most parts of India, vntill they returned againe to the first Me∣ridian, passing through the Fortunate Ilands; Some haue doub∣ted whether these Ilands called by Ptolomy the Fortunate I∣lands, be the same with the Canaries; because (as our Countrey∣man M^r Hues hath obserued) the Latitude giuen by Ptolomy to the Fortunate Ilands, agrees not exactly to the Canaries; but rather to the Ilands of Cape-Verde. Notwithstanding this obser∣uation, I rather sticke to the common opinion, thinking it no vnlike matter, that Ptolomy dwelling far Eastward, and trusting to other mens obseruations, should erre in this, as well as other matters. The reason why the first Meridian should bee placed here, rather then elsewhere, is thought by some to bee; because the Ancients supposed two Magneticall Poles in the Earth, which should bee the cause of the Variation of the Compasse. Now because in the Canary Ilands, was found no Variation at all, they thought it to bee the place where the Magneticall and the true Meridian should concurre, as wherein were both the Poles, of the World, and of the Load-stone: which made them to make it the first Meridian: But this reason I take to bee vnlikely; because as I finde it obserued by latter Writers, in the Canary Ilands themselues there is found a Variation of the Compasse, although very little: the reason whereof wee haue shewed to bee because it is the middest betwixt two great Con∣tinents, to wit, the one of Europe and Africa, the other of A∣merica. Whose magneticall temper being almost equall, will not suffer the magneticall Needle to moue more one way then another: Moreouer, I am certainely perswaded (as far as I can gather) that this placing of the First Meridian was appointed here before any certainty was knowne of the Variation of the Compasse. The more probable coniecture therefore is that Ptolomy here placed the First Meridian, because it was the vttermost verge of land toward the West, then discouered, neuer dreaming of a Westerne world afterward

detected and brought to light by Christopher Calumbus and Americus Vesputius. Some of the latter Geographers striuing to bee more exact, haue placed the First Meridian in their Mappes out of the Canaries in the Ilands of the Azores called S. Michaels Iland. So that the first Meridian of Ptolomy dif∣fers from the place of these latter Cosmographers about 9 degrees: which is diligently to bee noted of such as beginne the Science; because this variety not perceiued, will breed great errour and confusion: yet is not the first of Ptolomy out of vse, but retained of many good Geographers. Euery other Meridian in respect of this, may be called Common, or lesse no∣table, because this is most remarkable: yet may the rest com∣pared amongst themselues be ranged in a certaine order, as the Second, Third, Fourth, Fifth, and so along till we come againe to the First, being in all reduced to the number of 180, answe∣ring to 360 Degrees as wee haue taught. So much for the Me∣ridians.

11 The Parallels are equidistant Circles pas∣sing from the East to the West directly.

I haue defined the Parallell Circles in a larger sense then for∣mer Geographers vsually haue taken it in: as willing vnder this generall name, not onely to include the Parallels common∣ly so called, but also the Equatour: because I see no reason why the Equatour being euery where equidistant from each o∣ther Circle, should not suffer this acception. The common sort of Cosmographers, vnder this name, would onely com∣prize the minor Circles, which are conceiued to bee equally distant and correspondent to the Equinoctiall Circle, so that all should bee so called in respect of the Equatour, to whom they are said to answer, not in site and position; for as much as they decline from the middle of the Earth to the North and South: but in Comparison and Proportion; for as the Equa∣tour is drawne from East to West, and diuides the whole Spheare of the Earth into the North and South Hemispheares: So the other also diuide the Globe of the Earth, though not into two equall parts as the Equatour, but vnequall. These

Parallels many wayes are distingushed from the Meridians: first, because the Meridians are drawne directly from North to South: but the Parallels from East to West. Secondly, the Meri∣dians, how many soeuer they are imagined to bee, concurre and meete all in the Poles of the Earth: whereas the Parallels how∣soeuer drawne out at length, will neuer concurre or meete in a∣ny point. Whence it must needes follow that all Parallels and Meridians in the Globe must cut one the other, and make right angles. These Parallels although infinite in number, may bee in the Spheare reduced to the number of the Meridians, because they are drawne through the opposite points and degrees of the Meridian Semi-circle, which would make vp the number of 180: but yet for Conueniency they haue not painted so many in the face of the Artificiall Spheare; for as much as so many lines and circles might beget Confusion. Wherefore Ptolomy and the Ancients haue distinguished the Parallels on both sides the Equa∣tor, North and South, with such a Distance, that where the day should increase one quarter of an houre, a new Parallel should be placed. So that the longest day of one Parallell should surpasse the longest day of another, for one quarter of an houre. By which appeares that the Parallels are not of one greatnesse, but by how much neerer the Pole they are placed; so much lesse are they; and so much greater by how much farther off from the Poles, and neerest the Equatour. These Circles are of great vse in Geographie, as to distinguish the Zone: Climats, and Latitudes of Regions, to shew the Eleuation of the Pole, and to designe out the length and shortnesse of the day in any part of the Earth.

12 A Parallell Circle is of two sorts; either greater or lesser: The greater is the Equatour or equinoctiall Circle.

13 The Equatour is the greatest of the Pa∣rallels, passing through the middest of the

Earth, and exactly diuiding them from the Poles into two equall halfes or Hemispheares whereof the one is North, the other South.

This Circle is called the Equatour or Equinoctiall of Astrono∣mers; because, that when the Sunne passeth vnder it, as vpon the 11 of March, and the 13 of September, it makes the Day and Night equall. This Circle of Astronomers is esteemed the most notable, being the measure of the Diurnall and most regu∣lar Motions▪ The La••ines haue taken the name and appellation of this Circle from the Day, as the Greeks from the Night: Wherein the Sense is no way varyed; because the equality of the Day argues the like equality of the Night. The two Poles of the Circle, are the same with the Poles of the Vniuersall Earth: to wit, the Articke or North-Pole, and the Antarticke and Sou∣therne Pole: whereof the former is alwayes conspicuous in our Horizon, the other lies couched and hidde from our Sight. It is called the Articke-pole from the Constellation of the little Beare in the Heauens, neere to the which it is situated: in opposition to the which the other is called Antarticke. It hath manifold vse in Astronomy, copiously by Astronomers: And no lesse in Geo∣graphy: for without this Equinoctiall Circle, no Description of the Earth can be absolute & perfect, neither any Citie or Place. in the Terrestriall Globe or Mappe set in his due and proper place. This Equinoctiall Circle in regard of the Earth, passeth through the middle-most part almost of Africa, by Ethiopia, A∣merica, and Taprobana: So that it exactly diuideth the Globe of the Earth into two halfes, the Northerne and Southerne Hemis∣pheares; so that these people which dwell vnder the Equatour are said to inhabite the middle of the world, because they in∣cline neither to the North, nor to the South: hauing so much distance from the Articke Antarticke-Pole of the Earth. More∣ouer, by this Circle (as wee will declare hereafter) are noted out vnto vs the East and West part of the Spheare, no way to be neglected of Geographers.

1 Concerning the Equatour, two things are to be obserued: either the Inuention, or the Site and Position: The Inuention is either Astronomicall or Magneticall. The Astrono∣micall according to these Rules.

1 The Meridian being found out, to find the E∣quator.

[illustration]

This is easily performed by the helpe of the former Figure: for therein the Meridian line being found out (as we haue shewed) let there bee drawne by the Center E of that Circle, the line AC, making right Angles with the said Meridian: which line AC will bee the true Equatour, and will point out vnto vs the true East and West: as A the East and C the West. Whence it appeares that the two lines, to wit, of the Equa∣tour

and the Meridian doe diuide and cut the whole Horizon in∣to two equall Quadrants.

2 Without the helpe of the Meridian to find out the Equatour.

In the time of either Equinoctiall in some Horizontall plaine, in the Sunne-shine, let there bee erected a Gnomon: then in the day time, let there bee noted all the points by which the end or top of the shadow hath passed: for all those points in the time of Equinoctiall, are in a right line; be∣cause then the end of the shadow is carried in a line in the time of the Equinox in a Herizontall plaine: This line will bee the true Equinoctiall-line: the cause is giuen by Clauius in Gnomoni∣cis. lib. 1. prop. 1. Corollar. 2. which depending on many Geo∣metricall and Astronomicall principles, as too far from my pur∣pose, I omit.

15 The Magneticall inuention of the E∣quatour, is wrought by the Magneticall Inclinatory Needle, according to this Pro∣position.

1 Wheresoeuer at any place of the Terrestriall Spheare, the Inclinatory Needle shall conforme it selfe in a Parallell-wise, to the Axell of the Earth, through that place passeth the Equinocti∣all Line.

As to finde out the Meridian of any place, wee are to vse the helpe of the Directory Needle: so to the finding out of the Equatour, and Parallels, the Inclinatory Needle is most neces∣sary: because the former respects the Magneticall Motion of Direction, the latter of Declination: Now wheresoeuer wee shall see the Needle to conforme it selfe in such sort as it may lie Parallell with the Axell of the Earth, we may assure our selues

that such a place is vnder the Equinoctiall Circle: The reason whereof, wee

[illustration]

haue giuen in our 3 Chapter out of the Cō∣uertible nature of the Magnet, and here needs no repetition: only wee will insert this one figure where∣in the line CD drawne through the Centers of two Inclina∣tory Needles, lying Parallell to the Axell of the Earth, A. B. will expresse this Equinoctiall line which wee here seeke. For the Magneticall Inclinatory Needle being set in a Frame or Ring made for such a purpose, will vnder the Equator respect one Pole no more then another: but lie leuell with the Plaine of the Horizon: as vnder the Poles it will make right Angles with the Plaine of the Horizon. In the middle spaces betwitxt the Equatour and the Poles, it will conforme it selfe in such sort, as it makes certaine Angles with the Axell of the Earth, though not equall, yet proportionall to the Latitude; out of which an ingenious Artificer may deduce the Parallels of any place, without any obseruations of the Hea∣uens: as is taught by Instruments inuented by Gilbert, Ridley, and diuers others which haue vndertaken this subiect.

16 Of the Inuention of the Equatour wee haue spoken: In the site we ought to con∣sider

the placing of the Equator in respect of the world.

1 The Equatour is an vnmoueable Circle, whose Poles neuer vary from the ••ixt Poles of the world.

Whether the Poles of the Equator haue been any times varied from the Poles of the world, is a controuersie which hath exer∣cised the greatest wits: Ioseph Scaliger trusting (as it seemes) more to ancient History then Moderne experiment, seemes in two Epistles not only to make a doubt, whether the Poles of the Equatour haue continued the same with the Poles of the world; but super••iliously (as the manner of most criticks is) rather out of coniecture then Reason, to taxe the common opi∣nion of manifest errour and absurdity. The ground and origi∣nall of this doubt growes out of the obseruation of the fixt Stars, which haue since the Times of the Ancients, beene found to bee moued out of their places, or at least not to retaine the same points in the Period of the Sunnes Motion. The chiefest Instances are taken from the stars in the Hornes of Aries, which in Hyparchus time, which liued aboue 60 yeeres before Ptolomy, were obserued to bee not much distant from the Equi∣noxe, and before him in the very point it selfe; but in our time remoued about 28 Degrees off: Also it is obserued in the Cynosure or Pole-star, that in Hyparchus time it was di∣stant from the Pole about 12 Degrees, which wee finde in our time to bee scarce 3 Degrees distant. To salue this Apparence, Ptolomy inuented a slow motion of the Starry Heauen or Fir∣mament, whereby the Fixt stars might bee remoued farther off from the Equinoctiall points in the Eclipticke, whence of a consequence the Pole-starre should not keep the same positi∣on in respect of the Pole it selfe, but vary his site according to the Motion: which opinion hath a long time passed without contradiction; till Copernicus out of new grounds sought for this Motion in the Earth, to which hee assigned no lesse then three Motions. Since Copernicus, arose Ioseph Scaliger, who

contradicting the common receiued grounds, and yet for ought I see, not trusting to the suppositions of Copernicus, would bring in another opinion: to wit, that the Stars of the Firm••ment are not moued from the point of the Equinoxe, but rather that the point is carryed away from the stars. The decision of this point I dare not vndertake, better becomming the learned and indu∣strious endeauours of our worthy Professours, M. Doctour Bain∣brigge, and M. Henry Brigges, as best suiting with their Learning and Profession: Ipse semipaganus, ad sacra vatum carmen offero nostrum. Neuerthelesse as a Learner, for mine owne satisfaction, I would willingly enter a little into conference with this great and admired Oracle Ioseph Scaliger, to sound the certainty of his grounds. That the Pole-starre (saith hee) was so far distant from the Pole as 12 Degrees, was no true obseruation, but the errour of Hyparchus, who afterwards by his authority deceiued Ptolo∣my; and He, Posterity. The Reasons hee alleadged are, 1 Be∣cause Eudoxus which was more ancient then Hyparchus, ob∣serued the same star to bee in no other place, then where now it is. 2 Because that greater light of Astronomy, Copernicus percei∣uing the Equinoxes and Solstitiall points to be moued, was enfor∣ced to inuent other grounds; but because his demonstrations de∣pended only on the Apparences, hee sought out this effect in the motion of the Earth. If it were manners to oppose so great a Scholler as Ioseph Scaliger, I would aske a few questions, why we should not credite the obseruations of Hyparchus, Ptolomy, and all posterity, as well as of Eudoxus: sith Antiquity without consent & approbation, is no great argument of truth. Neuerthe∣lesse if the matter be well examined, we shall perhaps find Anti∣quity to be more firme on our side. The same reason (as I take it) may be giuen for the stars in the Hornes of Aries, as of the Pole-starre, because all the fixt-starres, by the consent of all, are imagi∣ned to keep the same vniforme site among themselues in such sort, as the varying of some would disorder all the rest: at least ar∣gue the like variety or change of all. Now to proue the stars of Aries to haue beene varyed, many of the Ancients (as Master Hues hath obserued) liuing in diuers times, haue confirmed. The first star of Aries, which in the time of Meto Atticus,

was obserued in the Vernall Intersection, in the time of Thales Milesius was before it 2 Degrees; in Tymocharis age it was af∣ter it 2 Degrees 24 Minutes: In Hipparchus time 4 Degrees, 40 Minutes; in Abbumazars 17 Degrees, 50 Minutes; in Alba∣rens 18 Degrees, 10 Minutes; in Arzachels 19 Deg. 37 Min. in Alphonsus his time 23 Deg. 48 Min In the time of Coperni∣cus, and Rheticus, 27 Degrees, 21. Min. In our time about 28. Against all these Testimonies, if we should oppose the Testimo∣ny of Eudoxus and Sca••iger, wee should bee thought very parti∣all to preferre them before the consent of Antiquity: Eudoxus though very Antient, being but one, and the other one of the last. If any should obiect, that Eudoxus spake onely of the Pole-starre, and not of the stars, in the hornes of Aries; I ans∣were, as before, that the same reason is to bee giuen of them both; For as much, as if the Pole-starre in Eudozus time mo∣ued in a Parallell, Equidistant from the Pole of the Equatour (which he seemes to contend) then must also the stars of Aries, which were found once to bee in the point of the vernall Equi∣noxe, moue alwayes in the Equinoctiall circle, and neuer vary from it; which is contrary to all the Testimonies before allead∣ged. Secondly, where he saith, that Copernicus perceiuing this error, left a base discouery, without any Demonstration, ex∣cept onely 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, I would know how Ioseph Scali∣ger by any other meanes came to know it? I alwayes supposed it a principle amongst Mathematicians, that the 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 had beene the surest ground of Mathematicall Demonstra∣tion: for euery reason which can be alleadged, must of necessi∣ty bee grounded on meere coniecture, as forged in a mans braine without any obseruation of Nature; or else suggested vnto vs from the things themselues. How little dependency is on the Former, let euery man iudge: where it is as easie for euery man to deny, as affirme; and such fancies are better reserued in the braine, wherein they were first hatched, then bee suffered to proceed further. If wee deriue our Argument (as we ought to doe) from the footsteppes of Nature; wee must draw it either from the Forme it selfe, or from some effect or propriety arising from it: The former is vnpossible I may well say in any

thing; because the first forme and nature, no wayes discouers it selfe to our vnderstanding, but by the apparent Accidents: much lesse can this bee hoped for in the Heauens, being as far distant from vs in space, as Nature. If then we are left only to the later, what other ground can we haue of our Argumentation, then the 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 or Apparences: which kind of way, Scaliger in Copernicus striues to sleight or reiect as weake or deficient: taking then this to bee the onely way to search as neere as wee can into the truth of their matters, wee will in the third place shew how far it may oppose Scaliger, and fauour our Asser∣tion. That the first Star of Aries is more distant from the Equi∣noctiall point, is a matter which seemes to bee agreed on by all sides. This Apparence must necessarily arise out of some Mo∣tion. This Motion must bee sought either in the Earth (as Co∣pernicus would haue:) or in the Heauens. That it cannot with any great probability bee in the Earth, wee haue shewed in the third Chapter, where wee haue proued it to haue a Magneticall verticity, whereby it continually respects the same Poles. The Arguments (I confesse) are only probable: but this is an opinion which Scaliger defendeth not. If wee seeke this effect in the Heauens, it must of necessity (which Scaliger confesseth) happen one of these 2 wayes: For either the stars standing vnmoueable, the Equinoctiall & Solstitiall points must bee moued, or els the stars themselues should moue, as Ptolomy defends. Here I cannot but remember a merry answer of that great Atlas of Arts, Sir Henry Sauile in the like question. Being once inuited vnto his Table, and hauing entred into some familiar discourses concer∣ning Astronomicall suppositions: I asked him what he thought of the Hypothesis of Copernicus, who held the Sunne to stand fixt, and the Earth to bee subiect to a Triple Motion: His answer was; hee cared not which were true, so the Apparences were solued, and the accompt exact: sith each way either the old of Ptolomy, or the new of Copernicus, would indifferently serue an Astronomer: Is it not all one (saith he) sitting at Dinner, whe∣ther my Table be brought to mee, or I goe to my Table, so I eat my meat? Such an answer would aswell befit this question: whether the first star of Aries should bee moued from the E∣quinoctiall

point, or the point from it, 'tis a matter should little trouble a Cosmographer; so either way might indifferently serue to salue the apparent obseruations: But how Scaliger vpon this granted supposition, would make all whole, without disturbing the order and forme of Nature in the celestiall Machine? what Regular motion he would giue the Sunne, whose period des∣cribes the Equinoctiall points, which he makes moueable? what other Poles he would assigne to the world besides that of the E∣quator? is a matter of a more curious search, and besides the li∣mits of my subiect: The full discussion of which points, as most of the rest: Illis relinquo quorum imagines lambunt—Hederae se∣quaces.

17 The lesser Parallels are equidistant lines ans∣wering to the Equator, which diuide the Globe of the Earth into two vnequall parts.

18 These lesser Parallels are againe of two sorts: either Named or Namelesse; Named are such as are called by speciall names, and haue more speciall vse in Geographie; such as are the two Tropicks, and the two Polar circles.

19 The Tropicks are Parallels bounding the Suns greatest declination, which is either to the North, and is called the Tropicke of Cancer: or towards the South, and is called the Tropicke of Capricorne.

The Tropickes haue taken their names from the conuersion or turning backe of the Sunne; because the Sunne declining from the Equinoctiall circle either North or South, proceedeth in his course no further then this circle, and so turneth backe: so

that in the heauens they are as limits and bounds, comprehen∣ding within them that space, without the which the Sunne ne∣uer moues: Consonant to these Celestiall Tropicks, are there imagined in the earth the like, immediately placed vnder them: which are apparent, not onely by Application of the Celestiall Globe, and his parts to the Terrestriall; but also out of the Magneticall disposition of the earth, as wee haue already shew∣ed: The Tropicke bounding the Suns greatest declination to∣wards the North, is called the Tropicke of Cancer; because the Sunne arriuing at that Tropicke, is lodged in the signe of Cancer: The other is termed the Tropicke of Capricorne; because the Sunne touching that Tropicke, is in that signe: The distance of these Tropickes, from the Equatour, is ordinarily put 23 De∣grees, and 30 Minutes; which is also the distance of the Poles of the Eclipticke, from the Poles of the world. The Tropick of Can∣cer, as it is conceiued in the Earth; passeth by the greater Asia, by the Red-Sea, or Sinus Arabicus, and China, and India: But the Tropicke of Capricorne, situate on the Southerne side, run∣neth along by the most Southerne coast of Africke, and that part of America which is called Brasilia; Besides many Ilands in the Indian Sea.

2 The Polar circles are Parallels answering to the Polar circles of the Heauens, drawne by the Poles of the Eclipticke: These are of two sorts: either the Articke compassing round the North-Pole; or the Antarticke compassing round the Antarticke or South Pole.

The Polar Circles, as they are conceiued in the heauens by A∣stronomers, are described by the Poles of the Eclipticke, car∣ried by the diurnall motion about the Poles of the world. Correspondent to these circles in the heauens are imagined two circles on the earth, which wee also call Polar; and if wee

beleeue Gilbert, with other Magneticall Philosophers, they are primarily in the Earth, as that which is the true subiect of diur∣nall motion. These circles thus described by the Pole of the E∣clipticke, must needs challenge the same distance from the Pole, which the Pole of the Eclipticke hath, to wit, 23. De∣grees, and 30 Minutes. The Greeks haue taken the Polar circles, in another sense then the Latines: for by these Polar circles (as it appeares by Proclus, and Cleomedes) they vnderstand not such circles as are described by the Pole of the Zodiacke: but two o∣ther circles; whereof the one is greatest of all the Parallels, which alwayes appeares aboue our Horizon; the other is the greatest of all those Parallels which lie hid in our Horizon per∣petually: The reason why the Graecians tooke it in this sense, was; because by these circles they could know and distinguish those stars; which alwayes are seene and neuer set, as those which are comprehended of the Articke circle; from those which alwayes lie hidde and neuer rise; as such as the Antar∣ticke containes: Whence it manifestly appeares, that the two Polar circles, as they are taken of the Graecians in all Regions, are not of the same quantity & greatnesse, but are greater in oblique Spheare then in a right: but our Polar circles are at all places a∣like in their quantity. Of these, the one tearmed Articke in the Earth passeth by Islandia, the top of Norway and Finland, with many adioyning Ilands, and the Southerne part of Green-land, as may appeare by our ordinary Geographicall Mappes. The o∣ther Polar circle called Antarticke, passeth through the South part of the world (as yet) vndiscouered, except for some few parcels, as Terra del Feugo, and Psiitacorum Regio, with some∣what more, lately discouered by the Spaniards. The chiefest vse as well of these, as other parallels, is to distinguish the Zones and Climates in the Globe, whereof wee shall haue occasion to treate hereafter.

21 The Namelesse Parallels are such as are not knowne by speciall Names, nor of so great vse in Geographie.

These namelesse parallels may bee well vnderstood by that which we haue aboue spoken: for howsoeuer they bee not cal∣led by particular and speciall names, yet are they all of the same nature: All these parallels beside the Equatour, though infinite in number, may notwithstāding in the spheare be reduced to the number of the Meridians; because they are drawne through the opposite points of the Meridian semicircle; so that wee might account 180: but yet there are not so many painted on the face of the Artificiall Globe; wherefore Ptolomy with the ancients, haue distinguished the parallels on both sides, North and South, beginning from the Equatour at such a distance, that where the day should increase one quarter of an houre, a new parallell should be placed: so that the longest day of one parallell, should exceed the longest day of another parallell by one quarter of an houre. Euery one of these parallels, is supposed to be diuided into 360 Degrees, as all the rest of the other circles; yet are we to note that the degrees and parts of a greater circle are greater; of the lesser, lesse, according to the proportion of the said circle; the same haue the proportion that a great circle hath to a lesse, so that the same degrees and parts of a quarter circle, to the de∣grees and parts of the lesser; as may be gathered from the first proposition of the second booke of Theodosius: now to know rightly this proportion, we must first finde out the summary de∣clination for euery region, which being once found, we may proceed in this manner, by the doctrine of Triangles.

1 Let the signe of the Complement of the Declina∣tion of the lesser Circle bee multiplied by the whole Circle, and the product bee diuided by the totall signe, there will arise the number of Degrees of the lesser Circle, such as whereof the greater consists.

The reason hereof is shewed in Geometry, and therefore need we not to insert a demonstration; for there we learne, that

as the totall ••inge is to the signe of the Cōplement of the Decli∣nation of any Parallell, so is the Periphery of the greater circle, to the Periphery of the Parallell▪ As for example, if we would know what proportion the Equatour hath to the Parallell, which passeth by the Verticall point of Rome; whose Declination is about 42 Degrees; I multiply the signe of the Complement of this Declination, that is, the signe of 48 Degrees, to wit, 74314, by 360; the product whereof is, 26753040; which I diuide agayne by 100000, and find 267 degrees, and ½▪ whence I ga∣ther that the Equatour to the Parallell of Rome, or a degree of the Equatour, to a degree of the Parallell of Rome, hath the same proportion that that 360 hath to 276 ½, which is the same that 4 hath to 3.

22 Hitherto haue we spoken of the Absolute Circles, such as are the Meridians and Pa∣rallels: wee are to treate in the last place of a Relatiue Circle, which is conceiued in respect to our sight: this Circle is cal∣led the Horizon.

23 The Horizon is a Circle which diuides the vpper and visible parts of the Ter∣restriall Globe, from the lower and in∣uisible.

The name of the Horizon is taken from the bounding or ter∣mination of the sight; because it is a Circle comprehending all that space which is visible of vs, distinguishing it from the rest which lurkes inuisible: as if a man should bee placed in a high and eminent place of the Earth, and should looke round about him euery way to the East, West, North, and South; Hee will seeme to see the heauens on euery side to concurre with the earth: so that beyond it, can be seene nor heauen nor earth: which concurrence of the heauens with the earth, will describe vnto vs the Horizontall Circle for that place assigned. But

here wee are to note, that the Horizon is two fold; either the Rationall or Sensible Horizon. The Rationall precisely diuides the Globe into two equall parts: But the sensible or apparent Horizon, is no other then that Circle in the earth, which is designed out by the sight, from which the name seemes to bee deriued. This sensible Horizon differs from the rationall diuers wayes; first, because the rationall diuides the whole spheare in∣to two equall parts; but the sensible into two vnequall parts. Secondly, because the rationall is alwayes certaine and the same, in the same place, and of alike greatnesse; whereas the o∣ther is greater or lesser, for the condition of the place or sight; for the semidiameter of the rationall, is the same with the se∣midiameter of the earth; but the semidiameter of the other, seldome or neuer exceeds 60 miles on the Earth. Thirdly, because the rationall Horizon passeth by the Center of the Earth; whereas the sensible toucheth onely the surface of it, in that point where the Inhabitant standeth: all which differen∣ces may bee seene

[illustration]

in this Figure; wherein the Line CD represents vnto vs the sensi∣ble Horizon: the Line AB the ra∣tionall: The for∣mer is called Na∣turall or Physicall; because it comes vnder the measure and apprehension of the sense: the other Astronomi∣call, because it is of great vse in Astronomy: in the resolution of the Hori∣zon into his parts, wee ought to consider two things: first, the Poles of the Horizon; Secondly, his Periphery, or circumfe∣rence: The Poles are commonly called Zenith or Nadir: The

Zenith is the Verticall point, directly placed ouer our Head: whereunto is opposite on the other side, the Nadir directly vnder our foote, and therefore may bee called the Pedall point. The parts or intersections in the circumferences, are designed out vnto vs, by certaine lines, discouering the coasts in the Ter∣restriall Globe: These lines are called either windes or Rhumbes: The windes with the Grecians were onely 8. But the latter Nauigators haue increased them to the number of 32, whereof foure were called Cardinall; to wit, such as are directed to the foure coastes of East, West, North, and South: The other are Collaterall, being placed on each side of the Car∣dinall windes. The Rhumbes are Lines passing by the Verti∣call

[illustration]

point of any place, as you may see in the Compasse going before: Now because one Rhumbe answers to two coasts or windes; the number of the Rhumbes is but halfe the num∣ber of the windes; to wit, 16. Here it is to bee noted, that a Rhumbe differs from a Winde; whereas a Rhumber is one line, pointing out vnto vs, two windes or coasts: These Rhumbes as they are conceiued in the Globe, were thought by Nonnus to bee the portions of greater Circles: But learned M^r Hues in his booke, out of vndoubted principles, strongly confutes him. The grounds which hee takes are these: First, that all Meridians of all places passe the Pole, and cut the Equatour and all his paral∣lels at right Angles. Secondly, If our course should bee directly any way else, then towards one of the poles, a new Meridian must succeed, and a new Horizon. Thirdly, that the Iron Needle being touched with the Load-stone, shewes the common section of the Meridian and the Horizon, and on one side perpetually respects the North, on the other the South. Fourthly, the same Rhumbe cuts all the Meridians atall places at equall Angles, and euery where respects the like coasts in the world. Fiftly, that a greater circle drawne by the Verticall points (if remoued from the Equatour) cannot cut diuers Meridians at equall Angles. Sixtly, a greater circle drawne by the Verticall point of any place, makes greater Angles with all other Meridians then with that, from which it was first drawne: whence it is necessa∣ry, that the line which shall bee supposed to make Angles with diuers Meridians (as the Rhumbes) should bee bowed to∣ward the Meridian. I know not what would bee more said against the opinion of P. Nonnus, who would haue all the Rhumbes to bee portions of greater circles. To illustrate fur∣ther the nature and vse of the Horizon wee will insert these Theoremes.

2 The Sensible and Rationall Horizon in the Earth, are much different; in respect of the Fir∣mament, all one.

* 1.12It may bee gathered out of the suppositions of Ptolomy and Alphraganus, and almost all other Astronomers, that no man be∣ing placed on the surface of the earth can precisely see the halfe of it. For that Horizon which terminates our sight, as we haue shewed, is a plaine superficies euery way circularly extended in the Earth, in such sort as men placed, either in the Sea in a ship, or in a great field or Countrey, would thinke the visible part of the earth to bee plaine, whose ends would seeme to touch the Heauens. Whence must needs come to passe that such an Horizon cannot diuide the Spheare of the ••arth into two equall parts. For so much will be found wanting, as is measured betwixt that superficies which toucheth the earth, and that which passeth by the Center of it, equidistant from the other: for this later only can diuide the earth into 2 equall parts,* 1.13 according to Theodosius, and may well bee seene in the * 1.14 former figure, wherein are expressed both Horizons, as well the visible as inuisible, touching the Spheare in a point on the su∣perficies: as the Rationall passing by the Center. Neuerthe∣lesse wee must consider, that the quantity intercepted betwixt these two Horizons in the Terrestriall Spheare, is of little or no moment, compared with the whole frame of the Heauens: For sith the Heauens are so farre distant from vs, it will come to passe that if two equidistant lines should bee drawne, the one from the Eye, the other from the Center of the Earth to the Firmament, they would according to sense, appeare one and the selfe-same; by reason of the wonderfull distance: as wee see in a long Gallery, whose walls haue an equall distance the one from the other; the walls will notwithstanding (accor∣ding to Opticall principles) seeme widest where they are nee∣rest, and to close and shut vp at the ends, or at least to con∣curre neerer: much more must wee imagine this to happen in the sight, if we compare the greatnesse of the Firmament with the Spheare of the Earth, in whose magnitudes wee shall finde a incomparable disparity. This will appeare by the Appa∣rences: for wee shall see the six signes of the Zodiacke, conspi∣cuous aboue our Horizon, and the other six vnder it, hid from our sight: Also the Sunne and Moone, when they are diame∣trally

opposed, almost at the same moment will appeare, the one in the East, the other in the West: at least the one will rise soone vpon the setting of the other: And (if we beleeue Pliny) the Moone was obserued to bee eclipsed in the East point; the Sunne at the same time being in a sort aboue the Horizon in the West. Such an Eclipse could not happen without a diametrall opposition of the two lights, and therefore can the Sensible and the Rationall Horizon haue no sensible difference in respect of the Firmament.

2 The sensible Horizon may be greater or lesser ac∣cording to the nature and disposition of the place.

In this consideration wee take no notice of the difference of sights, whether they be weaker or sharper; but suppose an eye sufficient to kenne so farre in the Earth, as the place will per∣mit: The difference then betwixt diuerse Horizons must bee sought out in the condition of the place. A Sight placed on the top of a high mountaine, may see much farther then one in a low valley, compassed about with hills; for as much as the Se∣midiameter of the sensible Horizon, which is equall to the Rayes or Lines drawne from the extreame parts of the visible Earth, are much greater. The most indifferent iudgement of this Horizon, may bee taken from the superficies of the Sea be∣yond sight of land: for a man thereon sayling in a ship, may per∣ceaue the surface of the Sea as a plaine, on euery side to bound the sight in a round circle, seeming together to terminate the end of the Earth, and protension of the sight. What the Semi∣diameter of this Horizon should bee, hath not beene yet agreed vpon by all: Erastothenes would haue it to bee 44 miles. Ma∣crobius 23. Proclus 250. Albertus Magnus 125. These diffe∣rences seeme too great to admit of reconcilement: yet taking into our consideration the disparity in account of miles betwixt the Moderne and Ancient Cosmographers; as also betwixt the Greekes and Latines: 2 the diuerse placing of the sight •• the various disposition of the places wherein they tooke their obser∣uations, with other circumstances, wee should diminish much

of admiration. But diuerse others whose opinion is more appro∣ued by moderne Cosmographers, haue defined it to be about 63 miles. The cause why this Horizon should bee so little in respect of the Rationall which passeth by the Center, is the roundnesse of the earth interposed betwixt the sight and the farther parts, which we haue formerly proued.

3 The eye may be so placed on the Earth, as it may behold the whole Hemispheare of the heauens, and yet no part of the Terrestriall Spheare.

This may seeme a paradoxe with vulgar iudgement; but it wants not a demonstration drawne from Astronomicall and Opticke principles. To explaine which, we must suppose out of the grounds already granted, 1 That the Sensible and Rationall Horizon in respect of the Heauens, ought to bee esteemed one and the selfe same, by reason of the great distance and dispropor∣tion betwixt the Earth and the Firmament. 2 That the eye of the beholder is in this sort supposed to bee in the Center; be∣cause in this consideration the distance betwixt the superficies of the Earth, and her Center, is insensible. 3 That the visuall Ray wherein the sight is carried, is alwayes a right line. Now

[illustration]

suppose (accor∣ding to our for∣mer figure) the Center of the eye wherein consists the sight, to be in the point of the Terrestriall sur∣face F, the di∣stance (as wee said) betwixt F and E the Center being insensible, the eye is imagi∣ned in the center: likewise the Horizons CFD, and AEB for the same cause

in respect of the Heauens are to bee esteemed one and the same; because CA and DB haue no sensible difference. It is then manifest, that the eye so placed will behold in the heauenly Spheare, all which is included betwixt A and B, to wit, the Hemispheare AGB, bounded by the Rationall Horizon AEB. Neuerthelesse in the Terrene Globe it can see no∣thing at all: For either it should see onely the point F, where∣in it is seated, or else some other point or part distant from it: the former cannot bee admitted, because the eye being there supposed to bee placed, should according to this suppositi∣on behold it selfe, which is against philosophy: For granting the sense only a direct and not a reflexe operation, it cannot bee imagined how it should perceiue it selfe. Finally, it cannot see any point in the Earth besides; for then this point would ei∣ther bee placed aboue the point F: but this cannot bee; because F being supposed in the superficies, admits of no point higher in the Spheare, or else vnder it: but this cannot bee, be∣cause CFD being a tangent line, and touching the Spheare in F only: there cannot according to Geometricall principles bee drawne any right line from the point F, which can touch any point in the said Spheare, but all will cut it, and so the section cause impediment to the sight, the Earth being an opacous and round body.

4 From the Horizontall circle is reckoned the ele∣uation of the Pole in any place assigned.

The finding out of the eleuation of the Pole is a matter most necessary for a Cosmographer; as shall appeare after, where we shall speake of the Latitudes and Climates. It is de∣fined to bee an arch of the Meridian betwixt the Horizon and the Pole. For the finding out of which many wayes haue beene deuised by Artificers: The first is taken from the Sunne, the se∣cond from the Pole-starre: From the Sun it may bee performed two wayes. 1 At the time of the Equinoxe. 2 At any other time of the yeere. At the time of the Equinoxe it may be found out by the obseruation of the Sunnes shadow at Noone-tide, in this manner: Let the Meridian height of the Sunne bee sub∣tracted

from the whole quadrant, which is 90 degrees: there will remaine the distance of the Zenith to the Equator, which is equall to the eleuation of the Pole. In the second place at a∣ny time of the yeere to know the eleuation of the Pole out of the Meridian height of the Sunne, it is necessary out of an Ephi∣merides, or any other way, accurately to finde out the place of the Sunne in his Eclipticke for the day proposed, together with his declination: for the declination of the Sunne, the Sunne be∣ing in the six Northerne signes, subtracted from the Meridian altitude; or added, the Sunne being in the six Southerne signes, will precisely giue the height of the Equator: or (which is the same) the Meridian heigth of the Sun in the Equinoctiall: which being once found, we may worke as in the former. By the Pole-starre wee may likewise find it out, if wee obserue it three di∣stinct times in the same night: for three points being giuen, e∣uery Geometrician will finde out the Center, which in this case must bee the Pole. Many other wayes haue beene inuented by skilfull Astronomers, which appertaining rather to Astronomy then Cosmography. I purposely omit.

24 Concerning the Horizon, two things are chiefly to bee noted, the Inuention and the Distinction. The Inuention is considered either as it concernes the Zenith or Pole: or the Plaine of the Horizon. For both which we will set downe these Rules.

1 The height of the Pole subtracted from the quadrant of 90 Degrees: the residue will shew the Zenith or distance of the Zenith from the Pole.

The reason is euident; because the height of the Pole, toge∣ther with the distance of the Pole and the Zenith make an arch, which is a whole quadrant: so that the height of the Pole sub∣ducted, the distance will remaine; as for example, if wee put the

eleuation of the Pole here in Oxford, to be 51 ½ degrees or there∣about (as hath been formerly taught: Let these 51 ½ degrees bee subtracted from 90, then will remaine 38 ½, which is the true Zenith for that place.

2 A line which makes right angles with a plummet perpendicularly falling on it, will designe the Horizontall plaine.

The practise of the proposition is vsually shewed by Artifi∣cers by a certaine instrument called a Leuell, which is made in a triangle forme: from the vertex, or head of which, a line with a plummet fals on the Basis. Now when it shall bee found to be so placed, that the line and plummet falling on the Basis, shall make right Angles with it, and cut the whole Triangle in∣to two equall halfes: wee may account the Base-line to bee the plaine of the Horizon: For of this plaine, such is the position, that it inclines no more on the one side then on the other, but lies euen: as wee see in the surface of the water, when it rests quiet without motion: for howsoeuer the water so resting (as we haue formerly demonstrated) is alwayes sphericall, yet in a small distance in the sensible Horizon, it may to sense be repre∣sented by a plaine.

25 So much for the Inuention: The Distin∣ction of the Horizon is into three sorts: for either it is a right Horizon, or oblique, or parallell.

26 A right Horizon is that which with the Equator makes Right Angles.

This distinction growes naturally out of the Respect of the Horizon to the Equatour. For sith the Equatour is one and the selfe-same immoueable circle; and the Horizon is mutable and changed according to his diuerse verticall points, they cannot alwayes keepe the same situation in regard one of the other. This they haue reduced into three heads: for either it is Right

or Oblique, or Parallell. The Right is so called from the right Angles which the Horizon makes with the Equator: wherein the two poles are alwayes couched in the Horizon, and the E∣quator

[illustration]

passing directly ouer their heads, as is plaine to be seene in this figure here af∣fixed: such an Horizon haue these Inhabitants which dwell directly vnder the E∣quinoctiall line, in the very middest of the Torrid Zone: such an Horizon agrees to a great part of Africke: to a part of Peru in America: Also to most of the Molucco Ilands, the Ilands of Taprobana, and S. Thomas: but no part of Europe is subiect to such a Right Horizon. The cause of this va∣riation of Horizons is the naturall roundnesse of the Earth: For the earth being supposed to bee sphericall, as we haue before demonstrated, it must of necessity follow, that the site of the poles should be changed according to the diuersity of the places. Also, because wheresoeuer we are placed on the Earth (as wee haue shewed) all impediments of the sight, as mountaines and vallies put apart, we can behold the Hemispheare of the Hea∣uens, which middle part being set downe is diuided from the part vnseene, by the Horizon it must needs bee, that either both the poles must be in the Horizon: and so make a Right Spheare: or at least one must bee aboue and seene, and the other hid from the sight, and so much as one is eleuated aboue the Horizon, must the other bee couched vnder it▪ For otherwise wee should see more or lesse then a precise moity, or halfe of the Heauens: sith the poles differ one from the other the halfe of the whole Hea∣uens: to wit, by the Diameter of the world.

27 An oblique Horizon is that which with the Equator makes oblique Angles.

Those Inhabitants are said to haue an oblique Horizon, whose

site and position declines somewhat from the Equator, either to the North or South towards either pole: yet so that the pole bee not eleuated so high as 90 Degrees: for then it becomes a Parallell Horizon, as wee shall shew in the next. The represen∣tation of such an oblique Spheare may bee seene in this Dia∣gram: wherein the Horizon cuts the Equatour at oblique Angles,

[illustration]

whence it is called oblique. Clauius seemes to adde ano∣ther reason of this appellati∣on: to wit, because in such an Horizon one pole is al∣wayes eleuated aboue, and the other hid▪ but this rea∣son seemes too generall, as that which agrees not onely to an Oblique, but also to a Parallell Spheare. From this Horizon, by Iohannes de Su∣crobosco, the Spheare is called Artificiall▪ because, as Clauius coniectures, it is variable, and doth naturally diuide the Globe. For whereas the Horizon of the Right Spheare passeth by either Pole, it seemes by it selfe (as it were) Naturally and Directly to diuide the Spheare: and this diuision is no way variable, as that it should bee more or lesse Right: but contrariwise in the oblique Spheare, sith one Pole is placed aboue, and the other beneath, it seemes to be placed out of his naturall site and position. Moreouer this Oblique Horizon is variable according to the diuersity of ha∣bitations, so that it may be to some more, to others lesse Oblique: for so much the more Oblique must it be, by how much the nee∣rer it is placed to the Poles. The Inhabitants of an Oblique Spheare are such as seated betwixt the Equator, and either of the Tropicks of Cancer and Capricorne, or such as dwell betwixt either Tropicke and the Polar-circle▪

28 A Parallell Horizon is that which lies Paral∣lell to the Equator, making no angles at all with it.

Such a kinde of Horizon those Inhabitants are said to haue which are included betwixt the Poles of the world, and the Po∣lar circles; whose Horizon cuts not the Equatour at any Angles at all, either Right or Oblique: but lies Parallell vnto it, as

[illustration]

we see in this Figure here set downe. Some haue reduced this kinde of Spheare to an Oblique Horizon: in regard that in this site our Pole is e∣leuated aboue the Horizon, and the other depressed vn∣der: in which opinion Claui∣us seemes to second Iohannes de Sacrobosco, on whom hee comments. But this is ridicu∣lous; because the Spheare is called Right or Oblique (as wee haue taught) from the Angles which the Horizon makes with the Equator: wherefore that Horizon which makes no Angles at all, cannot bee called either Right or Oblique, but is necessarily distinguished from either. On this distinction of Horizons is grounded the diuision of the Inhabitants of the Earth according to three kinds of Spheares: of whose accidents and proprieties wee shall more fully treat hereafter in the dictinction of the parts and Inhabitants of the Terrestriall Spheare, because such proprieties cannot so well be taught without the knowledge of the Artificiall Spheare, whose Nature and Fabricke wee shall labour (God willing) in our next Chapter to vnfold.

CHAP. VII. Of the Artificiall Representation of the Terrestriall Spheare.

1 HAuing hitherto treated of the Terre∣striall Spheare, as it is Naturall or re∣all:

wee are in the next place to speake of the Artificiall Globe: The Artificiall Globe is an expression or imitation of the Spheare of the Earth.

2 The Artificiall imitation of the Earth is either Common or Magneticall. The common is againe twofold; either in the Globe, or in the Geogra∣phicall Mappe, or Table.

3 The Geographicall Globe is a round solid Body, adorned with Lineaments & pictures, seruing for the vse of Geographers.

Who was the first Inuentour of this Artificiall Globe, it is not euident: some thinke with Pliny, that it was found out by Atlas, and carried into Greece by Hercules. Others haue ascribed it to Anaximander Milesius; some to Musaeus, as Diogenes Laërtius: others to other Authors, amongst whom Architas Tarentinus is not forgotten, as one that was esteemed the rarest Mathema∣tician of his time. But all these were out-stripped by Archi∣medes the Syracusan Mathematician, who is said to haue com∣posed a Spheare of transparent glasse, representing vnto the life the whole frame of the Heauens, wherein the Sunne, Moone, and Starres with their true motions, periods, and limits were shewed to the sight, in such sort, as if it were naturall where∣of Claudian the Poët elegantly wrote in these Verses.

Claudian. in Epigrammat. Iupiter in paruo cùm cerneret aethera vitro, Risit, & ad Superos talia dicta dedit: Huccine mortalis progressa potentia curae? Iam meus infragili ••uditur orbe labor. Iura poli, rerum{que} fidem▪ legés{que} Deorum, Ecce Syracusius transtulit arte Senex. Inclusus varijs famulatur spiritus astris,

Et viuum certis motibus vrget opus. Percurrit proprium mentitus signifer annum, Et simulata nouo Cynthia mense redit. Iam{que} suum voluens audax industria mundum, Gaudet & humana sidera mente regi. Quid falso insontem tonitru Salmonea miror? Aemula naturae parua reperta manus.

In a small glasse when Ioue beheld the Skies, He smil'd, and thus vnto the gods replies: Could man so far extend his studious care, To mocke my labours in a brittle Spheare? Heauens lawes, mans wayes, and Natures soueraigne right, This Stage of Syracuse translates to sight. A soule within on various stars attends, And moues the quicke-worke vnto certaine ends, A faigning Zodiacke runnes his proper yeere, And a false Cynthia makes new monethes appeare: And now bold Art takes on her to command, And rule the Heauenly Starres with humane hand. Who can admire Salmonean harmlesse Thunder, When a flight hand stirres Nature vp to wonder?

But this Spheare of Archimedes I take to be more then an ordinary Globe commonly vsed amongst vs, as may appeare by the Poëts description; so that it may rather be likened to the Spheare, lately composed by Cornelius Trebelius, and presented vnto King Iames. The like whereof Peter Ramus sayes he saw two at Paris; yet not of glasse, but of Iron; the one of which Ruellius the Physician brought from the spoiles of Sicily: the o∣ther of which Orontius the Mathematician recouered likewise from the Germane warres. But of such kind of Globes hauing neuer yet had the happines to see any, I intend no description: In the meane time our common Geographicall Globes may well serue our turnes.

4 In the Terrestriall Globe two things are to be considered: 1 The Fabrick or Structure.

2 The Vse. 3 The Direction. In the former is taught the composition of the Globe by resoluing of it into it's parts.

1 The parts whereof the Globe is Geographically compounded are circles and pictures.

To explaine the true composition of the Artificiall Globe, not Physically as it consists of timber and mettall, but Geogra∣phically as it represents the Earth, we are to consider, that the parts of it are either Externall or Internall: Externall I call those parts which are without the Spheare it selfe, yet necessa∣rily concurre to the constitution of it. These parts are such as concurre to the making of the Stocke or Frame whereunto our Spheare is set: where to let passe the footing or lower board, (wherein in the old Globes was engraffed a Marriners Com∣passe, with a Needle magnetically touched, very profitable for the direction of the Spheare) I will onely speake of the great Timber Circle, encompassing round the whole Globe: because it more immediatly concernes our purpose. This Circle repre∣sents the Horizon of the Naturall Spheare: In the Globe it is made but one, not that there is but one Horizon in the whole Earth; because (as we haue taught) the Horizon is varyed ac∣cording to the places: but because it is impossible to point and marke out the Horizons; for all places being infinite as the Ver∣ticall points: yet may this one serue for all places, because the Globe being moueable, may apply all his parts to this circle. This Circle representing the Horizon, is diuided into three borders or Limbes: whereof the first which is towards the Spheare, containes all the signes with the Planets thereunto be∣longing; euery of which is diuided into 30 Degrees, which in the Timber Circle are described by set numbers and markes. The second which is the middle-most and largest, contaynes the Calendar, with the Golden number, and seuerall names of all the Feasts throughout the yeare. The third and last is of the 22 Windes, seruing chiefly for the vse of Marriners, and may serue many wayes for a Geographer to distinguish the Coasts and

points of the Earth. But of these three borders distinguished in the Horizon, only the last hath vse in Geography; the other two are in themselues Astronomicall, and placed in the Geographi∣call Globe rather for ornament, then vse. The Internall parts of the Globe are either annexed or inscribed in the face of the Spheare. The Annexed part is that which represents the Meri∣dian, which is a Brasen circle: For as the Externall Frame of the Globe contained the Horizon as one circle; so this Meridi∣an is set but one, although it bee in it selfe various, according to the places to which it serue. Neither without good reason is this Circle made of brasse, because it should serue for diuerse vses, which require that it should bee often changed and turned to and fro, which being of Timber would miscarry. This Bra∣sen Meridian meetes with the Horizon at two opposite places, cutting it at right angles, that the Spheare included might bee raysed and set lower, as occasion requireth. The Meridian circle is agayne diuided into 4 Quadrants, each of which is againe di∣uided into 90 Degrees; so that on the one side the 90^th Degree must touch the Pole; on the other side the first degree; so that in all there will arise 360 degrees, described in the Brasen Me∣ridian. Through this Brasen Meridian by the two Poles doth passe a line or wier, which is called the Axell-tree of the Globe, about the which the Spheare is turned, the ends of which are commonly called the Poles; whereof the one representing the North point is called the Pole Articke; the other shewing the South, is termed Antarticke. To this Meridian Circle in the Globe is commonly fastned a little Brasen Circle, named Cyclus horarius or the houre-circle; but this rather appertaines to A∣stronomy then Geography, and therefore wee will forbeare to describe it: somewhat more vse haue wee of another Instrument fastned to the Meridian, called the Quadrant of Latitude; for∣as much as it may serue to measure the Distance betwixt any two places signed in the Globe: but in so grosse an Instrument little exactnesse can bee expected. Now for such matters as are inscribed in the Spheare it selfe, (to let passe ridiculous & idle pictures vsed of Painters for ornament) they are either Lines & Circles drawne on the face of the Globe: or else the pictures &

delineations of Countreyes and places, marked out in visible proportions; whereof the former properly appertaines to the Sphericall part of Geography; the latter to the Topicall. The Circular Lineaments are againe twofold: either Circles necessa∣rily appertaining to the constitution of the Globe; or else Lines thereon drawne to bee considered of Marriners, which we haue before called the Rhumbes. But these Lines also (as wee haue taught) appertaine to the Geographer, being as many sections of the Horizontall Circle; because they are alwayes imagined to proceed from a Verticall point wherein they meet. The Circles painted on the Globe are either the Parallels or Meridians, whose description we haue set downe in the chapter before: A∣mongst the Parallels the most remarkable is the Equatour, which is made greater then all the rest, in forme of a bracelet, distin∣guished into degrees, and marked at euery 10. degrees: Next to this are the Tropicks and Polar Circles, represented only by blacke Lines, yet framed in such sort, that they may easily bee discerned from other Parallels. Amongst the Meridians the most notable is the first Meridian passing by the Canaries, and pain∣ted much like the Equatour, cut into diuers sections and de∣grees, in such sort as wee haue described: For the Zodiacke which is vsually pictured in the Terrestriall Globe, I hold it al∣together needlesse in Geography, and made rather for orna∣ment, then vse; for as much as the periodicke course of the Sun, deciphered by the Eclipticke, appertaines rather to the Theory, of the planets, which is the hardest part of Astronomy. The pro∣portion of these Circles, Site, and Distance is taught before, and needs no repetition, sith it is the very same in representati∣on on the face of the Globe, which is really in the Earth it selfe. For the pictures and Topicall description of the Earth, wee re∣ferre it to the second and third part of this Treatise; where we shall haue occasion to speake of Countreyes and Regions, with their seuerall qualities, accidents, and dispositions.

2 The vse of the Artificiall Globe is to expresse the parts of the Earth so farre forth as they

haue a diuerse situation as well one n respect of ano∣ther, as of the Heauens.

The vse of the Artificiall Globe is two-fold, either generall or speciall: the Generall is expressed in this Theoreme: the Speciall shall be shewne in diuerse speciall propositions hereaf∣ter as occasion shall serue.

5 This Direction is taught in the Rule. 1▪ The Meridian for the place being found by the Sunne or Compasse. 1 Let the Globe bee so set, that the North Pole respect the North, the oppo∣posite the South. 2 Let the Pole in the Meridi∣an of the Globe be set according to the eleuation of the Pole at the place assigned.

6 A Geographicall Mappe is a plaine Table, wherein the Lineaments of the Terrestriall Spheare are expressed and described in due site and proportion.

Some would haue the name of a Mappe to be drawne from the linnen furniture wherewith it is endorsed; which is not vn∣likely, in regard of the affinity of the words in Latine. But more significantly by others it is termed a Geographicall Ta∣ble or Chart: A Mappe differs from a Globe, in that the Globe is a round solide body, more neerely representing the true fi∣gure of the Earth, whereas contrarywise the Charts of them∣selues are plaine, though representing a Spheare, inuented to supply the wants of a Globe. For whereas a Globe is more cost∣ly to be procured of poore Students, and more troublesome to be carried to and fro; a Mappe is more cheape to be bought, and far more portable: And howsoeuer it be not so apt an expres∣sion as the Globe, yet are there few matters represented in the other, which may not in some sort find place in this. And cer∣tainly

such is the vse and necessity of these Tables, that I hardly deeme him worth the name of a Scholler, which desires not his Chamber furnished with such ornaments. It is written of that learned man Erasmus Roterodamus, that hauing seene 50 yeares, he was delighted so much with these Geographicall Mappes, that vndertaking to write Comments on the Acts of the A∣postles, he had alwayes in his eye those Tables, where hee made no small vse for the finding out of the site of such places where∣of he had occasion to treate. And it were to bee wished in these dayes, that yong Students insteed of many apish and ridiculous pictures, tending many times rather to ribaldry, then any lear∣ning, would store their studies with such furniture. These Geo∣graphicall Mappes are of two sorts, either Vniuersall or Parti∣cular: The Vniuersall are such as represent the picture of the whole Earth. The particular are such as shew only some parti∣cular Place or Region. These particular Tables are againe of two sorts; some are such as describe a place in respect of the Hea∣uens, whereon are drawne the Geographicall lineaments by vs described, at least the chiefest: some againe are such as haue no respect at all to the Heauens; such as are the Topographicall Mappes of Cities and Shires, wherein none of the Circles are described. For the Vniuersall and first sort of particular Maps, there is no question but they properly appertaine to Geography: But the later deserue much lesse consideration, as being too spe∣ciall for this generall Treatise.

7 The Geographicall Mappe is twofold: ei∣thre the Plaine Chart, or the Planispheare: The Plaine Chart we call that which consistes of one face and Right lines.

Such a Chart wee find commonly set foorth vnder the name of the Marriners Sea-Chart: for howsoeuer it seemes to haue chiefest vse in Nauigation, yet is the Nature and vse of it more generall: as that which not onely expresseth the Sea, but the whole Terrestriall Globe: For as much as the Parallels, Meri∣dians,

and Rhumbes, whereof primarily it consists, are circles common to the whole, and not appropriated to either part.

8 In the Plaine-Chart we are to consider two things First the Ground. Secondly the In∣scription. The Ground is the space or Plat∣forme wherein the Lines are to be inscri∣bed: the Inscription teacheth the manner how to proiect the Lines.

In the Chart two things are remarkable; to wit, the plaine whereunto the Lines are inscribed: Secondly the Lines or In∣scription it selfe: so wee are here to handle two points: First how this Plaine-Chart should bee conceiued to bee produced out of the Globe; whereof it is a representation. Secondly what rule or method wee ought to vse for the inscription of the Meri∣dians, parallels, Rhumbes, and other Lineaments thereunto an∣nexed. Both which depend on these propositions.

1 The Geographicall Chart is a Parallellogramme conceiued to be made out of a Spheare, inscribed in a Cylinder, euery part thereof swelling in Longitude and Latitude, till it apply it selfe to the hollow su∣perficies of the said Cylinder.

This Theoreme seeming at the first obscure, consists of ma∣ny parts, which being once opened, will soone take light. First then to know the Ground-worke of this Parallellogramme thus defined, wee must suppose a Sphericall superficies, Geographi∣call or Hydrographicall, with Meridians and parallels to bee in∣scribed into a concaue Cylinder, their Axes agreeing in one. Secondly wee must imagine the superficies thus inscribed, to swell like a bladder, blowing equally in euery part, as well in Longitude, as Latitude, till it apply it selfe round about, and all along towards either pole, vnto the concaue superficies of the Cylinder; so that each parallell on this superficies, successiuely

growes greater from the Equinoctiall towards either Pole, vn∣till it challenge equall Diameter with the Cylinder: and like∣wise all the Meridians growing wider and farther off, till they bee as farre distant euery-where as is the Equinoctiall one from the other. Hence may easily bee vnderstood the true Mathema∣ticall production or generation of this part: for first of a Spheri∣call superficies it is made a Cylinder: and secondly of a Cylinder it is made a Parallellogramme, or plaine superficies: For the con∣caue superficies of a Cylinder is nothing else but a plaine Paral∣lellogramme, imagined to bee wound about two equall equidi∣stant circles, hauing one common Axell-tree perpendicular vp∣on the Centers of them both; and the Peripheries of them both, equall to the length of the Parallellogramme, as the distance be∣twixt those Centers is equall to the bredth thereof: In this Chart so conceiued to be made, all places must needs be situate in the same Longitudes and Latitudes, Meridians, Parallels, and Rhumbes, which they had in the Globe it selfe: because we haue imagined euery point betwixt the Equatour and the Poles, to swell equally in Longitude and Latitude, till it apply it selfe to the concauity of the Cylinder: so that no point can bee displaced from his proper seat, but only dilated in certaine proportion. And this I take to bee the best conceit for the ground-worke or plat∣forme of this Geographicall Chart.

2 Except the distances betwixt the Parallels in a Plaine-Chart be varied: it cannot bee excused from sensible errour.

It hath beene thought by many Geographers, that the Earth cannot aptly according to due symmetry and proportion be ex∣pressed in a plaine superficies, as it is in the Globe: for as much as that which is ioyned and vnited in the Globe, being of a Sphericall figure, is in the Mappe extended and dilated to a di∣uerse longitude and latitude from that Sphericall delineation: and although it hath been generally conceited by many writers, that no due proportion could bee obserued in a Sphericall super∣ficies, without sensible errour: yet most exception hath beene made against this Chart here mentioned, consisting of one face

and straight lines, which in substance (if we cōsider the Circles) differs not from the Nauticall Chart: of whose errours Martin Cortese, Peter Nonnus, and many others haue complained: which escapes are excellently opened and reformed by our Countryman Edward Wright in his Correction of Nauticall Errours. The reason or ground which drew these men to thinke that the Earth could not bee proportionably described in a plaine superficies, proceeded from the common proportion of the Lines and Circles on the Chart. For supposing the Parallels cutting the Meridians at equall Angles, to obserue an equall di∣stance euery-where one from the other; these errours and ab∣surdities must of necessity ensue. First, what places soeuer are delineate in the ordinary Chart, the length of them from East to West hath a greater proportion to the bredth from North to South then it ought to haue, except onely vnder the Equi∣noctiall: and this errour is so much the more augmented, by how much those places are distant from the Equinoctiall: for the neerer you approach the Pole, the proportion of the Meri∣dian to the Parallell still increaseth; so that at the Parallell of 60 degrees of latitude, the proportion of the length to the bredth is twice greater then it ought to bee; for as much as the Meridian is double to that Parallell, and so in all the rest: whence as Edward Wright obserues, the proportion of the length of Friesland to the bredth thereof, is two-fold greater then in the Globe which expresseth the true proportion; be∣cause the Meridian is double to the Parallell of that Iland. In like sort it is plaine, that in the Ilands of Grock-land and Groen∣land, the length to the bredth hath a foure-fold greater pro∣portion in the Common Chart, then in the Globe; because the Meridian is foure-fold greater then the Parallell of those pla∣ces. Wherefore it cannot be conceited, that the manner of fin∣ding out the difference of Longitude by the common Chart, can bee any-where true without sensible errour, except onely vnder the Equinoctiall, or neere about it; because in no other place the Parallell is equall to the Meridian. In other places the errour will bee sensible, according to the difference of the Meridian, and Parallell of that place: whereas if the contrary

were granted, it would follow, that two ships sayling from North to South, vnder two seuerall Meridians, would keepe the same distance the one from the other of longitude neere the Pole, which they had neere the Equatour; which is impossible: because Meridians cannot bee Parallell the one to the other, but by how much they approach the Pole, by so much they are neerer, that in the end they all concurre and meete in the Pole it selfe. Secondly this common Chart admitted, there would a∣rise great errours not onely in the situation of diuers places, which appeare to bee vnder the same Meridian, but also in the bearing of places one to the other. The reason is manifest, for that the Meridian is a certaine Rule of the site and position of places: therefore whensoeuer any errour shall be committed in the Site and Position of the Meridian, there must needs follow errours in the designation of the Rhumbes, and other points of the Compasse. And therefore euery respectiue position of place to place, set downe in the common Chart, cannot bee warran∣ted. A pregnant example wee haue in the way from India; for the Promontory of Africke, called the Promontory of three Points; hauing of Northerne latitude 4 Degrees and a halfe, and the Iland of Tristan, Acugna, hauing 36 degrees of Southerne latitude, are in the common Chart set vnder the same Meridian: But the Chart sheweth the distance betweene these Ilands, and the Cape of good Hope to come neere to 400 leagues; both which cannot stand together; for if all the coast from the Pro∣montory of Three Points, vnto the Cape of Good-hope be right∣ly measured, and the Promontory of Three Points lye also vn∣der the same Meridian with those Ilands, yet must the distance bee much lesse: But if it be not lesse, it cannot stand with reason that it should haue the same Meridian with the Promontory of Three Points, but must needes lye more Westward. Thirdly, there must needs arise a greater errour in the translating Sea∣coasts and other such places out of the common Chart, into the Globe; because they haue only a respect to the Numbers of Degrees of Longitudes and Latitudes found therein; so that not onely errours appeare in the Sea-Chart, but also other∣where thence deriued. These and many more errours haue been

detected in the common Sea-chart, which (as we haue said) res∣pecting the circles, ought to be imagined one and the selfe-same with the proiection of the lines in a Geographicall table; which ouersight Ger. Mercator in his vniuersall Map seemes to correct: yet leaues no demonstration behind him to teach others the cer∣taine way to draw the Lines, as Meridians, Parallels, & Rhumbes on the Chart, in such sort, as these errours might be preuented, and the due proportion and symmetry of places well obserued. But our industrious Countryman hath waded through all these difficulties, and found out the true demonstration of a proiecti∣on of these Lines to be inscribed in the Chart in such sort, as no sensible errour can shew it selfe, from whose copious industry wee will extract so much as may serue our purpose, onely con∣tracting his inuention into a shorter method, hauing many mat∣ters to passe through in this Treatise.

2 The Distances of the Parallels in the Chart must encrease proportionably as the Secantes of the la∣titude.

It hath been a conceiued errour (as we haue shewed) that all the parallels in the Chart here mentioned, should euery-where keep the same Distances one from the other, from the Equator to the poles; yet because no man (for ought I know) hath out of Geometricall grounds discouered the true proportion, be∣side my fore-named Author; I must herein also follow his dire∣rection as neere as I can in his owne footsteps; because I would not any way preiudice his Inuention. First therefore wee must consider in that Chart, because the parallels are equall one to the other, (for euery one is set equall to the Equinoctiall) the Meridians also must bee parallell and straight Lines, and by con∣sequence the Rhumbes, making equall angles with euery Meri∣dian, must bee also straight lines. Secondly, because the spheri∣call superficies whereof the Chart is imagined to be produced, is conceiued to swell and enlarge it selfe euery-where equally, that is, as well in Longitude as Latitude, till it accommodate it selfe to the hollownesse of the Cylinder, round about: there∣fore at euery point of Latitude in this Cylinder so dilated, a

part of the Meridian obtaines the same proportion to the like part of the Parallell, that the like parts of the Meridian and Pa∣rallell haue to each other in the Globe without sensible er∣rour. Now for as much as like parts of the wholes, haue the same proportion that these wholes haue; therefore the like parts of any Parallell or Meridian of the Spheare haue the same proportion that the same Parallels and Meridians haue: For example sake, as the Meridian is double to the Parallell of 60 Degrees, so a Degree, Minute, or other part, is also double to a Degree, Minute, or other part of the Parallell; and what proportion the Parallell hath to the Meridian, the same must their Diameters and Semidiameters haue one to the other: as is taught by Geometricians. Now the Signe of the Complement of the Parallels latiude or distance from the Equinoctiall, is the semi-diameter of the said Parallell; as in this Diagramme here inserted may

[illustration]

easily appeare: for AE the signe of AH the comple∣ment of AF, the latitude of the Pa∣rallell ABCD from the Equino∣ctiall is the semi-diameter of the Parallell ABCD; and as the semi-diameter of the Meridian or whole signe is to the semi-diameter of the Parallell; so is the secant or Hypo∣tenuse of the Parallells latitude to the semi-diameter of the Meridian, or to the whole signe, as FK (that is) AK, to AE (as is) GK, so is IK to FK: therefore in this Geographicall Chart, the semi-diameter of each Parallell being equall to the semidiameter of the Equinoctiall or whole signe, the parts of the Meridian at euery point of latitude, must of necessity en∣crease with the same proportion wherewith the Secants of the Arch contained betweene these points of latitude and the Equinoctiall encrease: out of which Geometricall

grounds thus explained, will arise a certaine and easie methode for the making of a table by the helpe of Trigonometry, where∣by the Meridian in any Geographicall or Hydrographicall table may truly and in due proportion diuide it selfe into parts, from the Equinoctiall towards either Pole: for taking for granted, each distance of each point of latitude, or of each Parallell one from the other, to comprehend so many points as the secants of the latitude of each point or Parallell containes, wee may draw out a table by continuall addition of the secants answerable vnto the latitude of each Parallell, vnto the summe compounded of all the former Secants; beginning with the secants of the first Parallels latitude, and thereunto adding the second Parallels la∣titude, and to the summe of both these, adding the third Paral∣lels latitude, and so forth in all the rest: and this Table will shew the sections and points of latitude in the Meridian of the Geographicall Mappe; through which sections the Parallels ought to bee drawne: which Table wee haue lately set out by Edward Wright in his Correction of Nauticall Errours, to whom for further satisfaction in this kind, I referre the diligent Rea∣der. Out of the same grounds we may also deduce the Rumbes: for sith that the Chart (as wee haue shewed) is nothing else but a plaine Parallellogramme, conceiued to be made of the extension of a Sphericall superficies, inscribed in a concaue Cylinder, it must needs be that the Rumbes make equall Angles with all the Meridians. Therefore if in the Chart a circle be drawne, di∣uided into 32 equall parts, beginning with the Meridian, pas∣sing by the Center of that Circle, the lines drawne from the center of these sections, will be the Rumbes for that place.

9 Of the Geographicall Plaine-Chart wee haue spoken; It behoues vs next to treate of the Geographicall Planispheare. The Planispheare is a table or mappe of two faces, whereon the lines are proiected circularly.

Betwixt the Planispheare and the Plaine-Chart, a double dif∣ference may be obserued: 1 That the former consists altogether of right lines, aswell in regard of the Parallells as Meridians: whereas the later is composed of circular or crooked lines, as well as right. 2 The former may well bee expressed in one forme or front, as we may see not only in the Nauticall and com∣mon Chart, which wee haue shewne to be all one with the o∣ther in respect of these Lines; but in many other common Maps, as namely those of Hondius, whereas the Planispheare cannot be expressed without two faces or Hemispheares; whereof the one represents the Easterne, the other the Westerne part of the Terrene Globe: For herein wee must imagine a Globe to be cut into two equall Hemispheares, which are at once represented to our sight: of this Description of the Earth by crooked Lines, Ptolomy in his 24 Chapt. of his Geography hath taught vs two wayes: whereof the first depends from the aspect of a Spheare, turned and moued round, in which all the Meridians are descri∣bed as right Lines; but the Parallels as circumferences or croo∣ked Lines. The other Delineation takes his ground from a Spheare represented to the sight, not moued, but resting still in his place, in which both Meridians and Parallels are drawne cir∣cular. These two wayes of Ptolomy (howsoeuer iudiciously in∣uented in those times, wherein a small part of the Earth was discouered, and Geography very vnperfect) haue beene by later Geographers much reformed and corrected. Yet amongst the later haue not all expressed themselues alike: some haue pour∣trayed out of the Earth in fashion of a Heart; some according to other figures: but in this (perhaps) as Painters, they haue beene more iudulgent to fancy, then common vse: others haue gone a∣bout to expresse the Globe of the Earth in Elipticke Lines, which the Machanicians call ouall. But wee as well in this as other matters, preferring choice before abundance, will con∣tent our selues with one or two, which vse hath stampt more current, and experience hath found most vsefull: to which as a ground we will premise this Theoreme.

1 The Planispheare is grounded on a certaine

aspect of the Terrestriall Spheare, wherein the Eye of the beholder is so conceiued to bee fixed in some point of the Globe, that it may see the one halfe or Hemispheare.

Concerning the position of the Eye, two things are here re∣markable: 1 Where the Eye is supposed to bee placed either aboue the conuexe superficies, or in the concaue: some seeme to place it aboue the conuexe superficies; of which opinion Gemma Frisius seemes to be, who would haue the Eye to be set at an infinite distance: others although not admitting of such an infinite distance, deny not the Eye to bee aboue the conuexe superficies: but neither way can be warranted: Not the former, because of the impossibility of the supposition. For to imagine the Eye to bee set at an infinite distance, were to deny a sight or aspect which they would haue to bee the ground of this proje∣ction: For no object can bee perceiued, but such as is bounded and determined in a certaine and proportionate space. Neither can the later way passe cleere without exception; because to such a projection, such a sight is required which can see the whole Hemispheare: for otherwise would it be vnperfect, and want of the perfection of the Globe: which containes two ab∣solute and entire Hemispheares. But now no place can be ima∣gined without the Globe, wherein the Eye can be so placed, as to see the one halfe or Hemispheare: for as much as it is impos∣sible from the opposite points of any Diameter, to draw two tangent lines which may meet together, or cut one the other in the same point, but will bee Parallell the one to the other: wherefore wee may conclude, that the Eye in this projection cannot be imagined without the conuexe surface of the Spheare, but rather in the concaue: How the Eye should bee imagined to be in the concaue superficies, may be in this sort explayned: wee must suppose a great Spheare of the Glasse, or other such Diapha∣nous matter, inscribed with all his Parallels and Meridians, in such sort as they are represented vnto vs in the Globe, the Eye (according to opticall Principles) may bee so placed neere the

Center of it, as it shall bee able to see precisely the one Hemi∣spheare described with al his circles, as we find it in the spheare. I say neere not in the Center: because the Angle of vision (as we finde it taught in the Perspectiues) doth not extend to a right Angle, but is somewhat lesse: 2 we must inquire in what point in the superficies the eye is placed. To which wee answer, that the place of the eye is of it selfe indifferent; because it may bee imagined any where in what point soeuer. Neuerthelesse wee will only fasten on two especiall wayes which are of most vse, wherein the propositions following shall informe vs.

9 This Planispheare is twofold: the first we tearme equinoctiall, which supposeth the eye to be fixed on some point of the equi∣noctiall circle; the other Polar, wherein the sight is conceiued to bee fixed on the Pole of the Terrestiall Globe: The ground and fabricke of the former is taught in these Propositions.

1 The eye conceiued to be fixed on any point of the equatour, will designe out vnto vs a Pla∣nispheare wherein all the circles are proiected circularly, except the Equator and that Me∣ridian which passeth by the said point.

This may easily bee shewne out of the Opticke principles, we will suppose for example sake the eye to bee placed in some point of the Equatour: which shall bee 90 degrees of longitude from the Equinoctiall point: which kinde of proiection wee haue in many of our common Geographicall Maps of the earth. In this manner of sight, if the terrestriall Hemispheare, which may only be comprehended by it, be distinguished by this Paral∣lells and Meridians ordered and ranged by distances of equall

Arches in such number as we please: It is most certaine that the Eye, seeing distinctly and separatly euery one of these Meridi∣ans and Parallels, will forme to it selfe so many visuall Pyra∣mides, called by Geometricians Cones, which cones by this meanes will be Scalenes, and will haue for their Bases those Me∣ridians and Parallels, the tops whereof will meet together in the same point and eye of the beholder, which according to this supposition is the Pole of the Meridian, which passeth by the Canaries, called the first Meridian, and representing vnto vs the Equinoctiall colure. Now because these lines are ••ut by the plaine of the Meridian passing by the Canaries, it followes out of the same grounds, that their common sections, and that of the Meridian are the proportions of circumferences, which repre∣sent vnto vs in this Plaine the Meridians and Parallels seene in this manner of sight. Notwithstanding that which is vnder the 90 degree of longitude, as likewise the Equatour, cannot (according to Opticke demonstration) be seene, but as right lines cutting one the other at Right Angles in the Center of the same Meridian of the Canaries: The Theory being expressed we will in the next proposition shew the manner of proiection.

2 How to describe the Meridians and Parallels in the Equinoctiall Planispheare.

To shew the practise of this Theoreme, let there be drawne a circle ACBD, as you see in this figure diuided by two Dia∣meters cutting on the other at right Angles in the Center into foure Quadrants, or equall parts: whereof each one is againe to bee diuided into 90 degrees. In this the line AB is imagined to expresse the halfe of the Equatour, as the line CD of the Meri∣dian; in which the two points C and D designe out the two Poles. Let a rule bee drawne from the Pole C by euery tenth or fift degrees of the halfe circle ADB, and let euery section of the Equatour and the rule be precisely noted. In like sort from the point B let the Rule bee moued by euery fift and tenth De∣gree of the semicircle CAD, and let euery seuerall Interfection of the rule and the Meridian CD bee precisely noted. Then pla∣cing

[illustration]

[illustration]

one foot of the compasse in the line CD (which must bee drawne out longer, because in it the Centers of the Parallels must be found out) let the other be moued in order to euery in∣tersection of the Meridian noted out: and let so many circles be drawne as intersections, which circles will bee so many Paral∣lels. The finding out of the Centers where the stedfast foot of the compasse ought to bee fixed in drawing of each circle, is a matter appertaining to Geometricians: who haue taught a way to bring any three points giuen into a circle, and to finde the Center from which it is described. Hauing thus described the Parallels, wee must proceed on to draw the Meridians in this manuer: let the one foot of the compasse bee placed in the

line AB, from which as the Center by euery Intersection of the rule, and the Equatour forenoted, let there bee drawne so ma∣ny circles as intersections; which circles so drawne will be the Meridians. If any man desire more curiously to bee informed in the Geometricall Demonstrations, whereon this Fabricke of the Planispheare is grounded, let him read Gemma Fri∣sius de Astrolabio, Stifelius: but especially Guido Vbaldus, who hath copiously and accuratly handled this subiect. Enough it may seeme for a Cosmographer to shew the vse of it, as wee shall hereafter in Geographicall conclusions, supposing the Fa∣bricke sufficiently demonstrated by Geometricians, to whom it of right belongs.

10 The ground and Fabricke of the Polar Planispheare, is taught in these Propo∣sitions.

1 The Eye conceiued to be fixed on the Pole will expresse in the plaine of the Equino∣ctiall a Planispheare, wherein all the Pa∣rallels are described by circles and Meri∣dians by right lines.

This may likewise be optically demonstrated: For the Eye be∣ing supposed to bee fixed on the Pole, the sight will forme to it selfe so many visuall Cones as there are Parallels described in the Spheare. These cones being supposed equally to be cut by the plaine of the Equatour, will haue for their Bases the said Paral∣lell circles represented in the plaine of the Equatour, as so many absolute circles; whereof the Equatour will be the greatest, and comprehending within it all the rest. Likewise the Meridians in this kinde of sight are supposed to terminate the sides of these Cones, and therefore according to the Opticks ought to be right lines.

2 How to describe the Parallels and Meridians

in the Polar Planispheare.

This proiection is easiest of all, as shall appeare by this Dia∣gram. Let there be described a circle from the Center E which shall be ACBD: Let the circle be by two Diameters AB and BC diuided into foure quadrants: each of which may againe

[illustration]

bee diuided into 90 parts: euery fift or tenth of these 90 parts being first marked out, so many Diameters may bee drawne from either side to the opposite part by the Center E: which Diameters so drawne will serue for the Meridians. Then let a∣ny one of these lines bee diuided into 9 parts, and diligently marked out, as the Semidiameter ED by FGHIKLMN: by

all which marks from the Center E, let there be drawne so ma∣ny circles. These circles so described will be the true Parallels: This kinde of proiection, though more vnusuall, yet wants not his speciall vse in describing the parts of the earth neere the Pole, which in our ordinary kinde of Tables proiected after the other manner, cannot suffer so large and proportionall a Des∣cription.

11 Hauing hitherto treated of the Common re∣presentation of the Terrestriall Globe, we are in the next place to speake something of the Magneticall. The Magneticall is a round Magnet called a Terrella.

This kind of spheare hath been by Gilbert aptly termed a Ter∣rella, or little Earth, being the modell and representation of the great and massie Spheare of the earth whereon wee dwell. Be∣twixt this kind of representation & the former, great difference may bee obserued. First because the former is grounded merely on Artificiall Imitation, implying nothing else but a Respect or application: whereas this magneticall Terrella not only repre∣sents externally the Earth, but Internally out of its owne Mag∣neticall nature and vigour, eminently containes and expresses all those motions and magneticall vertues, which we haue former∣ly shewed to bee in the Earth. 2 It skills not in the former of what Materiall substance the Spheare consists, so the parts of it answer in due symmetry and proportion to the parts of the Earth; but this represents the whole as a Homogeneall part com∣municating the same nature & substance with the whole spheare of the earth: In the Fabricke of this instrument wee must consi∣der, 1 the Matter: 2 the Forme: The matter (as wee haue already intimated) is a Magneticall substance which ought to be chosen out of a most eminent Mine, hauing all his parts pure and vnmixt, as possible wee can finde in any Magnet. For though all Loadstones haue the same inclination, yet in many the vigour is so weake, or at least so hindered by the mixture of some Hetero∣geneall

matter, that they will not so well and sensibly performe their office. The forme of it is the roundnesse & politure, wherin Art should shew as much exactnesse as shee can: such a Spheare may well be expressed in this Figure, whereof we had formerly occasion to make vse: wherein the footsteps of this Magneticall vigour are sensibly expressed, no otherwise then in the great Body of the Earth.

[illustration]

12 In this Magneticall Terrella two things are chiefly to bee noted, 1 the inuention of the Poles, 2 of the Parallels & Meridians: both which shall be taught in these Propositions.

1 To finde out the Poles in the Magneticall Terrella.

To performe this conclusion many artificiall wayes haue been inuented, 1 By the Inclinatory Needle: for being euenly hung in such sort vpon the Terrella, as may be seene in the former figure

it will according to diuers points diuersly respect the Terrella in his site: wheresoeuer then wee shall finde it to fall perpendi∣cularly as right angles, wee may assure our selues that that very point is the Pole: which being once knowne, it will be easie to finde the opposite Pole, either the same way, or by measuring. 2 By the Veyne or Mine of the Loadstone: for (as wee haue shewed in our fourth Chapter of this Treatise) that part which was situated towards the North, will afterwards direct it selfe Southward, and contrariwise, the South point will respect the North, whence the Poles may be discouered. 3 By a little boat, wherein the Loadstone being placed on the water, will moue round till such time as with one Pole hee may point out the North, with the other the South. Many other wayes may be in∣uented by Mechanicians, perhaps more curious, to whose indu∣stry I referre my ingenious Reader.

2 The circles in the Terrella are found out by the Magneticall Needle.

This needs no other ocular demonstration then we haue taught in the fourth Chapter, and may be conceaued in the former Dia∣gramme; First wee see the magneticall needle according to di∣uerse points diuersly to conforme it selfe, which hath giuen way to ingenious artificers to finde out the Parallels and Meridians. The Parallels are found out by obseruing the Angles of declina∣tion of the Needle hung ouer the Terrella which are found in proportion to answer to the degrees of Latitude; which D^r Rid∣ley in his Magneticall Treatise hath industriously calculated, as I haue here inserted, to saue others a new labour of calcula∣tion. The Meridians are more easily found by hanging any dire∣ctory wier or needle ouer the Terrella; one end of which poin∣ting towards the North, and the other towards the South, will discouer the Meridian line.

CHAP. VIII. Of the measure of the Terrestriall Globe.

1 HItherto haue we handled the Terrestriall Globe primarily: in such proprieties as absolutely agree vnto its nature. In the second place we are to handle such as secondarily a∣rise out of the former. Here wee are to handle two chiefe points. 1 The Measure. 2 The Di∣stinction.

2 The measure is that by which we find out the quantity of the whole Earth.

Good reason haue we to cal this the Secondary part of Geography; for as much as these accidents and proprieties we here consider, arise altogether out of the former. In the former Treatise wee haue diuided the Naturall Spheare of the Earth, from the Ar∣tificiall: But in this part, for auoiding of tedious repetitions of the same things, wee haue ioyned them together: For howso∣euer the measuring and dictinctions of the Earth bee truely grounded on the nature of the earth it selfe; yet can it not be well expressed and taught without the materiall Instrument: we haue therefore thought good to consider the measure of the earth, be∣fore wee come vnto the Distinction, because it is more simple and vncompound, depending on the lineaments and measure of one circle: whereas the Distinction necessarily requires the coniunction and combination of diuerse circles, as Meridians and Parallels compared one with the other, as shall bee taught hereafter. Whether the great masse of the earth can bee mea∣sured, or no, seemes a matter not agreed on by all; Some haue held an opinion that it cannot bee measured, in regard of

the infinite magnitude wherewith they thought it endowed: which opinion seemes deriued from some of the Platonicks, who ascribing to the Earth another figure besides the Sphericall, haue cast themselues vpon vncertainties, and being notable to reduce the Quantity of the Earth according to their owne grounds to a∣ny certaine measure, haue denied it to bee measurable: But the ground of this opinion wee haue taken away before, in prouing the earth to be of a true Sphericall nature and therefore circum∣scribed in certaine bounds apt to be measured. Another conceit more absurd then the former, is not only the common people, whose condition might excuse their ignorance, but of such as would bee esteemed learned▪ who contend, that the greatnesse of the earth cannot bee measured: the onely reasons they can al∣leadge for themselues are, 1 That a great part of the earth is vn∣accessible by reason of steepe rocks, high mountaines, spacious and thicke woods, moorish fogges, and such like impediments. 2 That the parts of it are for the most part vneuen, and subiect to no regular figure, without the which no measure can bee exact. The first cauill is of no moment; because whereas wee affirme that the Earth by man may be measured, we hold it not necessa∣ry that it should be trauersed ouer by iourneyes or voyages. For as much as to the finding out of the Quantity of the whole Ter∣restriall Spheare, it may seeme sufficient to know the measure and proportion of any little part in respect of the Heauens. As for example, what number of Miles, Leagues, or Furlongs ans∣wer to any degree or degrees in the Heauens: wherfore we sup∣pose the Earth to be measured ouer not with our feet, but with our wits, which may by Mathematicall rules be taught to march forward where our legges fayle vs: The second obiection only proues thus much, that the Earth partaking of so many vnequall parts and irregular formes, cannot in the measuring admit of so much exactnesse, as if it were endowed with one vniforme face: yet it is exact enough to contenta Cosmographer, who measureth not by feet and inches, but by leagues and miles, in which wee little regard such a needlesse curiosity.

1▪ The common measure by which the quantity of the Earth is knowne, are Miles and Furlongs.

Here is to be noted that such instruments as serue for measu∣ring are of two sorts, either greater or lesser; the smaller are of diuerse sorts, as a Graine, Inch, Foot, Pearch, Pole, and such like Some of these howsoeuer sometime vsefull in Topographie, can haue little or no vse at all in the vast greatnesse of the whole Earth. Wherefore the Geographer seldome descends so low, but takes notice of greater measures, such as are Miles & Furlongs: where we may obserue by the way, that the vsuall measuring a∣mongst the Grecians was by Stadia or furlongs, amongst many of the Latines by miles: vnder which we also cōprehend Leagues: these miles are diuersly varied, according to the diuersity of Countries, so that in some places they are esteemed longer, in other shorter: which differences may be learned out of this en∣suing Table.

The instru∣ments of measuring the Earth are

• 1 Furlong containing 125 Geometicall paces or 625 feet.
• 2 Mile which is either
  • 1 Proper containing 8 Furlongs or 1000 paces.
  • 2 Impro∣per, which is either
    • 1 League, which is either
    • 2 German mile which is either the
      • 1 Old, containing 12 Fur∣longs.
      • 2 Newer containing 16 Furlongs.
      • 3 Common of 24 Fur∣longs.
      • 1 Common, which is 32 Furlongs or foure Ita∣lian miles.
      • 2 Greatest, containing 5000 paces which is called the Suenian, or Heluetian mile.

Howsoeuer this Distinction of miles may be many wayes profi∣table especially in the Topographicall part, yet shall wee sel∣dome make vse of any other then the common Germane mile, or the common Italian mile: To which as the most knowne, the rest may easily be reduced.

3 The obiect here proposed to bee measured is the Spheare of the Earth. The Dimensions ac∣cording to which it is measured, are either Simple or Compound.

4 The simple is twofold, either the Perimeter, or the Diameter. The Perimeter otherwise called the circumference, is a great circle measuring the Earth round about.

5 The Inuention of the Perimeter of the Earth de∣pends on these following Propositions.

1 If two or more circles bee drawne about the same Center, and from the Center to the Circum∣ference be drawne two right lines; The Arches of all the Circles comprehended within the said right lines will bee like and proportionall one to the other.

This Proposition being meerely Geometricall, is taken here as a ground without farther demonstration: whereof if any man doubt, hee may haue recourse to Clauius Commentaries vpon Iohannes de Sacrobosco. This principle granted will beget these two Consectaries.

1 As one degree is to the number of correspondent miles, or furlongs, so all degrees of the circles to the number of miles or Furlongs measuring the quantity of the Perimeter of the Earth.

2 Wherefore one degree or portion of the Cir∣cle

being knowne by his number of miles or fur∣longs, the whole Circumference may be found out.

The reason of this consequence euery Arithmetician can ea∣sily shew out of the Golden Rule: The chiefe point then of the inuention consists in finding out the proportion of any proporti∣on, as a degree, halfe degree, or the like, to the number of miles or Furlongs answerable thereunto; for which purpose many skilfull Mathematicians haue inuented many excellent wayes of great vse and delight.

1 By the eleuation of the Pole, or obseruation of an Eclipse, or some knowne Starre, the circuit of the Earth may be found out.

By the Eleuation of the Pole it is performed after this manner▪ let there be obserued two Cities, or other notable Land-marks placed iust North and South vnder the same Meridian. In these two Citties, or markes, let the Eleuation of the Pole be exactly noted. Then substract the Eleuation of the Southerne Cittie which is lesser, out of the Northerne▪ which is greater: the re∣sidue containes the distance of these places in degrees; which being experimentally knowne by Miles, Halfe-miles, Furlongs or such like measures, will shew the true proportion betwixt a degree, and his number of miles: which being againe multi∣plied by 360, will shew the whole circumference of the Earth. For example sake, wee will take two famous Cities of England, Oxford and Yorke; which are situated, if not exactly, yet very neere the same Meridian. The eleuation of the Pole here with vs at Oxford is 51 degrees and 30 minutes; at Yorke it is 54 de∣grees 30 minutes, or neere there about: subtract the lesser from the greater, the distance betwixt Oxford and Yorke will bee three degrees; which distance experimentally knowne in miles, will shew the proportion: which wee shall finde to bee, (abating somewhat in regard of the crookednesse of the way) about 180, answering to three degrees of the Meridian:

wherefore to one degree will answer 60 Miles, which being multiplied by 360, the whole circle will produce 21600, the measure of the whole Earth. The like may bee performed by an Eclipse in two Citties lying vnder the Equinoctiall circle: two land-markes being once noted out, lying vnder the Equino∣ctiall, let there bee obserued in both the same Eclipse of the Moone, especially in the beginning: Now it being certainely found out how many houres the Eclipse beganne in the one place before the other, wee must resolue their houres into de∣grees, which is easily done: for as much as to euery houre an∣sweres 15 degrees in the Sunne Diurnall motion, according to Astronomers. Now the distance betweene these two Citties or markes (being supposed first experimentally to be knowne, will easily shew the correspondency betwixt the Degrees and miles, which is here sought. Another way is taught by Possido∣nius, as easie as the former, which is performed by some noted fixt Starre, as Oculus Tauri, Arcturus, Spica Virginis, or any other; let there bee obserued vnder the same Meridian in the Earth two places, whose distance is experimentally knowne: in both these places let the Meridian altitude of the Starre be ful∣ly and perfectly obserued: The difference of these two Altitudes will bee the number of degrees betwixt these two places: whence we may obserue how many miles, or other partsanswer to the number of these degrees betwixt these two places. This way by Clauius is preferred before the former; for as much as it requires not in any place the knowledge of the Eleuation of the Pole, which in any place cannot be certainely knowne, with∣out long and diligent search, and obseruation: As for Geogra∣phicall Tables, they are not alwayes at all times to be had, at least worthy credit.

2 By the obseruation of the Noone-shadowes the measure of the Earth may be found out.

This way was inuented by Eratosthenes a famous Mathemati∣cian: who by obseruation of the Noone-shadowes, obserued at the same time at two diuerse places, situate vnder the same Meridian, found out the circumference of the Earth. The pla∣ces

which he chose for this purpose were Siene, and Alexan∣dria, situated vnder the same Meridian: the one inclining to the South, the other to the North. The Distance betwixt these two places is supposed to be knowne, whence hee proceeded in this manner: First he erected a Gnomon at right Angles on the plaine of the Horizon: when the Sunne was in the beginning of Cancer called the Solstice, from which he imagined two Rayes or Beames to be cast at Noone: the one passing by Siene the most Southerne part, the other by Alexandria the most Northerne: so that at Siene, the Sun being then in the Solstice passed into the Center of the world; the place being supposed to haue beene situate vnder the Tropicke: The other passed by the Vertex of the said Gnomon: whence by proportion of the shadow to the Gnomon by a Geo∣metricall kinde of working he found out the place betweene A∣lexandria, and Siene: which demonstration, formoreeuidence wee will here set downe: Let

[illustration]

there bee in the Earth described a circle passing by Alexandria and Siene; in which let A bee the place where Alexandria stands: B the place of Siene: the Gnomon or Style erected at Alexandria, AD, The Sun-beame carried to the Center of the world at Siena FBC, The Sunne-beame passing by the Ver∣tex, or toppe of the Gnomon seated at Alexandria EDG, casting his shadow AG toward the North: let the Gnomon be conceaued to bee prolonged vn∣to the Center C: Now for as much as in the Triangle ADG, the Arch AG, without any sen∣sible difference may bee taken for a Right line, hauing an insen∣sible

magnitude in regard of the whole Earth: and the Angle A is a right angle, and the two sides AD, and AG knowne: the former by supposition, being a Gnomon taken at our pleasure; the latter by any measure, or at least by the knowne proportion of the shadow to the Gnomon, according to the Doctrine of Tri∣angles: the Angle ADG will bee knowne; For whereas the sides AD, and AG are supposed to be knowne, their Quadrants also will be knowne, which being equall to the square made of DG, by the 47 proposition of the 1 of Euclide, the right side DG will easily be knowne: out of these grounds by the doctrine of the Sines and Tangents is easily found out the Angle ADG, and by consequence the alternate Angle ACB, which by the 27 of the first of Euclide is equall vnto it: for as much as the two Radii FBC and FDG may be supposed to bee Parallels in so small a distance as Alexandria & Siene compared with the Sun: the Angle being knowne the Arch AB subtended to the Angle C, will also be knowne, which is the space intercepted betwixt Siene and Alexandria; and for example sake: if Eratosthenes (as some write) found out the Arch AB, to containe in degrees 85, and experience had taught the length of the Iourney betwixt these Citties to haue contained 6183 ½ Furlongs: It would ap∣peare by the Golden Rule that 360 degrees containing the whole circuit of the Earth must proportionally answer to 252000 Fur∣longs.

1 The opinions of Cosmographers concerning the measure of the Earth, are diuerse: which is chiefely to be imputed to their errour in obser∣uing the distances of places experimentally according to Miles, Furlongs, or such like measures.

How many Authors of great name and estimation haue diffe∣red amongst themselues, euery man may enforme himselfe out of this Table here inserted. These differences wee finde diuersly related: but of all others, which Authors haue set forth,

	Authors	Furlongs	Miles.
	Strabo and Hipparchus	252000	31500
	Eratos∣thenes.	250000	31250
The circuit of the whole earth con∣taines accor∣ding to Possidonius & the anciēt Arabians.	240000	30000
Ptolomie.	180000	22500
	The later Arabians	204000	25500
	Italians and Germans.	172800	21600

I preferre the iudgements of M^r Robert Hues; For as much as it is not grounded on common tradition, but industriously by himselfe deriued out of the Ancients by diligent search and ex∣amination, as by one, whose iudgement being armed as well with skill in the language, as the knowledge of antiquity, scornes to be iniured by translation. What should bee the cause of these differences, is a matter which hath staggered curious searchers into Antiquities more then the former. Euery opini∣on being supported with the names and authorities of such re∣nowned Authors, might challenge a pitch aboue the measure of my Decision: only I may not bee thought ouer presumptu∣ous

to coniecture where I cannot define, especially hauing so good a guide as my forenamed Author, to tread out the way before mee. Wherefore supposing as a ground, these Authors so much differing about the measure of the earth, to haue beene in some sort led by reason. The differences must needs arise out of one of these causes: either the errour or negligence of the ob∣seruers, in trusting too much to others relations without any farther search, or else the defect in the Mathematicall grounds out of which they deriued their demonstration; or the diuersi∣ty of measures vsed in this worke: or finally, from the misap∣plication of these measures to the distances; whence may arise some errour out of the experimentall measuring of places in the earth. In the first place it may perhaps be doubted whether A∣ristotle defining the measure of the Earth to bee 400000 fur∣longs, were not deceaued by relations: for as much as hee auou∣cheth it, from the Mathematicians of his times, whose authori∣ty and credit for ought wee know, deserues as well to bee for∣gotten as their names. But this answer might seeme too sharp in the other: for as much as wee find them registred for Masters in their science, and such as could not easily bee cosened by o∣thers impostures. Neither can wee imagine the second to bee any cause of their errour for the same reason: because the wayes these Mathematicians vsed in finding out the circuit of the earth, are by writers of good credit commended to posterity, as warrantably grounded on certaine demonstrations, being no other then what wee haue shewed before, which admit of no Parallogisme: In the third place wee ought to examin whether the diuersity of opinion concerning this matter pro∣ceeded from diuersity of the measures which were vsed in this worke. Nonnius and P••••ceru•• would needs perswade, that the Furlongs whereby they measured the earth were not the same: Maurolycus and Xilander talke of diuerse kindes of paces: Maurolycus labours to reconcile both, but without effect. First whereas they would haue diuerse k••nde of paces, it cannot be denied: but in the meane time we cannot learne that the Greci∣ans euer measured their Furlongs by Paces, but either by Feet, or Faddomes. A Faddome which the Greeks call 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 is the

measure of the extension of the hands together with the breast betwixt, containing six feet: which is a kinde of measuring well knowne vnto our Mariners, in sounding the depth of the Sea. This measure notwithstanding is by many translated a Pace: by what reason, let any man iudge. Xilander in translating Strabo renders it an Ell: Secondly for a Furlong it containes according to Herodoiu•• an ancient Grecian writer 600 Feet: which is al∣so testified by Suidas, being much later. A Furlong containes 100 Faddomes; euery Faddome foure Cubits. A Cubit, ac∣cording to Heron, a Foot and halfe, or 24 Digits. Now for the variety of Furlongs, it is true that Censorinus makes three kindes. For either it is called the Italian consisting of 625 Feet, which is of most regard in measuring the Earth; or the Olympian of 600 Feet: or the Pythian containing 1000 Feet. But to let passe this latter, we shall finde by serious consideration, that the Italian and Olympian Furlongs differ only in name, and are indeed the same. For the Italian containing 625 Roman Feet (according to Pliny in his second booke) is ••quall to the Olym∣pian, hauing 600 Grecian Feet. For a Foot with the Grecians exceeds the Roman Foot by a twenty fourth part: as much as is the difference betwixt 600 and 625. Hence wee see how lit∣tle certainty can bee expected of such as goe about to reconcile these opinions out of the various vse and acception of the mea∣sures. The most probable assertion then is, that the errour was grounded on this, that the distances of places, mentioned by the foresaid Authors, were not by themselues exactly measured, but taken vp vpon trust on the relation of trauellers, wherein they might easily bee mistaken. For instance wee will take Era∣tosthenes and Possidonius, as of greatest credit, who are notwith∣standing taxed for many errours in their experimentall obser∣uations: whereas it is cleere that Ptolomy grounded his opinion on the distances of the places, exactly measured, as is witnessed by his designation of the Latitude of the earth so farre as it was discouered and knowne. Eratosthenes, for mistaking in the mea∣sure of distances, is much taxed by Hyparchus, as we find in Stra∣bo: For betwixt Alexandria and Carthage, hee reckons aboue 13 thousand furlongs, whereas by a more diligent enquiry

there are found to bee but 9 thousand. Likewise Possidoniu•• is knowne to bee mistaken, in that hee made the Distance betwixt Rhodes and Alexandria to bee 5000 Furlongs, whereas out of the relation of Marriners, some haue made it 4000, some 5000, as it is witnessed by Eratosthenes in Strabo; who notwithstan∣ding, sayes that hee found by Instruments that it was not aboue 3750; and Strabo wou••d haue it somewhat lesse, as 2640. Mau∣rolycus, going about to defend Possidonius against Ptolomy, brings nothing but friuo••ous reasons vnworthy so good an author. Out of all which hath beene spoken our former Corollary will bee manifest, that the diuersity of opinions concerning the circumfe∣rence of the Earth, arose from the experimentall mistake in the distances of places, where they trusted to other mens relations, rather then their owne knowledge.

6 The Diameter is a right line passing by the Cen∣ter of the Earth from one side to the other▪ and measuring the thicknesse of it: the inuention of which depends on these Rules.

1 As 22 is to 7 so is the circumference of a circle to the Diameter: wherefore the circumference of the Earth multiplied by 7, and diuided by 22 will produce the Diameter.

The exact proportion betwixt the Circumferences of a circle, & the Diameter being the ground of the Quadrature of a circle, is a matter which hath set a work the greatest wits of the world: hauing notwithstanding as yet by no man been brought to dis∣couery, in so much as Pitiscus, and other good Mathematicians, might well doubt whether euer it would come to light. N••uer∣thelesse, where exactnesse cannot bee found, wee must come as neere as we can. The neerest proportion in numbers which any could yet light on, is as 22 to 7, which in so great and massie a bo∣dy, as the Earth may passe without any sensible or explicable er∣rour. Supposing then out of our precedent Suppositions the

whole circuit of the earth to bee 21600 Italian-miles (which is the common opinion now receaued) I multiply according to the golden Rule 21600 by 7, whence will arise 151200, which being diuided by 22 the Quotient will render 6872 11/8 which is the Diameter or thicknesse of the Earth: some lesse curious are content to take only the third part of the circumference for the Diameter, which will be 7200, which account is lesse exact, yet sufficient for an ordinary Cosmographer: for as much as 328 miles, which is the difference, is of no great moment in the mea∣sure of the whole Earth.

2 By the knowne height of some mountaine with∣out the knowledge of the circumference of the Earth, the Diameter may be found out.

This is a way inuented by Maurolycus, which proceeds in a contrary manner to the former: because the former by the cir∣cumference first supposed to be known, shewes vs a way to find out a Diameter: but this, first seeks out the Diameter, by which wee may finde out the circumfe∣rence:

[illustration]

the practise is in this man∣ner. Let the circuit of the Earth be conceaued to be BCD (as we see in this Figure) in which let there be chosen an high Mountain whose Altitude AB may bee knowne by the rules of measu∣ring altitudes: then from the Mountaines top A, by the rules of measuring longitudes must the whole space of Sea or Land bee measured so far as it can be seene: so that the visuall Beame AC, may touch the Superficies of the Earth in C: let the space thē which is seene in the Earth be BC, which although in it selfe it bee crooked and not plaine, yet can it not sensibly differ from a Plaine, for as much as the Arch BC, is ex∣traordinarily

little, if compared with the whole Earth. These grounds thus laid, we must proceed by a Geometricall manner of argumentation in this sort, Here are to bee obserued foure right lines: whereof the first is AB, the heigth of the mountaine obserued: the second is the visuall Ray AC: the third AD con∣sisting of the height of the mountaine, and the Diameter of the Earth. The fourth BC, the distance which is seene: for (as wee haue shewed) it may without sensible errour bee taken for a right line. Now for as much as AB, BC are knowne, their Qua∣drates by the 47 proposition of the first of Euclide, will also bee knowne, which being equall to the square of AC, the square of the right line AC will likewise bee knowne. But the square of the right line AC, sith it toucheth the circle, will be equall to a Right Angle Figure contained vnder DA, AB, wherefore the right angle so conceaued will be knowne. But AB is the knowne heigth of the mountaine, wherefore the right line AD will easily be knowne; if wee diuide the knowne right Angle contained vnder AB, AD: by the right line AB: for the Quo∣tient will giue the right line AD; from which if wee subduct AB, the knowne height of the mountaine: then will remaine the Diameter of the Earth BD, which was here to be perfor∣med: from this inuention will arise this Corollary.

1 The Diameter of the Earth first supposed to be knowne, the circumference may be found out in this manner: as 7 is in proportion to 22, so is the Diameter to the Circumference.

2 Wherefore let the knowne number of the Diame∣ter be multiplied by 22, and the Product be di∣uided by 7, the quotient will giue the Circum∣ference.

As for example according to our former instance: Let vs sup∣pose the Diameter of the Earth to bee 6872 8/11 this number being multiplied by 22, will produce 15120, which product

diuided by 7, wee shall finde in the Quotient 21600, which is the circumference of the Earth.

7 The compound dimensions, according to which the Spheare of the Earth is proposed to bee measured, are either the Superficies or the Solidity.

8 The Superficies is againe twofold, either Plaine or Conuexe: the Plaine is the space in∣cluded in the Perimeter.

9 The plaine Superficies may be found out two wayes: either by the Circumference, or the Diameter: both which wayes taught in these Rules.

1 If the whole circumference bee multiplied in it selfe, and the product bee diuided by 12 4/7 the quo∣tient will shew the Superficies included in the circle.

As in the former example wee will take the Circumference of the Earth to be 21600 Italian-miles: let this number be multi∣plied in it selfe, and the product thereof diuided by 12 4/7, the Quotient will amount vnto 9278180, which is the plaine su∣perficies of the Earth.

2 If the Semi-Diameter of a circle be multiplied by the halfe part of the Circumference: there will arise the measure of the Plaine Superficies contained in the Circumference.

The reason hereof is shewed by Clauius in his Tract de Isoperi∣metris Proposit. 4. where is demonstrated, that a Right Angle

figure comprehended of the Semi-Diameter of any circle, and the halfe of the Circumference will be equall to the Circle it selfe, of whose parts it is comprehended.

10 So much concerning the Plaine Superficies: the knowledge and inuention of the Conuexe, may bee performed two wayes: either by the Diameter and Circumference; or else by the Space contained within the Circumference, accor∣ding to these Propositions.

1 If the Circumference and Diameter be multiplied the one into the other, the product will shew the number of square miles in the face of the Terre∣striall Globe.

As for example, let the Diameter of the Earth containing ac∣cording to the common account 80111 9/12 furlongs, bee multi∣plied by the whole circumference, which is 252000, there will arise the Conuexe Superficies of the whole earthly Spheare which is 20205818181 9/11.

2 If the space contained in the greatest circle in the Spheare bee multiplied by 4, there will bee produced the whole conuexe Superficies of the Spheare.

How to finde out the space or plaine Superficies, is a matter taught before: which being once found is easily multiplied by 4, and so will giue vs the number sought.

11 The last and greatest compound Dimen∣sion, according to which the Earth is mea∣sured, is the Solidity, consisting of Length,

Bredth, and Height, or Thicknesse: This may bee found out two wayes either by the Diame∣ter, and Conuexe Superficies, first supposed to be known: or by the knowledge of a great circle without supposing the Supperficies to be first knowne: both wayes shall bee expressed in these Propositions.

1 If the Semidiameter of the Spheare be multiplied into the third part of the Conuex Superficies of the said Spheare, there will arise the whole Soli∣dity of the Earth.

This is demonstrated by Geometricians: For a solide Rectangle comprehēded of the Semidiameter of the Spheare, and the third of the Cōuex Superficies of it, will be equall to the Spheare it selfe. As for example, if the Semidiameter of the earth contai∣ning 40090 10/11 Furlongs bee multiplied by the third part of the Conuex Superficies containing, to wit, 67352727 3/11 there will arise the solidity of the earth, which will containe 27002-3:06611570 3/11 Cubicke Furlongs. That is the solidity of the earth will comprehend so many Cubes, cantaining euery side so many Furlongs, as there are vnities in the said number: For the Areae or spaces comprehended of Solide figures are measured by the Cubes of those lines, by whose squares the Conuexe Su∣perficies of those lines are measured.

2 If the greatest circle bee multiplied by ⅔ of the whole Diameter: the product will shew the soli∣dity of the Spheare.

This way is also demonstrated by Clauius in the same tract of measuring Magnitudes. It may Arithmetically bee deduced in this sort. If any Spheare whatsoeuer hath a Diameter of 14 Palmes, and should bee multiplied by 3 1/7, the circumference of

the greatest circle containing it will be found to be 44; whose halfe being 22, if it be multiplied into the Semidiameter 7, there will arise the Superficies of the greatest circle 154, which num∣ber if wee multiply by two third parts of the Diameter: that is by 9⅓ there will bee produced the solidity of the said Spheare, to wit, consisting of 1437 ⅔ Cubicke palmes. In the like sort may wee worke by miles or furlongs in measuring the whole terre∣striall Globe, which is a more conuenient measure for the massie Globe of the Earth.

CHAP. IX. Of the Zones, Climates, and Parallels.

1 OF the Measure of the Earth we haue trea∣ted in our former Chapter. In the next place wee must speake of the Distinction of the Terrestriall Spheare, which is either in re∣gard of Spaces or Distances.

2 Spaces are portions in the Spheare bounded by the Parallell circles: such as are the Zones, Climats, and Parallels.

3 These are againe considered two wayes; either in themselues, or else in their Adiuncts or Inhabitants belonging to them.

4 A Zone is a space included betwixt two

lesser and named circles; or else betwixt a les∣ser circle and the Pole of the world.

The spaces into which the Terrestriall Spheare is diuided, are either Greater or Lesser. The Greater is a Hemispheare which ariseth out of one only circle by it selfe, without the Combinati∣on of more. Such are chiefly of three sorts. The first is made by the Equatour: which diuides the whole Globe into the north and the South Hemispheare. The second is of the Meridian, whose office it is to part the Earth into the Easterne and We∣sterne Hemispheares: The third of the Horizon, which diuides the Spheare into the vpper and lower halfes: But these parts arising (as I said) out of one only circle, are handled before with the circles themselues. In this place wee are to speake of such parts, as arise out of the Combination and respect of circles one with another. Such as are the Zones, Climats, and Parallels. A Zone signifies as much as a girdle or band: because by it the spaces in the Earth are (as it were) with larger bands compas∣sed about. The Grecians haue sometimes giuen this name Zone to the Orbs of the Planets, as Theon, Alexandrinus in his Com∣ment on Aratus, in these words, 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉. There are (saith he) in the Heauens seauen Zones not con∣torminate with the Zodiacke, whereof the first is possessed by Sa∣turne, the second by Iupiter, &c. But this acception of the name is far off from our purpose. The name, Zone, as it is with vs in vse, is by the Latine Poëts rendred sometimes Facia, some∣times Plaga: both signifying one and the selfe-same thing: which is as much as a space comprehended within two Named and lesser Parallels: or at least betwixt such a Parallell and the Pole it selfe: because, as wee shall shew hereafter Zones are of two sorts: These Zones are in number fiue; which diuision hath beene familiar with our Latine Poëts, as may appeare by these verses of Virgil.

Quin{que} tenent coelum Zonae, quarum vna corusco▪ Semper Sole rubens▪ & torrida semper ab Igne: Quam circum extremae dextrâ laeuá{que} trahuntur.

Caerule â glacie concretae, at{que} imbribus atris. Has inter, Mediam{que}, duae Mortalibus aegris Munere concessae Diuûm, &c.

Fiue Zones ingirt the Skies; whereof one fries With fiery Sun-beames, and all scorched lies. 'Bout which the farthest off on either hand, The blew-eyed Ice and brackish showres command. 'Twixt these two and the midst the Gods doe giue A wholsome place for wretched man to liue.

Which description of Virgil little differs from that wee finde in Ouid, in these Verses.

—Duae dextrâ coelum totidem{que} sinistrâ Parte secant Zonae: quinta est ardentior illis: Sic onus inclusum numero distinxit eodem Cura Dei, totidem{que} Plagae tellure premuntur. Quarum quae Media est non est habitabilis aestu: Nix ••egit, alta duas: totidem inter vtram{que} locauit. Temperiem{que} dedit mista cum Frigore Flamma.

Two Girdles on the right hand, on the left As many cut the Skies: more hot's the fift. So God diuiding with an equall hand, Into so many parcels cuts the land. The midst through heat affords no dwellers Ease: The deepe snow wraps vp two: but betwixt these And the other Regions, are two places set, Where frosts are mixt with fires, and cold with heat.

But because this enumeration and description of the Zones set downe by the Poëts, seemes too popular and generall, wee will more specially diuide them according to the methode of our times in this manner.

5 The Zones are either Vntemperate, or Temperate: the Vntemperate are againe twofold either cold or hot.

6 The Intemperate hot Zone is the space con∣tained

betwixt the two Tropicke circles of Can∣cer and Capricorne.

How vnaptly these names of Temperate & Vntemperate agree to the Zones, considered in their owne nature, wee shall speake in our second part: yet because I thought it vnfit to vse other tearmes then the Ancients, I will not coine new names. This Zone, or space included betwixt the two Tropicks, circum∣scribes within it two great circles, whereof the one is the Equa∣tour running iust in the midst, neither inclining to the North or South: The other is the Eclipticke obliquely crossing it and mee∣ting the two Tropicks twice in a yeere, in the Spring and Au∣tumne. The extent or breadth of this Zone then is equall to the distance betwixt these two Tropicks, to wit, 47 degrees, which make 2820 miles: because from the Equatour to either Tropicke we account 23 degrees, which added and resolued in∣to miles, will make the said summe: within the compasse of this Zone is situate the greatest part of Africke, especially that of the Abyssines (which common opinion with little probabili∣ty, would haue to bee the Empire of Prester Iohn) also many Ilands as Iaua, Summatra, Taprobana, besides a great part of the South of America called Peruana: It was imagined by the Ancients, as Aristotle, Pliny, Ptolomy, and many other Philo∣sophers, Poëts, and Diuines, that this Zone through extreame heat was altogether vnhabitable: for which cause they called it Intemperate: The reason of this coniecture was drawne from the situation of this part in regard of that of the heauens. For ly∣ing in the middle part of the world, the Sunne must of necessi∣ty cast his rayes perpendicular, that is to say at Right An∣gles. Now according to the grounds of Peripateticke Philoso∣phy the Idol of this age, the heat deriued from the Sunne, ariseth from the reflexion of the Sunne-beames against the sur∣face of the Earth. Wherefore the heat was there coniectured to bee greatest, where the reflexion was found to bee greatest. But the greatest reflexion, according to all Mathematicians, must be in this Torrid Zone, where the Sunne darts forth his Rayes at right Angles, which reflect backe vpon themselues. Which

false coniecture was a long time continued by the exuberant des∣criptions of Poëts, and defect of Nauigation: hauing as yet scarce passed her infancy. But how farre these surmises come short of truth, wee shall declare in our second part, to which wee haue reserued those Physicall and Historicall discourses concerning the qualities and properties of the Earth.

7 The Intemperat cold Zones are those which are included betwixt the Polar circles and the Poles: whereof the one is Northerne, contained in the Arcticke circle, the other Southerne in the Antarcticke.

These two Zones are not made out of the combination of two circles, as the former: but by one circle with relation to the Pole. The greatnesse and extent of this Zone is about 23 degrees and a halfe: which resolued into Italian-miles will produce 1380. The Northerne cold Zone containes in it Groenland, Fineland, and diuerse other Northerne Regions, whereof some are partly discouered, and set out in our ordinary Maps, other some not yet detected. For the other Zone vnder the Antarticke Pole, it con∣sists of the same greatnesse, as wee know by the constitution of the Globe, hauing other such accidents correspondent as the Northerne, so farre forth as they respect the Heauens. For other matters, they lye hid in the vast Gulph of obscurity, this port ha∣uing neuer yet (for ought I know) exposed her selfe to the disco∣uery of the Christian world. Whether these two Zones be with∣out habitation, by reason of intemperate cold, as the other hath been thought by reason of too much heat, wee shall in due place examine.

8 The Temperate Zone is the space contained betwixt the Tropicke & the Polar circle: where∣of the one is Northerne contained betwixt the Tropicke of Cancer and the Articke circle: the

other Southerne comprehended betwixt the Tropicke of Capricorne and the Antarcticke circle.

Why these Zones are tearmed Temperate, diuerse reasons are alleaged. 1 Because the Sun-beames here are cast obliquely on the surface of the earth, and by consequence cannot produce so much heat, as in those places where they are darted perpen∣dicularly, if wee only consider the constitution and site of the heauens: For as we shall hereafter proue, this may sometimes be altered by the disposition of some particular place. 2 It may be called the Temperate Zone, because it seemes mixt of both extreames partaking in some measure the both qualities of heat and cold: the one from the Torrid, the other from the Frigid Zones. 3 Because in these Zones the distances betwixt Sum∣mer and Winter are very remarkable, hauing a middle difference of time betwixt them, as compounded of both extreames. These temperate Zones included betwixt the Tropicks and the Polar circles are twofold as the circles: The northerne temperate Zone comprehended of the Tropicke of Cancer and the Articke circle, containes in it the vpper and higher part of Africke, stretching euen to the mountaine Atlas: Moreouer in it is pla∣ced all Europe, euen to the Northerne Ilands in the Articke Zone, and a great part also of Asia: the other temperate Zone lying towards the South, is not so well knowne being farre di∣stant from our habitation: and awaiting as yet the farther indu∣stry of our English and Dutch Nauigators. The bredth of this Zone, as the other containes about 43 degrees which is the di∣stance betwixt the Tropicke and the Polar circle, which multi∣plied by 60, will be resolued into 2580 Italian-miles.

1 The Torrid Zone is the greatest of all: next are the two Temperate Zones: the cold Zones the least of all.

The Torrid Zone is found to be greatest as well in regard of

longitude as latitude, and is diuided by the Equatour into two halfes: the next are the Temperate; but the two cold Zones howsoeuer equall in Diameter to the Torrid, are notwithstan∣ding least of all: where is to bee noted that euery Zone is of the same latitude from North to South, beginne where we will, be∣cause it is contained betwixt two equidistant circles: but all in∣ioy not the same longitude from East to West, For the parts of euery Zone by how much neerer they are to the Equatour so much greater longitude will they haue: by how much neerer the Poles they are, so much the lesse longitude: for as much as the Parallels towards the Poles grow alwayes lesser and lesser. The inuention of the quantity of the Zones before mentioned, may briefly thus bee performed. The latitude of the torrid Zone is so much as the distance betwixt the Tropickes, which is A∣stronomically grounded on the greatest declination of the Sunne being doubled: This declination being by Clauius and others found to be 23 degrees 30 scrup. which being doubled will pro∣duce 47: which againe multiplied by 60, and resolued into miles, will amount to 2820: though the odde scruples of many Au∣thors are neglected. The latitude of the cold Zones is also drawne from the greatest declination of the Sunne: For the di∣stance of the Pole circles from the Pole it selfe is iust so much as the declination of the Eclipticke from the Equatour, to wit, of 23 degrees 30 scrup. to which answer according to the former Rule 1420 Italian-miles. The inuention of the latitude of the temperate Zones depends from the subtraction of the distance of the Poles of the Eclipticke, from the Equatour: that is from the greatest declination of the Sunne being doubled from the whole quadrant: in which subduction the residue will be 43, to which will answer 2580 Italian-miles.

1 The Zone wherein any place is seated may bee knowne either by the Globe or Geographicall Table, or else by the Tables of Latitude.

By the Globe or vniuersall Mappe wee may know it by the

diligent obseruation of the foure equidistant circles. For if wee find it betwixt the two Tropicks, we may without doubt, thinke it to be in the Torrid Zone: If betwixt the Tropicke circle and the Polar, it will be in the Temperate. If betwixt the Polar circle and the Pole it selfe, it must bee in the cold Zone. By the Tables of Latitude it may be found this way: Seeke the latitude of the places giuen in the Table, which if it bee lesse then 23 degrees 30 scruples, the place is in the Torrid Zone. If precisely it bee so much in the Northerne Hemispheare, the place assigned is vnder the Tropicke of Cancer, which is the bound betwixt the Torrid and the beginning of the Northerne Temperate Zone: But if it be in the Southerne Hemispheare, it will be vnder the Tropicke of Capricorne: which ends the Torrid Zone, and be∣ginnes the South Temperate Zone: Euery place hauing more Latitude then 23 degrees 30 scruples, yet lesse then 66 degrees 30 Minutes, is seated in the Temperate Zone, either Northerne or Southerne, as the places are in the Hemispheare. If the place be precisely of 66 Degrees 30 minutes, it will be iustly found to be vnder the Polar circle, either Arcticke or Antarcticke. Fi∣nally euery place whose Latitude exceeds the number of 66 de∣grees 30 minutes, is seated in the cold Zone either Southerne or Northerne. If it reach iust to 90 degrees, it will bee iust vnder the Pole it selfe.

9 Of the distinction of the Terrestriall Spheare by Zones we haue spoken: we must in the next place deliuer the Distinction of the earth according to Climates.

10 A Climate is a space of the Earth contained betwixt two Parallels distant from the E∣quatour towards either Pole.

Climates are so called because of their Declaration from Equatour; for as much as they are to bee accounted as so ma∣ny scales of ascents to or from the Equatour. Some haue defi∣ned it from the vse which is chiefly to distinguish the longest

time of the Artificiall day: because at the point of euery climate truely taken, the longest day is varied halfe an houre: al∣though this account agree not altogether with Ptolomie, and the ancient Geographers before him, as wee shall shew hereaf∣ter. This distinction of the Terrestriall Spheare into Climates is somewhat a more subtile distinction then the former by Zones; for as much as that is made by the combination of such Parallels as are principally named and of chiefe note, as the Tropicks and Polar circles. But this indifferently respects all without difference. This first beginning and measure, as well of this as all other measures of the earth is the Equatour, for that which is most perfect and absolute in euery kinde ought to be the measure of all other. But yet wee must vnderstand, that although wee beginne our account of the Climats from the Equatour; yet the Equatour it selfe makes no Climate, but on∣ly the Parallels which are thereunto correspondent. For as it is before shewed, vnder the Equatour it selfe, the artificiall dayes are all equall in length, containing only twelue houres: wherefore beginning from the Equatour betwixt that and the third Parallell, wee count the first climate: from the third to the sixt, the second Climate: and so all the rest, making the number of the Climates double to the number of the Parallels; so that one and the selfe same Parallell, which is the end, and bound of one Climate is the beginning of the next; whence wee see that to the constitution of euery Climate three Parallels concurre, whereof two are extreame, comprehending the bredth of the said Climate, and one diuiding it iust in the midst. A Parallell therefore differs from a Climate, as a part from the whole, be∣ing one circle correspondent to the Equatour, whereas a Cli∣mate is a space contained in three Parallels. Secondly, as a Pa∣rallell is conceaued to adde to the artificiall day one quarter or fourth part of an houre; so a Climate makes halfe an houre; so that by how much any Climate is distant from the E∣quatour, by so many halfe houres the longest day of that Climate goes beyond the longest day of the place vnder the Equatour. These Climates therefore cannot bee all of one e∣quall quantity; because the Equatour is a greater circle, and

comprehends the greatest space in the Earth: so that it must needs follow that these Climates neere the Equatour being made by the combination of greater circles are greater then those neerer the Poles. But because all Climates are made by the combination of Parallels; wee are to vnderstand that there are three sort of Parallels to bee knowne in Cosmographie: The first are those which doe distinguish the latitude of places, ta∣king their beginning from the Equatour; and are in an ordinary Globe of Mappe distinguished, sometimes by 10, sometimes by 15 degrees. The second kinde of Parallels are those that make the Zones, which are indeed some speciall named Parallels, as the Tropicks and the Polar circles: The third sort are called Ar∣tificiall Parallels; because they shew the distances of artificiall dayes and nights, which are commonly noted in the margent of a Geographicall Mappe, which last sort of Parallels are here chie∣fly to be vnderstood.

1 The Zones and Climates agree in forme but differ in greatnesse, number and office.

The Climates are so called (as we haue said) because they de∣cline from the Equatour, and are spaces of the Earth containing two Parallells, in which the longest day is varied by halfe an houre. These agree with the Zones in some sort: for both of them are spread by the latitude of the Earth, and by Parallell circles compasse it about as so many girdles: Ne∣uerthelesse they differ one from the other. 1. In Greatnesse, be∣cause the Zones are greater, the Climates lesser spaces in the Earth. 2. In Number, because there are only fiue Zones, but ma∣ny more climates. 3. In Office, vse and effect, because the Zones are to distinguish the mutation of the quality of the aire and shaddowes according to diuerse Regions of the Earth: but the Climates are vsed to shew the greatest differences of houres in the day: to shew the variation of the rising and setting of the starres, for places vnder the same Climate haue the same quan∣tity of dayes and nights, the same rising and setting of the starres, whereas places seated vnder diuerse climats haue a great vari∣ation in the dayes and nights, and a diuerse rising and setting of

the stars: for as often as the longest or Solsticiall day of one place, differs from the longest day of another by the space of halfe an houre, a new Climate is placed: wherefore vnder the Equatour or middle part of the earth the dayes are alwayes equall, to wit, of 12 houres: which beginning from the Equatour, if wee ap∣proach towards either Pole, so far as the greatest artificiall day amounts to 12 ½, we may assure our selues that wee are come to the first Climate: and so forward still the greatest day of our Cli∣mate will by so much exceed the greatest day of the other. As the Climates differ one from the other by halfe houres, so the Parallels by quarters, as we haue shewed: and shall more fully explaine in this Chapter.

2 The Climates compared one with the other, are not all of the same greatnesse.

Although the Climates are placed according to equall increase of dayes and nights, yet suffer they a great inequality: For no clime is equall to another in the same Hemispheare, but are still greater then other, by how much neerer they are to the Equino∣ctiall circle; for the latitude of the first Climate is reckned to be about 8 degrees, which make 480 Italian-miles: but of the last not so many minutes as quarters of miles.

11 In Terrestriall Climates, two things are to be vnderstood; 1 The Inuention: 2 The Distin∣ction. The Inuention teacheth the manner how to find out in what Climate any place lieth. The finding out of any climate depends vpon the obseruation of the length of the day; for the length of the day being once known, the Climate will also bee found out by this Rule.

1 Double the houres aboue 12, and the Product will shew the Climate▪

The reason of this rule is intimated before; to wit, that the cli∣mates are distinguished the one from the other by the space of halfe an houre of the longest day: Now the dayes vnder the e∣quatour are alwayes equall, containing 12 houres in length: from which towards the Pole they are increased by degrees: where∣fore the number of the Climates must needs bee double to the number of houres aboue 12: as for example, if I should find out in what Climate England is situated: I find the length of the longest day to be about 18 houres, which is six houres more then 12; this I double, and it will be 12; whence I collect, that Eng∣land is situated vnder the 12 Climate: A more compendious way of finding out the Climate of any place, is by a certaine Table, wherein against euery Eleuation of the Pole is set the iust Climate: which Table we shall insert hereafter. Here must bee noted that this rule which wee haue taught is to bee vnder∣stood of the Climates as they are absolute in nature, and not of Ptolomies Climates: If any man would finde out the Climates of Ptolomie, hee must first cast away three quarters of an houre, which is 45 minutes; because his Climates, as wee shall shew, beginne not immediatly from the Equatour, but from the lati∣tude of 12 degrees.

12 Thus much for the Inuention: the Distinction of Climates in Northerne and Southerne Cli∣mates: both these againe are of two sorts, either proper or improper.

13 The proper Climates are those which are placed between the Equatour and the point neere the Polar circle: The improper are those from the Polar circle to the Pole it selfe.

Wee must vnderstand that the climates are considered two manner of wayes, 1 Absolutely in respect of the whole Terre∣striall Spheare. 2 Comparatiuely, in respect of the knowne ha∣bitable

part of the Earth: According to the latter consideration the ancient Geographers haue otherwise distinguished the Cli∣mates then the new writers: whence ariseth a great difference and confusion amongst them, in defining the number of the cli∣mates. For sometime they will haue a new climat put whenso∣euer the day increaseth a quarter of an houre: sometimes at halfe an houre, sometimes at difference of an whole houre or day. But the doubt is easily answered, and reconciled by our former di∣stinction; for whereas they put the difference of climates to be halfe an houre, it is to be vnderstood of these which are pro∣per climates betwixt the Equatour and the Polar circle, for it is certaine that beyond this circle the artificiall day increa∣seth, not only by houres, but by dayes, weeks, months; so that another account must bee made of such climats then of the former. But it hath been generally taken for those climates of the Ancients: now the distinction of climates amongst the An∣cients is of two sorts. The first was of the Geographers before Ptolomy who placed the vttermost bound Northward in the 25^th degree of Latitude or Eleuation, and so made only seuen climates. These 7 climates were all vnderstood to bee in the habitable parts wherein they were marked and designed out vnto vs by names taken from Citties, Mountaines, Regions, and such like remarkable places, where we are to conceaue that cli∣mate as neere as may bee guessed to runne through the middle of any such Region, whereof it taketh its name: But the better to vnderstand the Distinction of the climates, as well with the Ancient as Moderne Cosmographers, we will insert this follow∣ing Theorem.

1 In the placing and Number of the Climates and Parallels, there is a great diuersity be∣twixt the Ancient and Moderne Geogra∣phers.

This hath been before mentioned: but for better distinction we haue reserued the handling of these differences to this pro∣position,

which may serue as a Carollary to the rest. First wee take it as granted that Ptolomy so appointed the Parallells (out of which the climates must arise) that he numbred 38 both wayes from the Equatour: to wit, 38 towards the South, and so many towards the North. These Parallels he so distingui∣shed, that 24 he numbred by quarters of houres, foure by halfe houres, foure by whole houres, and six by whole months. Hence is it that Geographers say, that a new Parallell is to be placed sometimes whereas the longest day increaseth by a quarter of an houre; sometimes where it increaseth by a halfe, sometimes by a whole houre, sometimes by a whole moneth. The first is to be vnderstood of those 24 Parallels which were deliuered by the Ancients before Ptolomy. The second, third, and fourth of such as were vnknowne vnto those Ancients before Ptolomy. To reduce all into order we will set downe this distinction. The distinction of the Climats is either ancient or new. The Anci∣ent was againe twofold: either former or latter. The former was that which was set downe before Ptolomies times, where∣in there were assigned seuen Climates according to the com∣mon opinion (though Mercator grants but 5) These Authours placed their Northerne bound in the 25 degrees or eleuation: The later distinction was almost the same, but somewhat corre∣cted by Ptolomy, who placed 9 Climates towards the North. The first passed by Meroe a Citty of Ethiopia, where the longest or Solstitiall day is 13 houres. The second by Siene in Egypt, where the longest day is 13 ½: The third by Alexandria in Egypt, where the longest day is 14 houres, the 4^th by the Iland of Rhodes, where the longest day is of 14 ½. The fift by Rome, where they haue the length of the longest day 15 houres. The sixt by Pontus, where the longest day is 15 ½ houres. The seauenth by the mouth of Boristhenes where the longest day is of 16 houres. Neuerthelesse some haue drawne the 6 Climate by Boristhenes in Sarmatia, and the sea∣uenth by the Riphaean mountaines. Ptolomy to this number addes two more, and so reckons them that the 8 should passe by the Riphaean mountaines, and the 9 by Denmarke where the day at longest is 17 houres. To these Northerne Climats they

opposed so many towards the South, which they called Anti∣climates. These as it should seeme in Ptolomi••s time were I∣maginary altogether, because few or no places were discoue∣red at that time beyond the Line. But to leaue P••olomy and his old Authors, and examine the industry of later Geographers, wee shall finde the Distinction of the Climates to bee twofold; either vnperfect wherein they numbred onely 19 Climates; or perfect, wherein they accounted 46 or 48, of which 23 or 24 were Northerne, and the other on the opposite part, to wit, in the South. The perfect distinction of the Climates is againe (as later writers speake) either certaine or vncertaine. The certaine they call that wherein the Climates are distin∣guished and ranged from the Equatour to the Polar circle: For sithens the Northerne Regions are now discouered beyond 70 degrees of the Eleuation of the Pole, and a Climate is defined to bee a space comprehended betwixt three Parallels in the ha∣bitable Earth: wherein the length of the longest day is increa∣sed by halfe an houre; Therefore it must needs be, that from the Equatour to that habitable part of the Earth, wherein the lon∣gest day is 24 houres (which is not farre from the Pole-circle) there should be placed 24 Climates. The vncertaine distinction they call that which is betwixt the Polar circle, and the Pole it selfe, which may bee tearmed Improper; because in these Cli∣mates the day is not increased by halfe houres, as in the former, but first by whole Dayes, then by We••kes, and last of all by whole Moneths: In so much that vnder the Pole it selfe they haue 6 Moneths perpetuall day, and so long againe a continu••ll night. The Parallels whereof the Climates are made, were set downe by Ptolomie 38 (as wee haue said) but the later wri∣ters haue placed them so farre Northernly, that they reach to that tract wherein the Sunne tarries aboue the Horizon a whole 24 houres, and so haue numbred 23 or 24 towards the North, and so many towards the South. The cause of this diuersity is be∣cause some draw the first by the mouth of the Redde-Sea: o∣thers by Meroe: for the farther consideration of these climates corrected by later Goegraphers, they beginne their account from the Equatour it selfe, which in this case is the best rule of

certainty: because we hold that whole tract of Earth to bee ha∣bitable, as we shall proue in our second booke.

14 A Parallell is a space wherein the longest day is increased by a quarter of an houre.

Concerning the Parallels, little can be said more then were haue opened in the doctrine of the Climats: for (as we shewed) the one cannot be well vnderstood without the other: only to auoid ambiguity of speech, wee must consider that a Parallell may bee taken either for a Line or Circle, in which senfe wee tooke it in the fift Chapter; where we diuided them into Named or Name∣lesse: or else for a space bounded by circles as wee here vnder∣stand it. The neglect of this distinction hath made some Geogra∣phers speake sometimes improperly. The Parallell is found out by this rule.

1 Let the number of the longest day aboue 12 be multiplied by 4, and the Product will shew the Parallell.

The reason is giuen before in the doctrine of the Climates, be∣cause the Parallell space, according to Latitude, is but halfe the Climate: so that as in finding out the climate for any place wee ought to double the houres of the longest day aboue 12: so here wee ought to quadruple them, which is to multiply them by 4: As for example at Rome we finde the longest day to be about 15, which exceeds 12 by 3; which being againe multiplied by 4, will produce 12, which is the Parallell for the place.

2 The Parallels no where diuide the Climats in∣to two equall parts.

In the climates wee are to consider two things, either their la∣titude or bredth from North to South: or their longitude or extent from East to West. In respect of the former wee may hardly without sensible errour call the Parallell halfe the Cli∣mate, in regard the three lines whereof the climate consists, to wit, the middle and the two extreames, are not alwaies of like distance: but if we consider the extent of the Circumference as

is stretcheth i selfe betwixt East and West, we must needes ac∣knowledge much more: to wit, that of two Parallels, diuiding the same climate betwixt them, that that is manifestly the grea∣test which is next the Equatour, and that is the least which is neerest to the Pole: because the Circles which comprehend their Parallell spaces, continually decrease towards the Pole: so that if we imagine two men to trauell round about the earth, the one in a Parallell neerer the Equatour, the other neerer the Pole, in the same space of time; it must needs follow that he should goe far faster which is neerer the Equatour then the other neere the Pole: for howsoeuer Columella seemes to make a Parallell to haue in bredth 60 foot, and to intimate by consequence an e∣quality of the Parallels amongst themselues, yet must this bee vnderstood of Parallels which are neere one to the other neerer the Equatour, which comprehend a great space of land, and admit no sensible difference. Other matters which concerne the Climates and Parallells, shall be (God willing) vnfolded in our Tables in the next Chapter, when we haue spoken of the Inha∣bitants, and such other adiuncts appertaining▪ without the which this treatise will be vnperfect, depending for a great part on such circumstances as our method admits not in this place, but immediatly follow.

CHAP. X. Of the distinction of the Inhabitants of the Terrestriall Spheare.

1 HAuing hitherto treated of the distin∣ction of spaces bounded by circles in the Terrestriall Globe, to wit, Zones, Climates,

and Parallels; wee are now to treate of the Inhabitants, as such adiuncts as pro∣perly belong to such spaces; so farre as it concernes the constitution of the whole Spheare.

2 The distinction of the Inhabitants is two∣fold, either Absolute or Comparatiue: Abso∣lute as they may be considered in themselues without any comparison of one with the other.

3 The former is againe twofold: either from the Position of the Spheare, or the differences of their Sun-Shadowes: According to the po∣sition of the Spheare the Inhabitants may be said to haue either a Right, Oblique, or Parallell Spheare according to their Horizons.

What these three Spheares are, may appeare by that which we haue formerly spoken concerning the distinction of Horizons in the sixt Chapter of this Treatise, and therefore needs no farther repetition: we are in this place to treat of the seuerall accidents, and conditions of the Inhabitants. Out of the distinction of the threefold Spheare will arise 13 manners of habitation: which for more order sake, wee will reduce into certaine heads in this manner.

4 The people of a right Spheare are such as in∣ioy aright Horizon, whose proprieties shall be declared in this Theoreme.

1 The Inhabitants of a Right Spheare in respect of the heauens haue the same accidents.

These accidents are chiefly foure, 1 They inioy a perpetuall Equinoctiall, hauing their dayes and nights alwayes equall the one to the other: because the Sunne neuer swaruing from his Eclipticke, hath his course equally diuided by the Horizon. 2 With them all the starres equally set and rise; because all the Pa∣rallels wherein the starres make their Diurnall Reuolution are equally cut of the Horizon. 3 To them the Sunne is twice in the yeere verticall, that is directly ouer their heads, and twice againein the yeere Solstitiall: The former in the first degrees of Aries and Libra, the latter in the first degrees of Cancer and Capricorne: which diuerse propositions of the Sunne, some later Geographers haue tearmed foure Solstices: two higher and two lower. 4 Hence comes it to passe that they yeerely enioy two winters, and two Summers: likewise two springs and two Au∣tumnes. Their Summer when the Sunne is to them verticall: their winter when it is seated in either of the Tropicks. Their Spring and Autumnes while the Sunne is passing through the middle spaces betwixt both.

5 The people inhabiting an Oblique Spheare are such whose Horizon is oblique. The proprie∣ties belonging vnto them are either Generall or Speciall.

6 The Generall are such as agree to all those which inhabit an oblique Spheare.

1 All the Inhabitants of an oblique Spheare agree in two proprieties.

These two proprieties wherein they agree are these. 1 To all the Inhabitants without the Equatour vnder what Parallell soeuer, the dayes are equall to the nights only twice in a yeere, to wit, either in the beginning of the Spring, or the beginning

ofthe Autumne. At other times either the dayes increase aboue the nights as in the Summer, or grow lesser as in the winter. 2 To these inhabitants some stars are perpetually seene, as such which are neere the Pole to which they incline: some are neuer seene, as such as are farthest off from the said Pole: some rise and set, which are those which are in the middle space betwixt both; which are sometimes visible, and sometime lie hid.

7 The speciall Accidents of an Oblique Hori∣zon, are such as agree to speciall places in the same Spheare.

1 The Inhabitants of an Oblique Spheare of fiue sorts, inioying so many correspondent pro∣perties.

The first sort are of those, whose Zenith is betwixt the Equator and one of the Tropickes, euen vnto the 23. Degrees, 30. Scruples of eleuation of the Pole: In such a sort, towards the North be∣twixt the Line and the Tropicke of Cancer, are placed the inha∣bitants of Zeilan, the extreame part of the East Indies, His∣paniola, Guinea, Nubia, with some part of Arabia foelix, and all other places betwixt the Equatour and the Tropicke of Cancer in the Torride Zone. Towards the South in the same La∣titude, are placed the Brasilians, the Peruuians, the Iauans, with many others. The Accidents which happen vnto these Nations are these, 1. They may see all the starres except a few which are neere the Pole. 2. Their dayes and nights are some∣what vnequall, so that their longest day, or longest night, is not alway of the same quantity. 3. Twice in the yeare they haue the Sunne-verticall, but without the Equatour. 4. They haue two Summers, and two Winters, but not equally tempe∣red. 5. The length of their longest day reacheth to 13. ½ houres.

The second sort are such as inhabite vnder the Tropicke it selfe, whose eleuation of the Pole is equall to the greatest de∣clination

of the Sunne, which is 23. degrees, 30 Scruples. Vn∣der the Tropicke of Cancer is placed a great part of Arabia foe∣lix, East India, the Southerne parts of China, the higher parts of Egypt, and Siene. Vnder the Tropicke of Capricorne are pla∣ced the people of Monomotapa, and Madagascar, with other places: The accidents belonging vnto them are these, 1. To them appeare all the starres comprehended in one of the circles, but none of the other. As for example, to those inhabiting the Tropicke of Cancer, the starres included within the Articke Circle alwayes appeare, but neuer those which are in the An∣tarcticke: likewise to those which dwell vnder the Tropicke of Capricorne, all the starres appeare which are contained within the Antarticke Circle, but none of those included within the Articke Circle. 2. By how much neerer the Sunne approa∣cheth to their Zenith or Verticall point, by so much are their dayes lengthened; and by how much farther it goes off, by so much are they shortned: so that they inioy then their longest day, when the Sunne directly passeth by their Zenith. 3. To them the Sunne is verticall but once in the yeere: to wit, to those vnder the Tropicke of Cancer, when the Sunne enters into the signe; as to the other when it toucheth the first Degree of Capricorne. 4. They haue but one Summer and one Winter throughout the yeere.

The third sort, are such inhabitants as dwell in one of the temperate Zones betwixt the Tropicke and the Polar Circles from 24. Degrees of eleuation, to 66. Degrees, 30. Scruples. Such inhabitants towards the North, are (as wee haue shewed) almost all the inhabitants of Europe, Asia maior, and part of Africa: as on the other side towards the South, the Chylienses, the farthermost Africans, and those that dwell neere the straits of Magellane. Their properties are chiefly these, 1. Many starres are by them alwayes seene, and many neuer appeare. 2. Their dayes notably differ in inequality. 3. The sunne ne∣uer arriues at their Zenith, but is alwayes on the South of those which inhabite betwixt the Tropicke of Cancer, and the Articke Circle, and alwayes on the North side of such as dwell in the opposite temperate Zone. 4. They haue in the

yeere but one Summer and Winter, but by reason of the diuer∣sity of places much vnequall: for where the eleuation of the Pole is greater, the winter is much harder; but where it is lesser it is more temperate.

The fourth kinde of inhabitants, are those which reside vn∣der the Polar Circle, (which is their Zenith) where the tem∣perate Zone endes, and the cold beginnes: where the eleuati∣on of the Pole is beyond 66. Degrees 30. Minutes, in which Tract lies Noua Zembla, with many other Ilands not yet well discouered in the North: and perhaps as many more vnder the Antarticke Circle towards the South, lesse knowne than the o∣ther. The accidents belonging to them are these, 1. Those which inhabite vnder the Arcticke Circle, see all the starres in∣cluded within the Tropicke of Cancer, but neuer those with∣in the Tropicke of Capricorne: Likewise, those which liue vnder the Antarcticke Circle, see all the starres within the Tropicke of Capricorne, but neuer those within the other Tropicke of Cancer. 2. Their longest day at Midsummer is 24. houres, their night then being but a moment: likewise their longest night, as at Mid-winter, is but 24. houres, their day passing not a moment. 3. The Center of the Sunne euery yeere twice toucheth at their Horizons. 4. The Sunne at Noonetide is alwayes on the South of those which dwell vnder the Ar∣cticke Circle, except it bee in the Summer Tropicke, when it is the Mid-night, or Northerne point: likewise to those that are vnder the Antarcticke Circle, the Sunne at noone is alwayes on the North side, except vnder the Winter Tropicke. 5. They haue in the yeere one Winter and one Summer: but the Win∣ter farre colder, and the Summer slacker then in the forenamed places.

The fift and last habitation, is of those which are included betwixt the Polar Circle, and the Pole it selfe, from 66. De∣grees and 30. minutes of ••leuation to 90. In which Tract, little is discouered Northward, and in the South climate no∣thing at all. The speciall Accidents appertaining to them are these, 1. With them a few starres are seene to set and rise. 2. They haue an Equinox•• the Sunne touching the first De∣gree

of Aries and Libra. 3. They of the North Zone haue more dayes about the middle of Summer, and more nights in the Win∣ter: likewise, they of the South frozen Zone, the contrary. 4. They haue extreame cold Winters, and in stead of Summer, a small remission of cold. 5. The signes of the Zodiacke to them preposterously rise.

8 The inhabitants of a Parallell Spheare are discouered in this proposition.

1 The inhabitants of a Parallell Spheare enioy but one kinde of habitation, in respect of the Heauens.

A Parallell Spheare, I here accurately vnderstand for that po∣siture of the Globe, wherein the Pole of the world is precisely placed in the Zenith, or eleuated to 90. degrees of Altitude: be∣cause onely in such a site, the Equ••tor and the Horizon agree in one, and lye parallell to all the rest of the Parallell Circles: which places, whether it bee at all capable of habitation by reason of cold, wee shall discusse hereafter in the second part: but out of supposition admitting a place of habitation, these accidents will happen, 1. The fixt stars which they see, are alwayes seene so, that with them there is no point of East or West; for the starres neuer rise nor set. But the Planets rise and set, but not by their diurnall, but proper motion. 2. They haue a continuall day of sixe moneths, and a night also as long, the Sunne rising conti∣nually in the first degree of Aries, and setting in the first of Libra. 3. The Sunne in the Equinoctiall points, for all the time that hee is aboue the Horizon (as all the other starres) is turned round about in manner of a wheele. 4. The Equatour serues in place of the Horizon, and the Equatour is euery where equi∣distant from the Pole 5. They haue one Winter and one Sum∣mer, the former exceeding cold, the latter lesse warme then ours.

9 The second distinction of the inhabitants

of the earth is taken from their Noone-shad∣dowes.

The Sunne in diuers parts of the earth diuersly spreads his shaddow, because the Gnomons or Opacous bodies by which the shadowes are made in the earth, are in diuers places diuersly op∣posed, or obiected to the Sunne: for whereas the Sunne so runs in his Eclipticke Circle betwixt the two Poles, that though his passage be in an oblique Circle, yet he neuer comes so farre as the Poles themselues: it necessarily must be, that sometimes he should shoot forth his beames perpendicularly, as when it is in the verticall point of a place; sometimes Obliquely, as when he de∣clines either one way or other from the verticall point; some∣times in parallell wise, for as much as in some places of the earth, the Sun cleauing as it were to the Horizon, casts out his beames parallell and equidistant to the plaine of the Horizon. The right or perpendicular▪ beames of the Sunne, falling on the superficies of the earth at right Angles, are turned and reflected into them∣selues, and so make no shaddowes at all. But the oblique beames, in that they are not reflected into themselues, must of necessity produce shaddowes, yet in diuers manners; for those Sunne-beames which obliquely proiect themselues on the plaine of the earth, so as they come not from the Horizon it selfe, will make such kinde of shaddowes as shall proportionally agree with their Gnomons, or Opacous bodies, and such whose magnitude may in a manner be designed out, and certainly measured by the sight. But on the contrary part, the beames which are esteemed paral∣lell to the plaine of the Horizon, finding no solide obstacle or let, shoot forth infinitely, making no Angles on the superficies of the earth, and can haue no proportion at all with their Gnomons, that the shaddow may be any way designed by our eyes. But here we are to consider, that the shaddowes chiefly to be considered, are the Meridian or Noone-shaddowes, which take their distinction from the diuers incidency of the beames, which the Sunne casts forth at noone. According to this manner.

10. The inhabitants of a place in respect of the shaddowes are either Amphiscij, Heteroscij, or Periscij. The Amphiscij are those, whose Noone-shaddowes (but at diuers times of the yeere) are ••ast both wayes; that is to say, North and South.

Amphiscij signifies as much as people of a double shaddow: such are they which inhabite betwixt the Equatour and the Tropickes, where the eleuation of the Pole equals not 24. de∣grees: These men haue the Sunne twice euery yeere in their Zenith or verticall point, and then they make no shaddowes at all; and therefore they are called Ascij, or without shad∣dowes. But when the Sunne passeth from their verticall point towards the Northerne signes, then at noone it will cast the shaddow towards the Southerne coast: But contrarywise, com∣ming from the Zenith toward the Southerne signes, the shaddow will bee darted toward the North, which is euident out of the Opticke principles; because the shaddow is alwayes found to be opposite in place to the Sunne-beames, the Gnomon, or darke body interposed.

11. The Heteroscij are those, whose Noone-shaddowes turne only one way, that is, either toward the North, or toward the South.

These Nations inhabite in a, temperate Zone, betwixt the Tropicke and the Polar Circles, whereas such as dwell in the temperate toward the North, betwixt the Tropicke of Cancer and the Polar Circle Articke, haue their noone-shaddowes cast Northward. But those on the other side of the Equatour▪ dwelling betwixt the Tropicke of Capricorne, and the An∣tarcticke Circle, cast their shaddowes Southward: Of the for∣mer

sort are Grecians, Italians, French, Spaniards, Germans, Po∣lonians, Suedians, Danes, English, and the rest inhabiting our temperate Zone: which gaue occasion of that speech of Lucan the Poët, concerning the Arabians comming into Thessaly, in the warre of Hanniball and Pompey;

Ignotum vobis Ar••bes venistis in orbem, Vmbras mirati nemorum non ire sinistras.

Y'are come Arabians to an vnknowne land, Wondering the shades nere take the Southward hand.

Which verses are in this sense to be vnderstood; Poets are said to looke and turne their faces towards the West, so that the South must of neces••ity be counted the left side: Now the place whereunto the Arabians came, being a part of Thessaly, where such dwell who only cast their shaddowes one way, to wit, Northward; but Arabia their naturall Countrey, being suppo∣sed to be included in the Torrid Zone, where the shaddowes were said to be cast both wayes, they are said to wonder: The reason why our shaddowes at noone are cast alwayes toward the North, and the others toward the South, is related before, to be because the shaddow doth alwayes occupie or possesse the place opposite to the Sunne, or light body.

12 The Periscij are such in habitants whose shad∣dowes are mooued round about them in a circular forme.

In some places of the earth the Noone-shaddowes take not their beginning from our heads, but of one side, and are extended forward to the plaine of the terrestriall Horizon, and so moo∣ued round about the Opacous body, as about a Gnomon: whence they are called Periscij; which is as much to say, as men hauing shaddowes mooued round about; such is their habitation which are included in the Frigid Zone, circumscri∣bed within the Polar circles, and the Poles: Here the Sunne neuer directly passeth by the crowne of their heads, but at one side: so that they haue the Pole for their verticall point, but

the Equatour, as it were, for their Horizon. These Periscij are of two sorts, for some are contained in the Arcticke circle, the other in the Antarcticke, whereof both are as yet vndiscoue∣red; especially the Antarcticke, being farthest off from our climate.

1 The habitation of the Amphiscij comprehends 7. Parallels, of the Heteroscij 41. of the Pe∣riscij 6. Moneths.

Of the nature and accidents of these three sorts of people there needs no more to be spoken, then wee haue deliuered before in this Chapter; Neuerthelesse, for a recapitulation of our former doctrine in this & the precedent Chapter, it will not be amisse to insert this table of Climates, set out by our exactest Geographers; wherein is expressed (as it were) to our view the respect and seuerall accidents, which belong to these seuerall inhabitants.

13 Thus much for the Inhabitants absolutely considered: The inhabitants compared one with the other according to their position, are the Perioeci, Antoeci, and Antipodes.

14 The Perioeei are those inhabitants which dwell in the two opposite points of the Pa∣rallell circle.

15 The Antoeci are such as dwell vnder the same Meridian, but in diuers Parallels equally di∣stant from the Equatour.

16 The Antipodes are such as inhabite vnder one Meridian, but vnder two Parallels equidistant from the Equatour, and two opposite points of those Parallels.

A Table of the Climates belonging to the three sorts of Inhabitants: Pag: 229.

Inhabitants belonging to severall Cli∣mats.	Climes	Parallels	The long∣est summer day. Hou. Scr.	Latitude & elevati∣on of Pole. Scr. Degr.	The breadth of the Climats. Deg. Scr	The places by which the Climates passe.
	0	0 1	12 0 12 15	0 0 4 18	4 18	The beginning from the Aequatour.
	1	2 3	122 30 1 45	8 34 12 43	8 25	Sinus Arabicus or the Red Sea.
Amphiscij.	2	4 5	13 0 13 15	16 43 20 33	7 50	Meroe an Iland of Nilus in Aegypt.
	3	6 7	13 40 13 45	23 10 27 36	7 3	Siene a Ci••ty in A∣frica.
	4	8 9	14 0 14 15	30 47 33 45	6 9	Alexandria in Ae∣gypt.
	5	10 11	14 30 14 45	36 30 39 2	5 17	Rhodes and Baby∣lon.
	6	12 13	15 0 15 15	41 22 4•• 3••	4 30	Rome and Helle∣spont.
	7	14 15	15 30 15 45	45 29 47 20	3 48	Venice and Mil∣laine.
	8	16 17	16 0 16 15	49 21 50 33	3 13	Podalia and ••he les∣ser Tartary.
	9	18 19	16 30 16 45	51 58 53 17	2 44	Batavia and Wit∣••enberge.
		20	17 0 17 ••••	54 ••9 55 ••4	2 17	R••stoch.

	11	22 23	17 30 17 45	•••• ••7 57 34	2 0	Ireland and Mos∣covy.
Ieteroscij.	12	24 25	18 0 18 15	58 26 59 14	1 40	Bohus a Castle in Norwey.
	13	26 27	18 30 18 45	59 59 60 40	1 26	Gothland.
	14	28 29	19 0 19 15	61 18 61 53	1 13	Bergis in Norwey.
	15	30 31	19 30 19 45	62 25 62 54	1 0	VViburge in Fin∣land.
	16	32 33	20 0 20 15	63 22 63 46	0 52	Arotia in Sweden.
	17	34 35••	20 30 20 45	64 6 64 30	0 44	The mouth of Dare∣cally a riuer of Swedē
	18	36 37	21 0 21 15	64 49 65 6	0 36	Diverse places of Norwey.
	19	38 39	21 30 21 45	65 21 65 35	0 29	Suecia, Alba Rus∣sia.
	20	40 41	22 0 22 15	65 47 65 57	0 22	With many Ilands
	21	42 43	22 ••0 22 45	66 6 66 14	0 17	Therevnto adioy∣ning,
	22	44 45	23 0 23 15	66 20 66 25	0 11	Wanting speciall names,
	23	46 47	23 30 23 45	66 28 66 ••0	0 5	And Landmarkes.
	24	48	24 0	66 31	0 0	Island vnder the A••¦tick circle.
	Here the Cli∣mats are accoū∣ted by the mōths from 66 Degr.	Menses	1	67 15	These Climates are supposed to passe by Diverse Ilands within the Artick circle, as

These names being originally Greeke are taken from the di∣uerse manner of dwelling of one nation in respect of another. The Perioeci are called such as dwell (as it were) about the He∣mispheare in the same Parallell in two opposite points: the one in regard of the other being Easterne, the other Westerne: so that they are supposed to differ the one from the other 180 de∣grees which is

[illustration]

the semicircle: where we are to note, that these degrees are to be num∣bred, not in a greater but a lesser Parallell, which is lesse then the Equa∣tour. For they which are vn∣der the Equa∣tor it selfe in 2 opposite points are to bee ac∣counted rather Antipodes, although (for ought I see) the name might agree. The Antoeci (as the name imports) are such as dwell one against another, hauing one selfe-same Meridian and equall distance from the Equatour, the one in the Nor∣therne, the other in the Southerne Hemispheare. The Anti∣podes (otherwise called Antichthones) may popularly bee des∣cribed to bee such as dwell feet to feet one against the other: so that a right line being drawne from one side to the other, will passe by the Center of the world▪ whence they precisely are distant the one from the other 1800 in a greater circle: wherein they are distinguished from the Perioeci, which are diuided by the degrees of a lesser circle: such compared one to the other are the Americans and the Easterne Indians about the riuer Ganges; the Inhabitants of Peru and Calecute: those of Peria &

Summatra to England I finde no other Antipodes but the Sea, or at least some parcell of land in the South continent neere Psittacorum Regio: Here is to be noted that the former defini∣tion of Antipodes giuen by the ancients, was only to bee vnder∣stood of the knowne habitable part of the Earth; because such as dwell directly vnder the Equatour, or either of the Poles, although they may bee Antipodes agree not to that definition: by reason the former are Antipodes only in opposite points of the Equatour: the other of the Meridian. Whether there were any Antipodes or no, was made a question amongst the Anci∣ents, in so much that Saint Augustine in his booke de ciuitate Dei, and Lactantius in his third booke of Institutions, seemes stiffely to defend the contrary: which opinion is supposed to grow out of their contempt or neglect of Mathematicall stu∣dies, in those ages wherein the zeale to religion was most vn∣necessarily opposed to Philosophie, and the mistresse forsaken of her best hand-maides: which ignorance of the Ancients was so farre deriued to posterity, that in the yeere of our Sauiour 745 one Boniface Bishop of Mens, was accused before the Pope Zachary Virgilius Bishop of Salisburg, for heresy, in that hee, auerred there were Antipodes: The matter being first preferred to the King of Bohemia, and an appeale made vnto the Pope, it happened that the honest Bishop for this assertion, was flatly condemned for hereticall doctrine, and inforced to recant his opinion: yet is it wonderfull how such matters were thus deci∣ded: for granting these two easie grounds. First that the earth is Sphericall, a proposition proued in their time; 2 That euery place, or at least two opposite places in the Terrestriall Spheare may bee habitable; it must of necessity follow, that such Anti∣podes must bee granted: which makes me to imagine that Saint Augustine absolutely and grossely denied not the Antipodes; because in setting downe the premises and grounds of our opi∣nion, hee seemed to vnderstand them too well to deny a ne∣cessary induction, being a man of so great a wit and apprehen∣sion: but questionlesse he thought that the Torrid Zone, which by most of the Ancients in his time, was reputed vnhabitable and vnpassable, no man had yet set his foot in those remote

parts beyond the line: so that it seemed in him not to arise out of ignorance of the constitution of the earthly Globe: but out of the receaued opinion of the Torrid Zone, and the vast Ocean: the one of which hee held vnhabitable, the other vnpassable: from whence also sprang vp an argument, or rather an idle fancie, that the Antipodes could not be admitted without granting another Sauiour, and another kinde of men besides Adams posterity: for if this coniecture had not taken place, the Pope (I suppose) would neuer haue proued himselfe so ridiculous a Iudge, as to haue condemned Virgilius for heresie. As for Lactantius (how∣soeuer otherwise a pious eloquent Father) the weakenesse and childishnesse of his arguments, will to any indifferent reader dis∣couer his ignorance in the very first rudiments of Cosmogra∣phie. Here we may learne how farre religion it selfe is wron∣ged by such who set her opposite to all her seruants. But what∣soeuer the Ancients out of their glimring reason haue coniectu∣red, our times haue sufficiently decided this controuersie; wher∣in such Antipodes are established both by reason and experience: which mat••er wee shall reserue to our second booke; wherein we shall declare how farre, and in what sense the Earth may bee tearmed habitable.

1 Those which are to vs Perioeci, are the Antoeci to our Antipodes: our Antoeci the Periaeci to our Antipodes: likewise our Perioeci are the Anti∣podes to our Antaeci.

This Proposition as a Corollary may by necessary consequence be deduced out of the precedent definition, and be well expres∣sed out of the constitution of the artificiall Globe, and needs no farther demonstration.

2 The Perioeci, Antoeci, and Antipodes are di∣uersly distinguished in respect of the celestiall ap∣parences.

The proprieties of the Perioeci are chiefly foure. 1 They haue the same eleuation of the Pole, and therefore the same temper

of the yeere, and the same length of dayes and nights. 2 They dwell East and West in regard one of the other. 3 They haue contrary times of dayes and nights: for when the one hath his Noone, the other inioyes his mid-night: likewise when the Sun with the one riseth, it setteth with the other. 4 They haue the same Zone, Climate, and Parallell; but differ by a semicircle▪ to wit, 180 degrees. To the Antoeci they haue likewise assigned 5 proprieties▪ viz. 1 They inhabite the like Zones, but in di∣uerse Hemispheares. 2 They haue the same eleuation of the pole, but not of the same pole: because the one sees the pole Arcticke, the other the pole Antarcticke, equally raised aboue his Horizon. 3 They haue Noone and Mid-night iust at the same times. 4 They inioy the same temper of the Heauens▪ 5 They haue the seasons of the yeere contrary. For when the Southerne Antoeci haue their Summer, the Northerne haue their Winter; and contrariwise: when the Northerne haue their spring, these haue their Autumne. To the Antipodes they haue allotted 3 Pro∣prieties. 1 That they haue the same eleuation of the pole, though not of the same pole. 2 They haue the same temper of the yeere, and the same quantity of dayes and nights. 3 They haue all the other accidents contrary: For when the one hath Night the other hath Day, when one Winter, the other Sum∣mer; when the one the Spring, the other Autumne; and con∣trariwise. These accidents and proprieties here mentioned, must be vnderstood in respect of the Heauens only. The qualities ari∣sing from diuerse other Accidentall and particular causes in di∣uerse places of the Earth, we shall differre vnto our second part▪

CHAP. XI. Of the Longitudes and Latitudes.

1 THe distinction of the Terrestriall Globe according to certaine Spaces, being for∣merly explaned, we are now to treat of the Distinction of the said Spheare according to certaine Distances.

2 A Distance here we vnderstand to be a direct line drawne betwixt two points in the Earth: such a Distance is twofold, either Simple or Comparatiue.

3 The Simple Distance is taken from the two great circles, to wit the Meridian, or the Equatour: which is either the Longitude or La∣titude.

The diuision of Distances into the Simple or Comparatiue, is most necessary: for it is one thing for a place absolutely taken in it selfe, to be distant from some fixt point or other in the Globe: Another for two places to be compared betwixt themselues in regard of such a fixt point: for as much as the former implies on∣ly the distance betwixt two points, the other the distance of two such points or places in respect of the third. These points, from which such points are said to be distant, are either found in the Meridian Circle, from which the Distance is called Longitude; or else in the Equatour, whence we call it Latitude.

4 The Longitude is the distance of any place Eastward from the first Meridian.

To vnderstand the better the Longitude, we must consider that it may be taken two wayes: either Generally, or Specially: In the former sense it is taken for the Distance of the whole Earth, stretched from the West vnto the East, and contrariwise from East to West. The bounds or limits of this Longitude were by Ptolomie and the ancient Cosmographers set no farther distant then the halfe circle, containing 180 degrees; because the rest of the Earth lay at that time vndiscouered. The end of this space towards the East, was the Kingdome of China, at the far∣thest part of all India, distant, as wee said, from the Fortunate Ilands where Ptolomie placed the first Meridian, 180 degrees: which being taken in the Meridian, and resolued into Miles, ac∣cording to our former rules, will giue 10800 Italian miles: but this space delineated out by the Ancients, was very scant and narrow in respect of the other parts since found out, being added to the former. For beyond the bound set by Ptolomie in the East, it is manifest that 60 degrees are found out and made knowne. An example whereof wee haue in Scythia with∣ou•• the mountaine Emaus, which is knowne to extend it selfe 60 degrees Eastward towards the Kingdome of Cathay, disco∣uered by the Portugals: so that the breadth of the Earth East∣ward is fully knowne so farre as 240 degrees, which being mea∣sured in the Equatour will amount vnto 14000 miles. More∣ouer towards the West, beyond the Fortunate Ilands, it is knowne to stretch to the farthest border of America; so that 340 degrees of the earth is fully detected, if not all the rest be∣ing only 20 degrees, which are only deficient to make vp the whole circle. Which wee may the sooner credit; because our times haue brought forth (for ought any Authors haue related) the most excellent Nauigators of all ages, which haue say∣led the vast Globe of the Earth round about, and left behinde them a foundation whereon others might easily build. But to let passe the Generall Longitude of the Earth betwixt the East and the West; Wee must vnderstand that the Longitude here

mentioned is to bee taken in a more speciall sense, for the Di∣stance of any place from the first Meridian, being placed either in the Canaries, as the Ancients would haue it, or in one of the Azores according to the latter Geographers. This then must be the bound from whence wee must beginne our account; The subiect wherein the number of degrees may bee taken, may bee the Equatour or Parallell. Whence by some the Longitude of a place is defined to bee an Arch of the Equatour or Parallell in∣tercepted betwixt the first Meridian and the verticall point of the place proposed: so that by necessary consequence, such places as are subiect to the same Meridian, in the same Hemispheare, Easterne or Westerne, haue the same Longitude, which is the distance from the point of the West: but places declining more towards the East haue the greater Longitude; but neerer to the West, les••e.

1 Places inioying the same Longitude are not al∣wayes equally distant from the first Meridian, and contrarywise places equidistant from the first Meridian haue not alwayes the same Longitude.

The reason is euident out of that which hath beene often spoken before: because the degrees of a greater circle are greater, of a lesser lesse, according to the greatnesse of the circle. Now the Longitude of a place measured in the Equatour, will answer to 60 Italian miles: but in other Parallels lesse.

2 The difference of Longitudes begets the diffe∣rence of Times: Those therefore which exactly are subiect to the same Longitude, haue their Noone at the same moment: but where the Longitudes are different, the Noonetides are also different.

That the difference of time is varied according to the difference of Longitude in diuerse parts of the Earth, is a matter obuious to euery mans vnderstanding, out of two premised grounds. 1 That the Earth is Sphaericall. 2 That the Sunne in his Diurnall course once in 24 houres compasseth it round: whence it comes to passe that places situate Eastward, see the Sunnes sooner then those which are placed in the West, and that with a proportionall difference of time, that to euery houre in the Sunne motion is assigned a certaine number of correspondent miles: which is in some sort expressed in a Geographicall Globe or Map, wherein we shall finde described 12 Meridians, which diuide the whole compasse of the earthly Spheare into 24 equall parts; in such sort that betwixt each of the two neerest Meridians, are reck∣ned 15 degrees, which make one houre: by which wee may more easily vnderstand how soone the Noone-time happens in one Citty before another: for if one Citty stands Eastward from another the space of three of those foresaid Meridians, it is eui∣dent that it will inioy noone three houres before the other. The reason of this difference of times, is the difference of Longitudes, wherein to euery houre the Cosmographers haue allotted 15 degrees in the Sunnes Diurnall motion: so that 15 degrees mul∣tiplied by 24 houres, which is the whole naturall day, there will bee produced 360 which is the number of degrees in the whole circle,

3 If two men from the same place trauell, the one Eastward, the other Westward round about the Earth, and meet in the same place againe: they shall finde that he which hath gone Eastward hath gotten, and the other going Westward hath lost a day in their account.

This is without difficulty to be vnderstood, out of the change of Longitudes, seconded by their trauell, varying perpetually the quantity of the day: for it is manifest, that hee who from a∣ny place assigned saileth Eastward mouing continually against

the motion of the Sunne, will shorten somewhat of his day; taking away so much from it, as his iourney in proportion of di∣stance, hath opposed and anticipated in the time the Di∣urnall course of the Sunne: so that daily gaining something from the length of the day, which must bee elsewhere recom∣penced. It must needs be, that in the whole circuite of the earth, it will amount to 24. houres, correspondent to the whole cir∣cuite of the Sunne, and the compasse of the earth, which will make another day: Likewise, if we suppose another in com∣passing about the earth, to goe Westward, it cannot bee otherwise imagined, but that seconding the course of the Sunne, by his owne iourney; hee will daily adde some∣what to the length of his day, answerable to his distance, from the place wherein hee began to follow the Sunne in his course from East to West. The daily addition to the length of the day, proportionall to the longitudes which he changeth, (the Sunne running a like course) must daily diminish somewhat of the Di∣urnall course of the Sunne, and so at his iourneyes end, which was supposed to be the whole circuite of the earth, answerable to 24. houres in the Sunnes course, it will loose a whole day. To demonstrate both these cases, wee will imagine in supposi∣tion, that of these two trauaillers going the one Eastward, the other Westward, the former should take away from the length of the day, or the latter adde to it for euery 15. miles one mi∣nute. Then by the golden Rule, if 15. miles either subtract or adde one minute in the length of the day, must 21600. miles, which is the whole compasse of the earth, accor∣ding to the same proportion, either subtract or adde 1440 mi∣nutes, which make 24. houres, the length of the naturall day. To confirme the demonstration by popular experience, I remem∣ber I haue read in the Hollanders discouery of Fretum de Mayre, that comming home into their owne Countrey, they found by comparing their accounts with their countrey∣mens at home, they had lost one day, hauing gone West∣ward, and so compassed the earth round. Hence will arise di∣uers consectaries not vnpleasing to be scann'd. One I will touch not much dissonant from our purpose; That three men residing

in the same place at one time, shall notwithstanding all vary one from the other in the dayes of the weeke, keeping yet an exact ac∣count: which to explaine the better, wee will suppose a Iew, a Sarazen, and a Christian, residing in the same towne together: It may so happen according to our former grounds, that the Sa∣razen according to the Law of Mahomet, shall obserue his Fri∣day, the Iew his Saturday, being his Sabboth: and the Christian the Lords day, being the Sunday; yet so, as all shall happen on the same day: all of them excluding any errour in their calcu∣lation. For supposition sake, wee will place them all at one time all together in Palestine on a Saturday; at which time, let vs imagine the Sarazen to take his iourney Westward, the Christian Eastward, so as both of them in their coasts com∣passe the world, to meet againe in the same place: The Iew all the while we suppose resident in the same place: it will follow by necessary consequence, that the Sarazen go∣ing about the earth Eastward, will loose one day; the Christian iourneying Westward, will gaine one day: the Iew remaining in the same place, will neither gaine nor loose. These three men then, meeting together againe after a yeere, two, or three, at the same place, must needs make a diuers account; for one and the selfe-same day, will bee to the Sarazen Friday, to the Iew Saturday, and to the Christian Sunday, if they ex∣actly calculate the time from their first meeting, to their re∣turne vnto the same place. Mee thinkes this, if there wanted other Arguments, were a reason sufficient to conuince some strait-laced men, who rigidly contend our Lords day (which they erroneously tearme the Sabboth) to bee meerely morall, as grounded on the Law of nature. If it were so, according to our premises before demonstrated, this absurditie would en∣sue necessarily: That the Morall Law, which they call also in a sort the Law of nature, is subiect to manifold mutation, which by our best Diuines is vtterly denied. The conseque••ce will easily follow, because it cannot be denied by any Christian, but that all nations of the world issued from Noahs Arke, the Seminary of mankinde, and spread themselues from thence o∣uer the face of the whole earth, some farther, some at a shor∣ter

distance: whereby changing the longitude with their habi∣tation, they must of necessity alter the differences of times, wher∣on they seeke to ground their Sabboth. Neither at this day can any man exactly and precisely obserue any one day, either as it was first appointed by Moses in the Leuiticall Law, as it was instituted by Christs Apostles afterwards; by reason of the ma∣nifold transportation of colonies, and transmigration of Nations from one Region into another, whereby the times must neces∣sarily bee supposed to vary. And if any more moderate should vrge, that not the exact seuenth day from the first institution, bound vs to obseruation; so one day in seuen bee obserued: it can hardly passe without exception, for as much as if any man, as Magellane, Drake, or Candish, should trauaile the world about, a day must needs be varied, as we haue shewed. Here I would willingly demand, whether such trauailers returning home into their owne countreyes, should celebrate the same Lords day ac∣cording to the institution of their owne Church; or else as they finde according to their owne account: If they obserue the lat∣ter, they must schismatically diuide themselues from the Church, and keepe a Sabboth of their owne, which in euery mans iudge∣ment would be thought absurd, as the mother of many inconue∣niences: If the former take place, then must the d••y be change∣able in his nature, and so one day of seuen of them should not be obserued. I speake not this to cherish any neglect of the duty we owe that day, but rather to proue it not meerely to be groun∣ded on the Law of Nature, as some would perswade; but rather an Ecclesiasticall constitution, deriued (as it seemes most proba∣ble) from the Apostles, though not in practice in Christs time, wherein the Iewish Sabboth was not yet abolished: But I haue dwelt too long on this, & may perhaps incurre sharpe cēsure, for wading too farre into the depth of Diuinity: But my Apology shall be this, that albeit I haue gone beyond my present subiect, I ••••ue not yet transcended the limits of my profession: I serue no faction, and therefore dare aduenture my language as free as my opinion.

5 Concerning the longitude, two things are to be knowne, 1. The Inuention. 2. The Ex∣pression. The Inuention proposeth vs the way and manner of the first finding out of the lon∣gitude of places.

There are few things in nature which haue more perplexed the wits of ingenious Mathematicians, then the exactest way of finding out the longitude of places: Not that the matter was o∣uer difficult in it selfe, but that they sought out a way to per∣forme this conclusion, not depending from the obseruation of the celestiall bodies and motions; a matter as yet neuer found out, and I feare mee vnpossible: Because they proposed to themselues one of these two wayes to finde it out; either by some magneticall instrument, or else by industry of nauigation: neither of which can much profit. Not the former, because there haue neuer beene any fixed points found in the Equatour, be∣twixt East and West, as betwixt North and South haue beene obserued: so that nothing can proceed out of the meere nature of the earthly Globe, whereon wee may ground any difference of longitude: Neither is the second very beneficiall, for that all voyages both by Sea and land, are very irregular and vncertaine, either by reason of sundry impediments, as rockes, mountaines; woods, contrary winds, and other dangers turning aside the di∣rect course of passengers from any direct way, or obseruation; or else by the Ignorance of Mariners, which seldome passe so farre on discouery: and if they doe, know not perfectly to de∣lineate out their iourney, as a Cosmographer would expect, to a∣ny tolerable satisfaction. Neuerthelesse, by Astronomicall ob∣seruation, wee haue many wayes left vs for the performance of this conclusion, as shall bee taught in these following proposi∣tions.

1 By an Eclypse of the Moone, the longitude may be found.

This conclusion is in this sort to bee performed: First, it be∣hooueth you to know, as you may by an Ephemerides, at what houre an Eclipse shall happen at some knowne place, whereof you are well informed of the longitude: Then must bee ob∣serued by an Astrolable, or other Astronomicall instrument, at what houre this Eclipse begins at that place, whereof you would willingly know the longitude: If the Eclipse doe be∣ginne in both places the selfe-same time, you may assure your selfe that these two places differ not in longitude. But if there be a difference in the time, then must there be a difference in the longitude, which to finde out, you may in this sort proceed: Take the lesser summe of houres out of the greater, and there will be remaining, either houres or minutes, or both: If there remaine houres, then multiply the same by 15; if minutes, di∣uide the same by 4; (for in this account as wee haue taught, 15. Degrees make an houre) and adde the difference so found vn∣to the longitude, if the Ecclipse appeare there sooner: but if later, subtract it from the longitude formerly knowne. If there remaine any minutes after the diuision, you must multi∣ply those minutes by 15; and so shall yee haue the Minutes of Degrees. To explaine this the better, wee will take this famili∣ar example from some of our later writers. The longitude of Pa∣ris was set downe by Ptolomy, to be 23 degrees; now we may be informed by an Ephemerides, that a certaine Eclipse of the Moone beginnes there 3 houres after midnight; out of this I would willingly learne the longitude of Tubing a towne in Sueuia: In this towne I obserue by some Astronomicall instru∣ment, at what houre the Eclipse there beginnes, which I finde to bee at three of the clocke and 24 minutes after midnight. Then by the subraction of the lesser number of time out of the greater, I finde the remainder to be 24 minutes, which diuided by 4. which makes one degree, the quotient will bee 6. degrees: and that is the difference, which if you adde to the knowne longitude of Paris (because the Eclipse begins there sooner then at Paris) it will amount to 29 degrees: wher∣by we may collect that the Longitude of Tubing is ••9. degrees. To this rule for the most part are squared all Cosmographicall

Tables of longitude, but yet in this happen diuers errours: 1. Be∣cause oftentimes in the Artificer there wants diligence in obser∣uing the right houre & moment of the Eclipse. 2. The diuers. E∣pacts & latitudes of the Moone are commonly neglected; wher∣fore some haue thought it the best way (if it were to be hoped) that diuers exact Astronomers should at diuers places obserue the same Eclipse, and so by conferring together according to the former Rule, finde out the longitudes of those places. But exact Astronomers cannot be so easily found in euery citie, wher∣of we desire to know the longitudes; or if there were such, they keepe not alwaies such correspondency in friendship; nei∣ther is an Eclipse of the Moone alwayes at command. Neuer∣thelesse, this way is not to bee despised, because where better wayes are wanting, wee must content our selues with what we finde.

2 By a Clocke, Watch, or Houre glasse, to finde out the longitude of a place.

This conclusion is to be performed in this manner; You must get you a watch or clocke, apt to runne (if you can) 24 houres; this watch must you, by the helpe of an Astrolabe, rectifie and set iust at such time as you depart from the place where you are, as bound to any other place, whereof you de∣sire to inquire the longitude: during which time, your diligent care must be to preserue your watch in motion without inter∣mission: being at last arriued at the place whereof you inquire the longitude, you were best to stay till such time as the Index shall precisely point out some perfect houre: At the same in∣stant it must bee knowne by an Astrolabe, what houre it is at the place where you are arriued; for if your Astrolabe and Watch should both agree in one, you might assure your selfe that there is no difference of longitude betwixt the place whence you came, and the place whereto you are arriued: For it is euident that in this sort your iourney hath beene either directly North or directly South vnder the same Meridian. But if this differ either in houres or minutes, they must be reduced vnto degrees in such sor•• as we haue shewed in the former way. Through

which you may finde out the Longitude which you desire to know: This inuention is by our Countryman Blundeuill ascri∣bed to Gemma Frisius; although I should take it to bee more an∣cient: but whose inuention soeuer it was, certainly it cannot but commend the Authour. Peter Martyr in his Decades, seemes to preferre this way before all the rest; neuerthelesse in this I cannot assent to his opinion, being one I had rather trust as an Historian, then as a iudicious Cosmographer: because the way cannot but admit of great vncertainty: in so much as a Watch or Clocke will moue inequally, being corrupted with rust, especially on the Sea, which alwayes abounds with moist va∣pours: wherefore on the Sea, some haue thought an Houre-glasse more conuenient, which is true in comparison of the Watch; but neither will the sands of an houre-glasse keepe al∣waies the like motion: If any certainty may bee this way, it must bee by the helpe of the Automaton or perpetuall moueable, of whose inuention we may sooner despaire then of finding out this conclusion.

3 By the distance betwixt the Moone and some knowne Starre, which is situate neere the Eclip∣ticke, the Longitude may be found out.

This way was taught by Appian, illustrated by Gemma Frisi∣us and Blundeuill, to whose manner of explication, wee haue for farther illustration added a figure of the Parallax where∣on this inuention is grounded. First then to shew this conclu∣sion, wee must first lay this ground: that the Distances betwixt the Moone and other starres in the firmament are varied accor∣ding to the difference of places: In so much as two men liuing farre distant in diuers places of the earth, beholding at one time the Moone and some other knowne fixt starre, will not finde the like distance betwixt them: whereof if any man doubt, he may be informed by this figure. Wee will imagine O to be the place of the Moone, as seated in the lower Orbe; G to bee the place of the fixt starre, whose distance from the Moone is inquired: E and F two stations and habitations of men dwelling on the earth, whereof wee may imagine the one to bee in Europe, the

[illustration]

[illustration]

other in America: It will be manifest that the inhabitant situ∣ate in F will behold the Moone in the point B; and the said fixt starre in G: (because as the Optickes teach vs, all things are seene in the places opposite to the eye) so that the distance be∣twixt the Moone and the said starre, will bee the Arch of the greatest Circle BG of the other side: the inhabitants situate in E, will behold the Moone by the ray EC in C. as like∣wise the said fixt starre G in the point G, by the ray EG: so that the distance betwixt the Moone and the fixt starre, will bee in that station the Arch of the circle CG. Now by the first common Axiome of Euclide, euery man must grant that the Arch of BG is greater then CG, the former being the whole, and this the part. Secondly, out of the same ground, wee may as easily collect that this distance be∣twixt the Moone and some other knowne fixt starre is varied proportionally, according to the distances of the places on the earth, because so many places as there are, so many di∣uersity

of aspects will arise, being increased or diminished, ac∣cording to the distances of places on the Terrestriall Globe: This conclusion thus demonstrated, wee must proceed to pra∣ctice in this manner, as is taught by Gemma Frisius: First, it behooueth you to search out by the helpe of Astronomicall Tables, the true motion of the Moone, according to the Longitude, at that time of your obseruation at some certaine place, for whose Meridian the rootes of those Tables are calculated. 2. You must know the Degree of Longitude of some fixed starre, nigh vnto the Eclipticke, either preceding or following the moouing of the Moone. 3. You must seeke out the Distance of moouing of the Moone, and the said starre. 4. The distance once had, apply the crosse-staffe to your sight, and so mooue the Crosse to and fro, till you may behold the Center of the Moone, at the one ende, and the fixed starre with the other. So shall you see expres∣sed by the Degrees and Minutes marked on the staffe the distance of the Moone and the said starre correspondent to the place of your obseruation: which being noted, set downe also the distance betwixt the Moone and the foresaid Starre which was first calculated. Then subtract the lesser from the greater, the residue will shew the least difference: which being diuided by the moouing which the Moone maketh in one houre, you shall know the time in which the Moone is or was ioyned with the first distance of the foresaid starre. Then hauing con∣uerted that time into degrees and minutes, the rest will be per∣formed either by addition or substraction of the Product there∣of to or from that Meridian: for which the Tables where by you first calculated the motion of the Moone, were appoin∣ted and verified. If the distance betwixt the Moone and the fixt Starre of your obseruation bee lesser, then must you adde the degrees and minutes to the knowne Latitude, so shall you finde the place of your obseruation to bee more Eastward. If it bee greater, then substract the degrees and minutes from the knowne Longitude, and the place of your obseruation in this regard will bee more Westward. These rules are so farre true that the Moone bee supposed to bee more Westward then the

fixed Starre: for if otherwise, your working must be cleane con∣trary: to wit, if the distance betwixt the Moone and the fixed Starre bee lesser, you must subtract the degrees and minutes from the knowne Longitude: so shall the place of your obser∣uation bee more Westward: but if it bee greater, then must you adde the degrees and minutes vnto the knowne Longitude, and the place of your obseruation shall bee sound Eastward. This way, though more difficult, may seeme better then all the rest: for as much as an Eclipse of the Moone seldome happens, and a watch, clocke, or houreglasse cannot so well bee preserued, or at least so well obserued in so long a voyage: wherea•• euery night may seeme to giue occasion to this experiment: if so bee the ayre bee freed from clouds, and the Moone shew her face aboue the Horizon.

4 By the obseruation of the difference in the Sunnes and Moones motion, the Longitude of places may be found out.

To explane this proposition, wee will set downe three things. 1 Certaine Postulata, or granted Axioms. 2 The example. 3. The manner and practise: The grounds or propositions which wee take as granted of all Mathematicians are these. 1 That the motion of the Moone is 48 minutes of an houre slower in 24 houres, or 360 degrees, then that of the Sunne. 2 That by ob∣seruation of the heauens, and other Mathematicall helpes, an Artificer may know in any place first the Meridian: Secondly the houre of the day: Thirdly the time of the Moones com∣ming to the Meridian. 3 The time of the Moones comming to the Meridian may bee knowne by an Ephemerides: These things granted, wee will suppose for example, that in London the Moone on some set day comes to the Meridian at foure of the Clocke after Noone: 2▪ That in some part of the West-Indies, the Moone bee obserued to come to the Meridian the same day at 10 minutes after foure. These grounds thus set downe, the distance of Longitude of that place Westward from London may bee found out. The manner of practise is thus to bee

wrought by the golden Rule. If the difference of the Sunnes and Moones motion bee 48 minutes of an houre in 360 degrees, what will it be in 10 minutes? The fourth proportionall num∣ber will bee 75 degrees, the distance of Longitude of the place assigned from London, in West Longitude; from which number the Longitude from London being subtracted, and the remainder from 360, the residue will shew the Longitude. If the Moone in the place assigned come sooner to the Meridian, wee must count so much in East Latitude. This way I first found in M^r▪ Purchas his relation of Halls discouery of Groenland, written by William Baffin since this Chapter came vnder the Presse: the expression of which, being as I suppose shorter and easier then in the Author, I doe owe for the most part to my worthy Chamber-fellow, M^r. Nathanael Norrington, to whose learned conference, I confesse my selfe to owe some fruits of my labours in this kinde, and all the offices of friendship. This manner of inuention, for mine owne part, I preferre before all the rest, both for certainty and facility and (as it should seeme by Baffins practise) it is more in vse amongst Marriners then the former, howsoeuer lesse mentioned amongst writers.

14 Thus much for the Inuention of the Longi∣tude: the Expression is the imitation of the Longitude on the face of an Artificiall Globe or Mappe; which is directed by these Rules.

1 The place whereof wee desire to know the Lon∣gitude being brought to the Brasen Meridian, the degrees of the Equatour will shew the Longitude.

This Rule may easily be explaned by these three precepts. First that you must turne round the Globe on his Axell-tree, till you bring the place whereof seek the Longitude vnder the bra∣sen Meridian. 2 You must diligently and exactly marke what

degree the Meridian cuts in the Equatour. 3. You must num∣ber how many degrees that point is distant from the first Meri∣dian, and the number will giue you the true Longitude sought after This also m••y be performed without turning of the Globe, if so be any other Meridian in the globe signed out shall passe by the said place. For this Meridian will cut the Equatour in some degree or other, which being numbred▪ as before from the first Meridian, will shew the direct Longitude: the like of which we haue in the second case.

2 The Meridian running through any place of the Geographicall Table, will point and designe out in the Equatour the degrees of Longi∣tude.

This may easily bee taught by the former way performed on the Globe: as for example, if I should inquire the Longitude of Paris the Metropolis of France, in a Geographicall Map, I finde a Meridian markt out which runs, if not directly through yet ve∣ry neere the said City. This Meridian I trace along to the Sou∣therne part, till I finde it to meet and cut the Equatour. Then obserue I in what degree of the Equatour it makes his interse∣ction, and I finde it to bee 23 degrees 20 minutes, which is the Longitude of the place.

15 Hauing spoken of the Longitude, the La∣titude comes in the next place to bee hand∣led: the Latitude is the Distance of any place from the Equatour, either North or South.

What we haue spoken of the Longitude must also agree to the Latitude, that it is taken sometimes absolutely and generally, sometimes specially: in the former sense it signifies any di∣stance or space betweene North and South, or contrariwise from South to North. Amongst the Ancients was the bre••dth or Latitude held to bee about 80 degrees, so that the vtmost

bound or limit to it Northward was called Thule, which com∣monly is supposed to bee Island. But the latter Nauigatours through their diligence haue detected so much land that it is found to stretch beyond 81 degrees toward the North, and 45 toward the South, and much farther if we will beleeue the re∣lation of Ferdinand de Quir, a Spaniard, who boasts a more ample discouery of the South I••dies, then euer before hath beene knowne. But howsoeuer, the Latitude here define is taken in a more speciall and stricter sense for the distance of any place from the equinoctiall line, bee it either toward the North or the South. The bound therefore from which we begin our account of Latitude is the Equatour: but the subiect wherein it is measured is the Meridian: so that it is cleane opposite to the Longitude, for that was limited by the Meridian, and mea∣sured in the Equatour. The Latitude of a place is alwayes e∣quall to the Eleuation of the Pole, as wee shall shew hereafter, and is diuided into the Northerne and the Southerne Latitude, whereof the one is from the Equatour Northward, the other Southward.

16 Concerning the Latitude are to bee conside∣red the Inuention, and the Expression: the In∣uention is againe twofold, Astronomicall or Magneticall.

17 The Astronomicall Inuention of the Latitude is by obseruation of the Starres, which is directed by these Propositions.

1 The Meridian Height of the Sunne at the time of the Equinoctiall subtracted from 90 degrees, will shew the true Latitude of the place.

The height of the Sunne at Noone may be found by the Astro∣labe, Crosse-staffe; Quadrant, and many other Astronomicall

instruments, but in taking the Meridian Altitude, it is very fit and requisite that it bee obserued diuerse times one after ano∣ther with some little space betwixt, to trie whether it increas∣eth or decreaseth; for if it doth increase; then assure your selfe it is not full Noone; if it decrease it is past Noone: hauing thus found out the Meridian Altitude, you must subduct it from 90 degrees, and the residue will bee the true Latitude of the place, if so bee it bee obserued at the time of the Equinoctiall, when the Sunne enters the first point of Aries, or Libra as for example here at Oxford I obserue the Meridian height of the Sunne about the eleuenth of March, and I finde it to bee about 37 degrees, or thereabout, which I subtract out of 90, the whole Quadrant, and the residue will bee 51½, which is the Latitude of the place. But if you would know the Latitude at any other day, or time of the yeere, then must you proceed in this manner: hauing taken the height of the Sunne at Noone (as before) you must by the Table of Declination learne the true degree of the Sunnes declination. 2 If such declination bee Northernely, then must you subtract it from the foresaid Alti∣tude or height. But if Southernly, you must adde it to the Alti∣tude: and by such addition and subtraction, shall you haue the height of the equinoctiall aboue the Horizon. 3 This height of the Equinoctiall aboue your Horizon, being as before sub∣tracted from 90, will bee the true Latitude of the place assig∣ned: as for example, the 15 of August I obserue the Declinati∣on of the Sunne to bee about 10 Degrees, the Sunne being in 2 Degrees of Virgo: I finde the Meridian height of the Sunne to be 48 degrees or thereabouts▪ Now because the Sunne being in Virgo, hath a Northerne Declination, I subtract 10, which is the number of the declination, out of 48 the height of the Sunne, and there will remaine 38, which againe taken ••ut of 90, the residue will be about 52, the common receaued Latitude of the place.

2 The Meridian height of any Starre, the De∣clination subtracted, if it bee Northerne, or

added if it bee Southerne, being subtracted out of 90, will shew at any time of the yeere the Degrees of Latitude.

The former rule serues onely for the day; because it is perfor∣med by the obseruation of the Sunne, but this latter may bee more necessary for Marriners, who now and then are inforced to inquire the Latitude of a place in the night when the Sunne shines not: wherfore they must flie vnto some knowne Starre, by obseruation of which they may easily performe the same; ac∣cording to the rule: which differres nothing at all from that which wee speake of the Sunne out of the Equinoctiall, and therefore need no other exposition then a bare example: let the fixt starre you best know, bee Arcturus, whose Meridian Al∣titude you finde by your Mathematicall instrument to bee 59 Degrees, and 30 minutes: then shall you learne by some Ta∣ble that this Declination Northward is 21 degrees, 30 minutes: now because his declination is Northward, you must subtract it out of his Meridian Altitude, and you shall finde the remain∣der to bee 52 Degrees, which is the Latitude for the place: as it is commonly taken, although I confesse it might be more exact: being obserued here at Oxford, be found rather 51 Degrees and 30 minutes.

18 The Magneticall Inuention is performed by the Magneticall Inclinatory Needle.

The ground of this Magneticall inuention is from the propor∣tion betwixt the magneticall inclinatory Needle, and the La∣titude of the Earth: for as wee haue proued in the 13 Proposi∣tion of the 3 Chapter; the Magneticall inclinatory Needle will at euery point of Latitude conforme it selfe to certaine An∣gles with the Axell of the Earth proportionally to the De∣grees of that Latitude: vpon which grounds D^r Ridley hath inuented a curious instrument to finde out the Latitude for a∣ny place assigned, and for this vse hath calculated Tables, which wee hope will bee inlarged by our famous Professor M^r Brigges: for my part, hauing neuer seene this instrument,

such time as I shall haue occasion to acquaint my selfe with it.

19 The Expression is the imitation of it on the artificiall Spheare: which is againe either Astronomicall or Magneticall. The former is performed by the ordinary Globe accor∣ding to this rule.

1 The point of any place or Citty first found in the Globe being brought to the brasen Me∣ridian, will shew in the Degrees of the same Meridian the true Latitude of the same place.

This may easily be shewed in this manner by an example; If I would willingly finde out the Latitude of Oxford in the Globe. I first finde out the place in the Globe, which hauing found, I turne the Globe till I haue brought the place iust vnder the brasen Meridian: then I note what degree it designes, and that shewes mee the true Latitude of the place, which I finde to bee 52, or thereabouts: but if you would finde it in a Mappe or Chart, in which there is no such brasen Meridian, you must take the Parallell of the place, or at least the next vnto it, pointed in the same Mappe: Then note what degree the said Parallell cuts in the first Meridian; for that will shew the true Latitude of it by the right Parallell of the place, if not the next; so that by additi∣on, or subtraction, you may easily guesse at it.

20 The Magneticall Expression depends from the Application of the Inclinatory Needle to the Terrella.

The Magneticall inclinatory needle is said to conforme it selfe in the same manner to the Terrella or Loadstone, being artifi∣cially thereunto applied, as it doth to the great Globe of the Earth: so that no doubt is, but an imitation of the Latitude

¶ A Table expressing the proportion of the Magneticall Inclination to the degrees of Latitude, and Eleuation of the Pole.

Eleuat. Poli.	Inclination to the Hori∣zon. 1.11.	Eleuat. Poli.	Inclination to the Hori∣zon. 1.11.	Eleuat. Poli.	Inclination to the Hori∣zon. 0.1.11.
1	2	11	15	31	52	26	38	61	79	28	51
2	4	10	13	32	53	46	55	62	80	31	36
3	6	26	55	33	54	53	51	63	80	37	54
4	8	31	23	34	56	3	56	64	81	10	47
5	10	33	41	35	57	13	25	65	81	42	36
6	12	23	50	36	58	21	19	66	82	13	23
7	14	37	53	37	59	27	50	67	82	43	9
8	16	27	52	38	60	32	59	68	83	11	56
9	18	21	50	39	61	36	46	69	83	39	45
10	20	13	47	40	62	39	0	70	84	6	37
11	22	3	45	41	63	39	56	71	84	32	30
12	23	51	46	42	64	39	29	72	84	57	24
13	25	37	52	43	65	37	41	73	85	21	22
14	27	22	4	44	66	34	31	74	85	44	24
15	29	4	23	45	67	30	0	75	86	6	31
16	40	44	53	46	68	24	10	76	86	27	44
17	32	23	34	47	69	17	2	77	86	48	5
18	34	0	27	48	70	8	38	78	87	7	36
19	35	35	35	49	70	58	59	79	87	26	18
20	37	9	0	50	71	48	7	80	87	44	9
21	38	40	42	51	72	36	0	81	88	1	10
22	40	10	41	52	73	22	38	82	88	17	23
23	41	38	58	53	74	8	2	83	88	32	49
24	43	5	37	54	74	52	11	84	88	47	29
25	44	30	26	55	75	35	6	85	89	1	22
26	45	53	43	56	76	16	51	86	89	14	30
27	47	15	25	57	76	57	28	87	89	36	54
••••	••••	••••	••••	••8	77	••6	••••	88	88	••8	••••

may bee expressed on the little earth, or loadstone: for which vse, diuers curious instruments haue beene deuised by magneti∣call Philosophers, to whom I referre my Readers: because I (as I said) haue little acquainted my selfe with the vse of such in∣struments.

CHAP. XII. Of the distances of places compared one with another.

1 OF the simple and absolute distinction of distances, wee haue treated in the former Chapter: wee must in the last place handle it comparatiuely; that is to say, one place compared with another: whereof wee are to consider the Inuention and Expression.

2 The distance is the measured space betwixt two places: which is, either vniforme, or various: vniforme is in places different, either in Longitude onely, or in Latitude onely.

3 Those places differ in Longitude onely, which are situate vnder the same or like Parallels, but diuers Meridians; or at least vnder op∣posite

points of the same Meridian.

Of place•• differing onely in Longitude, there may bee three ca∣ses: For 1. they may be vnder the same Parallell, as the Iland of ••••int Thomas, and Summatra, which lie directly vnder the Equatour; or Noremberg and Hamberg, which hauing very neere the same Latitude, differ in Longitude, and lie in the same Parallell without the Equatour. 2. They may be vnder the like Parallels, that is, in points equidistant from the Equatour. As Siene in Egypt, vnder the Tropicke of Cancer; and Beach in the South continent, vnder the Tropicke of Capricorne. 3. They may be vnder the same Parallell and Meridian, but in opposite points of the said Parallell: such as are the Perioeci, spoken of in the 10. Chapter.

4 Places differing onely in Longitude, whose distance is here proposed to bee sought out, are seated in the same, or diuers Hemi∣spheares.

5 In the same Hemispheare, when both places haue either Easterne or Westerne Longitude. This againe may haue two cases; for either the places are vnder the Equatour, or with∣out it: in both which, the finding out of the distance shall bee opened in these Rules.

1 If two places vnder the Equatour in the same Hemispheare, differ in longitude: let the lesser longitude be subtracted from the greater, and the difference conuerted into Miles, and the di∣stance will be knowne.

As for example, wee will suppose of two places, whose di∣stance is to bee sought out, the former to be the Iland of Saint Thomas in Africa, the other the Iland Summatra in the East Indies, both situate directly vnder the Equatour; and there∣fore differing onely in Longitude. To expresse which, in this figure, let the first

[illustration]

Meridian from which the Longi∣tude is to be mea∣sured, be ABCD: the place where Saint Thomas I∣land is seated, K: and the place of Summatra, F. Thē subtracting AK, the Longitude of Saint Thomas I∣land, being lesser, out of the Longi∣tude of Summatra AE, the residue KE will shew the distance in degre••s: which being multiplied by 60, and so conuerted into Italian-miles, will shew how many miles the said places are distant the one from the other. As in this present example, wee finde the Lon∣gitude of Saint Thomas Iland to bee 32 degrees 20 minutes of Summatra, to bee 131 degrees: The lesser summe subducted from the greater; to wit, 32 degrees 20 minutes, out of 131; there will remaine 98 degrees 40 minutes: which being againe multiplied by 60, will produce 5920 Italian-miles, the true distance betwixt the said places.

2 Of two places in the same Hemispheare, situ∣ate without the Equatour; the distance may be knowne two wayes: either by the resoluti∣on of the Sphericall Triangle, or else by ta∣bles

of the miles answerable to the degrees of Latitude.

The former way is performed in this manner: Let the Tri∣angle of two equall sides FBG in the figure before, bee re∣solued; in which the two equall sides FB, and GB are the complements of equall Latitudes; to wit, AF, and EG. The Angle FBG is the difference of Longitude, which Angle, whether it bee a Right Angle, or Oblique Angle, will easily bee knowne, if by letting a perpendicular line BI from B to I it bee parted into two Triangles FBI and IBG: for because those two Triangles according to the grounds of Geometry are equall; the Arch IG in the Triangle IBG being found out, the Arch also IF in the Triangle FBI will also bee knowne: which beingthus demonstrated, wee must proceed in this manner, according to the Golden Rule. As the Right angle BIG is to the complement of the Latitude BG, so is IBG the middle difference of Longitude to IG the middle distance: Pitiscus in his Trigonometry to this addes another manner of de∣monstration, expressible by the precedent figure: let the per∣pendicular IB be continued vnto K, that BK may make a whole Quadrant. Now will the Triangle IHK haue Right Angles at I and K, at I by supposition, at K by his 57 proposition demonstra∣ted in his first booke: because, If a greater circle of the Spheare passe by the Poles of a greater cîrcle, it will cut it at right Angles, and contrariwise: wherefore the sides IH and KH must bee quadrants: because, as hee shewes in his 68 proposition of his first booke; In a sphericall Triangle hauing more then one Right Angle, the sides subtending those Right Angles are Quadrants: Finally, because the Arches GH and EH, are the complements of the Arches IG and KE: by the 9 definition of the first booke▪ For as much as of any Arch lesse then a Quadrant, the complement is that which wants to make it vp 90 parts. We may by the helpe of the 57 proportion of his first booke, seeke out the comple∣ment of the third side GH; which will be the Arch GI: which will shew vs the probleme which wee sought, by redu∣ducing

it vnto the Table of signes, and Tangents, exactly se•• out by our forenamed Author and others. For an example of this, wee may take two famous cities of Germanie, Noremberg and Hamberg, which without any sensible difference haue the same Latitude, but differ in Longitude: For the Longitude of Noremberg is 31 degrees 45 minutes: of Hamberg 32 degrees 30 minutes: the difference of Longitude then is 0 degrees 45 minutes. These things supposed to be knowne, we will ima∣gine Noremberg to be in F, Hamberg in G▪ and therefore AF, or EG will haue 49 degrees 23 minutes: FB or GB will haue 40 degrees 37 minutes: FBG or AE will haue 0 degrees 45 minutes: KE 0 degrees 22 ½ minutes: EH 89 degrees 37 ½ mi∣nutes: if we worke by the Table of Signes, Tangent••, and Se∣cants, the knowledge whereof is required to this Probleme. But because the former way may seeme difficult to such as are not much acquainted with Trigonometry, some haue set downe ••n easier way, depending on the vse of a Table, wherein i•• cal∣culated the number of miles answering to euery degree of eue∣ry Parallell of the Spheare: in which working▪ we ought to bee directed by this Rule: If two places without the Equatour differ in longitude only, subtract the lesser number out of the greater, and multiply it by the n••mber of miles answerable to a d••gree of that Parallell, ••nd the product will giue the distance. As for exampl••, if you would know the distance betwixt London and Antwerpe, which haue in a manner the same Latitude, but differ in Longi∣tude: I finde them to differ in Longitude by 6 degrees, which number being multiplied by 37 miles answerable to 51 degrees of Latitude, these will arise to 247 miles, and 54 seconds of a mile.

A Table of Miles answerable to one Degree of euery seuerall Latitude.

1	2	3	4	5	6
D	M	S	D	M	S	D	M	S	D	M	S	D	M	S	D	M	S
1	59	59	16	57	41	3	51	26	46	41	41	61	29	5	76	14	31
2	59	58	17	57	23	32	50	53	47	40	55	62	28	10	77	13	30
3	59	55	18	57	4	33	50	19	48	40	9	63	27	14	78	12	28
4	59	51	19	56	4	34	49	45	49	9	22	64	26	18	79	11	27
5	59	4	20	56	23	35	49	9	50	38	34	65	25	21	80	10	25
6	59	40	21	56	1	36	48	32	51	37	46	66	24	24	81	9	23
7	59	33	22	55	38	37	47	55	52	36	56	67	23	27	82	8	21
8	59	25	23	55	14	38	47	17	53	36	7	68	22	29	83	7	19
9	59	16	24	54	49	39	46	38	54	35	6	69	21	30	84	6	16
10	59	5	25	54	23	40	45	58	55	34	25	70	20	31	85	5	14
11	58	54	26	53	6	41	45	17	56	33	33	71	19	32	86	4	11
12	58	41	27	53	28	42	44	35	57	32	41	72	18	32	87	3	8
13	58	2	28	52	59	43	43	53	58	31	48	73	17	33	88	2	5
14	58	13	29	52	29	44	43	10	59	30	54	74	16	32	89	1	3
15	57	57	30	51	58	45	42	26	60	30	0	75	15	32	90	0	0

6 The distance of places differing only in Lon∣gitude in diuerse Hemispheares is found out by this rule.

1 Let the greater longitude be subtracted from the whole circle, and vnto the residue added the lesser longitude, there will arise the distance betwixt those places.

As for example, Lisbone in Spayne hath in East longitude 13 de∣grees: and Cap de Los Slanos in America, hath in West longi∣tude 334 degrees: to know the distance betwixt those places, you must first subduct 334, which is the greater Longitude out of 360 the whole circle, and there will remaine 26 Degrees, to which if wee adde the East longitude of Lisbone, which is 13 degrees, it will make 39 degrees, which is the true difference of those longitudes: which being multiplied by the Number of miles in the Table going before, answerable to the latitude of the said places (if they differ only in longitude) there will arise the number of miles contained in the Distance.

7 Distant places which differ onely in latitude, are such as lye vnder the same Meridian, but di∣uerse Parallells: These are supposed to be either in One, or in Diuerse latitudes or Hemispheres.

8 In One, when both the places haue either North latitude, or both South Latitude: The finding out of which distances depends on these Propositions.

1 If the latitude of each place be towards the same P••le, subtract the lesser from the greater lati∣tude, and the residue conuert into miles.

The reason may bee explained in this Figure: wee will imagine

[illustration]

EF to bee the lesser, EG the greater la∣titude. There will remaine an Arch of the Meridian FG: which being multi∣plied by 60 (being part of a great circle, will make the nūber of miles answerable, to that distance. For an example we will take two Citties of England, Oxford and Yorke. The latitude Oxford, we take to be 31 degrees 30 minutes: of Yorke 54 degrees 30 minutes. The lesser latitude subtracted from the greater, there will remaine three degrees, which being multiplied by 60, will render 180 Italian-miles, the Distance of thse two places.

2 If two places in latitude only distant, be situate in diuerse kindes of latitude, adde the latitude of the one to the other, and the whole summe shall be the distance.

As for example, in the former Diagram, imagining as in the former case BD to be the Meridian of those distant places, and AC the Equatour, we will suppose the one place to bee situate towards the North Pole, as G, the other towards the South, as in H: then as appeares by sense, will the distance bee the Arch of the Meridian GH, whereof GE, and EH, are parts, whereof it is compounded: wherefore it must needs follow that those parts added together make the whole distance: for example we will take Bellograde in Europe, and the Cape of good hope in Afri∣ca, which haue neere the same longitude, to wit, 48 degrees 30

minutes: but they differ in latitude in such sort, as the former hath of the Northerne latitude 44 degrees 30 Minutes; the o∣ther of Southerne latitude about 35 degrees 30 minutes. These two numbers added together, will make 80 degrees, which be∣ing multiplied by 60 will produce 4800 miles the distance of those places.

9 Hitherto of the distances of places which are Vniforme, that is to say, of such as differ either only in longitude, or onely in latitude: wee are next to consider of such distances as are vari∣ous, wherein the places differ both in longitude and latitude.

10 The Inuention of such a distance, may bee performed two wayes, either Abstractiuely by the resolution of Triangles, or else Mechanically by instruments. The former againe may bee two wayes, either by the Right-line Triangle, or by the Sphericall: The inuention of the di∣stance by the Rigt-line Triangle depends on these following Propositions declaring two wayes of inuention.

11 The first is by a Rectangle Triangle barely considered by it selfe, according to this Theo∣reme.

1 The square Root of the number made of the diffe∣rences of longitude and latitude of two places di∣stant, will shew the distance of those places.

The ground of this Proposition is taken from the 27 Proposition

of the first booke of Euclide: where it is demonstrated that the square of the Hypotenusa, or greatest side of a Rectangle Trian∣gle is equall to the two squares made of the two other sides: which being well vnders••ood, will lend an easie light to this pro∣position. To performe which we must first take the difference of longitude, which is imagined to make one side of this Triangle. Then wee must obserue also the difference of latitude, which is supposed to make another side. Then are we sure by the former Proposition of Euclide that the squares of these two sides, are e∣quall to the square of the Hypotenus••, or third side; which is to be sought out, and expresses the distance betwixt those places: wherfore we must first multiply these two sides in themselues, whence they will become squares. 2. We must adde them toge∣ther. 3 We must out of the totall extract the quadrat root, which will shew the distance: as suppose according to this Figure, two Cities d••stant and differing both in longitude and latitude: wher∣of the one shall haue in longitude 21 degrees, in latitude 58: the other is supposed to haue in longitude 26 degrees, in latitude

[illustration]

52. Here first I subtract the lesse lon∣gitude out of the greater, to wit, 21 out of 26, and the residue will bee 5, which I suppose to be one side of the Rectangle Triangle. Then likewise I subtract the lesse latitude as 52 out of 58, the residue will be 6, which I make the other side of my Triangle, which done, I multiplie 6 in it selfe, and it makes 36, which is the square of one side: Then I multiply 5 in it selfe, and the product will be 25, the square on the other side. These two squares added together by the foresaid Proposition must be equall to the square of the Hypo∣teneus▪ orthird side 61, whereof the square root being extracted, will shew the side it selfe, which will be 7 7/25 which is the di∣stance: If any man desire to know this distance according to miles, he must reduce the degrees of longitude and latitude into miles according to our former rules, before he begin to worke:

because (as wee haue shewed) the degrees of longitude being measured in the Parallells are not alwayes equall, the Parallels being somewhere great••r, somewhere lesser. This way must needs bee more exact, in that a Mile is a smaller part then a De∣gree, and (as Pitiscus notes) the Fractions which fall out in ex∣traction of roots can hardly bee reduced to any proportion. Ne∣uerthelesse this way of finding out the distance by a Right-line Triangle, howsoeuer common and receaued, is very vnperfect and subiect to great errour, especially in places far distant: for as much as it supposeth the Meridians with the Parallels on the Globe to make true squares, whereas indeed all the Meridians meet in the pole, and so by consequence cannot make true squares: But yet this errour is far lesse in a lesser distance; be∣cause in a small space of earth, the roundnesse and conuexity of the Earth is insensible, or at least of very small importance: so that this way cannot be altogether vnusefull.

12 Another is found out more exact then the former by the tables of Signes, Tangents, and Secants. This is performed by finding out the numbers: whereof the former is called Inuen∣tum primum, or the first found number. The se∣cond Inuentum secundum, or the second found number. The working of which Probleme depends on these rules.

1 Multiply the Right Signe of the difference of the longitude into the summe of the complement of the lesser latitude, and diuide the product of that multiplication by the totall summe, & then by the rules of Signes and Tangents the Arch of that Quotient found out will giue the first found number.

2 Multiply the right signe of the lesser latitude by the totall signe, and hauing diuided the product thereof by the signe of the complement of the first number, subtract the Arch of that quotient out of the greater latitude which giues the second found number.

3 Then multiply the signe of the complement of the first found number into the signe of the complement of the second found number, and hauing diuided the product by the Totall Signe, Let the Arch of the quotient be sought out by the Tables, which Arch subtracted out of the whole quadrant, will giue the degrees of a distance in a great circle.

To expresse the practice and manner of working according to our former Rules, we will suppose the two cities, whose di∣stance is here sought out to be Ierusalem and Norimberge in Ger∣many. Ierusalem hath in longitude 66. degrees. 0 min. and in latitude 31 degrees, 40. minutes. Againe Norimberge hath in longitude 28. degrees. 20. minutes, and in latitude 49 deg. 40. min. The difference of their longitude is 37. deg. 40. minutes. The right signe whereof is 36664: (for here wee make 60000 to be the totall signe, rejecting the two last figures on the right hand in the tables of Regiomontanus.) Now you must multiply 36664: into the signe of the Complement of the lesser latitude, which is 51067: the product of which two signes being multi∣plied the one by the other, there will arise 1872320488: which if you diuide by the totall signe 60000, the quotient will giue you 31205, whose Arch is 31 deg. 20 min. and this must be your first found Number.

For the finding of the second Number, you must proceede in this māners: Multiply the right signe of the lesser latitude, which

is 31498 by the totall signe 60000, and the produ••t will bee 1889880000: which summe, if wee diuide by the signe of the Complement of the first-found Number, which is 51249, wee shall finde in the quotient 36876; the Arch whereof is 37 de∣grees, 55 min: which Arch subtracted out of the greater lati∣tude, there will remaine 11 degrees, 29 min: and this is our se∣cond-found Number. These things thus supposed to bee found out, wee must multiply the fore-said signe of the Complement of the first-found Number, which is 58798, and the product will arise to 3013338702, the Arch whereof is 56 deg. 50 min: which being subtracted out of the whole quadrant, viz: 90 de∣grees, there will remaine 33 degrees, 10 min: of the greater circle. These 33 degrees if we multiply by 60, there will arise 1980 miles, whereunto if we finde the 10 miles answerable to the 10 min. wee shall finde the distance betwixt these places to be 1990 Italian-miles. This example is vsed by Appian, and wrought according to his owne Tables, and farther explained by our countryman Blundeuill in his Exercises. The same way of working hath been deliuered by Clauius, Iunctinus, and others, although not according to the same Tables. This was of measu∣ring the distance by the Signes and Tangents according to these Authors, may be warranted more exact than the other, because it admits of smaller parts in the calculation; yet will it come far short of truth.

10 Another way of finding out the Distances of places, differing both in longitude & latitude, is by the Resolution of a Sphericall triangle.

This way of all the rest must needs be most certaine: for as much as this kind of triangle best expresseth the sections of the Globe. The methode of which working I finde no-where better taught then in Pitiscus his Trigonometry: of whose ingenious industry notwithstanding little vse can bee made, except the Learner first acquaint himself with his principles, because in his Geographicall Problemes, he briefely referres his Reader to his former grounds and Axiomes, accurately demonstrated in his former books: For mine owne part it might perhaps seeeme as absurd in this Trea∣tise,

to intermixe all his preparatory demonstrations, being meerely Geometricall, and without the limites of my subject, as by leauing out so necessary a way to mangle my discourse. Wher∣fore intending a middle way, I will (God-willing) in such sort set downe these propositions, that I may giue some light to this excellent inuention, and referre my Reader to Pitiscus his Axi∣omes for farther Demonstration.

14 The Distances proposed to be measured by Sphericall triangles, admit of two cases: 1 When two places are so situate, that the one is vnder the Equatour, the other without. Secondly, when both are without the Equa∣tour.

15 The former againe is three-fold: For either the difference of longitude betwixt those pla∣ces is Equall to a quadrant, or Lesse, or Grea∣ter. The seuerall wayes of inuention on shall bee directed by these Rules.

1 If the Difference of longitude be Equall to a qua∣drant, the distance will also be a quadrant.

As for example in this present figure wee will imagine the circle ABCD to bee the first Meridian: the places whose di∣stance is sought out A and G: whose Distance AG will bee a quadrant. For A will be a pole of a Greater Circle BGD, by the 56 prop. of the 1 of Pitiscus: wherefore all the Arches drawne from thence to BGD will bee quadrants by the same propositi∣on. For a more familiar instance wee will take the Iland Suma∣tra, which hath in longitude 131 degrees, but no latitude, be∣ing sited vnder the Equatour: and the city Buda the Metropolis of Hungary, which hath in longitude 41 degrees, in latitude 47 degrees; The difference of longitude is 90 degrees; for 41 be∣ing

[illustration]

[illustration]

subducted out of 131, there will remaine 90, wherefore the distance betwixt those places will be 90, which being multipli∣ed by 60, will produce 5400 Italian-miles.

2 If the difference of longitude bee lesse then a qua∣drant as AF: the Triangle AEF here is to bee resolued into his parts, according to the 4^th Axi∣ome of Pitiscus.

As for example the places, whose longitude is here sought out, shall be A and F; The Triangle here to be knowne is AEF; whose Resolution depends on our Authors 4^th Axiome. For the Diffe∣rence of longitude is ABF; because the measure of a Sphericall Triangle being taken in a great circle, is an Arch of a greater circle, described from the Angular point, and comprehended be∣twixt the two legges of the Triangle so farre as a quadrant, as is taught in the 58 proposition of his first Booke. For a more speci∣all instance we will take two places; whereof the one shall bee the Iland of S. Thomas before mentioned, which hath in longi∣tude 32 degrees and 20 minutes. The other Amsterdam in Hol∣land,

which hath in longitude 26 degrees, 30 minutes. The for∣mer we imagine in A; the later in F. The Difference of longi∣tude ABF will be 5 degrees, 50 min: Then the distance sought out must be AF: so working according to the fourth Axiome of Pitiscus, we shall find the Arch AF, which is the distance, to be 54 degrees, 19 minutes.

3 If the Difference of longitude bee greater then a quadrant, as of the two places of F and C, the Triangle to bee resolued will bee FCE, being a Rectangle at E.

Here because the Triangle FCE hath his two sides FC, and EC, greater then quadrants, insteed of it you may worke on the Triangle AEF, adioyned to the Triangle FEC: and the whole worke will be dispatched: for by the resolution of the Triangle AEF, you shall find out the Arch FG, which being added to the quadrant CG, there will be produced the Arch FC, which is to be ••ought out. As for example, we will imagine Heidelberge as it were placed at F, to haue in longitude 30 degrees, 45 mi∣nutes, in latitude 49 degrees 35 min: Then wee will suppose Summatra, as placed at C, to haue in longitude 131 degrees, but no latitude: The difference of longitude will be EC, of 100 de∣grees, 15 minutes: and the complement AE 79 degrees, 45 minutes. Then working according to the Rules of Trigonome∣try, we shall find the signe of the Arch FC, to be 6 degrees, 37 ½ minutes; which being added to FC, being 90 degrees, will pro∣duce 96 degrees, 37 ½ minutes, to which Arch there will ans∣wer 1449 German-miles.

16 The second Case is, when both places are si∣tuate without the Equatour: This is againe twofold: For either the two places are vn∣derstood to be situate towards the same Pole, or else one place toward the Northerne, the

other towards the Southerne Pole. Both which Cases shall be taught in these Rules.

1 If both places whose distance is sought, be situate towards the same Pole, there will arise a Trian∣gle, whose sides and Angles will be knowne by the fourth Axiome of Pitiscus in Trigonometry the fourth Booke.

As for example, in this present figure, let the two places giuen bee FG, the

[illustration]

Triangle to bee knowne, will be FBG, whose a∣cute Angle will be at B. Let the places giuen bee as FH; the Tri∣angle to bee re∣solued & known will bee FBH, hauing a right Angle at H. Fi∣nally, if the pla∣ces suppos••ed to be giuen, are as FI, the Triangle to bee knowne will bee FBI, with an obtuse Angle at I.

2 If the one place be situated towards the North-pole, and the other towards the South-pole, there will arise a Triangle, whereof the one side about the Angle which is giuen, will be greater then a quadrant.

As in the former figure, let the places giuen be as G and K, al∣so

H and K, also I and K: There will still fall out a Triangle▪ whose one side containing the Angle giuen, will be greater then a quadrant, as BK: wherefore for the side BK, you must take his complement to the Semi-circle BF, that is, for the Triangle GBK, you must worke by the Triangle GBF: and insteed of the Triangle HBK, you must take the Triangle HBF: and for the Triangle IBK, you must worke by the Triangle IBF, ac∣cording to the fourth Axiome of the fourth booke of Pitiscus, to which I had rather referre my Reader, then intermixe our Geographicall discourse with handling the Principles of Geome∣try, which here are to be supposed so many precedent propositi∣ons; which, expressed as they ought, would transcend the bounds of my intended journey.

17 Of the Astractiue way of finding out the Di∣stance of places, we haue spoken: The Me∣chanicall depends on the vse of Instruments and Mechanicall operation, whereof wee will shew one way in this Theoreme.

1 By the working with a Semi-circle, the Di∣stance of two places may be found out.

This inuention by M^r Blundeuill, seemes to be ascribed to Ed∣ward Wright, yet hath it beene taken vp of forreine Writers as their owne, and vsed in their Charts and Mappes. The manner of operation is thus: First, let there be drawne a semi-circle vpon a right Diameter signed out, will be the letters ABCD, where∣of D shall be the center, as you find it deciphered in this present figure. The greater this Semi-circle be made, so much the more easie will be the operation; because the degrees will be larger. Then this Semi-circle being drawne, and accordingly diuided, imagine that by the helpe of it, you desire to find out the distance betwixt London and Ierusalem, which cities are knowne to di∣ffer both in longitude and latitude. Now, that the true distance betwixt these two places may bee found out, you must first sub∣tract the lesser longitude out of the greater, so shall you finde the

Difference of their longitudes, which is 47 degrees. Then rec∣kon that Difference vpon the Semi-circle, beginning at A, and so proceed to B; and at the end of that Difference, make a marke with the letter E, into which point by your Ruler, let a right line be drawne from D the center of the Semi-circle. This being in this sort performed, let the lesser latitude be sought out, which is 32 degrees in the foresaid Semi-circle, beginning your accompt from the point E, and so proceeding towards B, and at the end of the lesser latitude, let another point bee marked out with the letter G: from which point let there be drawne a per∣pendicular, which may fall with right Angles vpon the former line, drawne from D to E; and where it chanceth to fall, there marke out a point with the letter H: This being performed, let the greater latitude, which is 51 degrees, 32 minutes, be sought out in the Semi-circle, beginning to reckon from A towards B, and at the end of that latitude, set downe another point, signed out by the letter I: from whence let there bee drawne another perpendicular line, that may fall with right Angles vpon the Diameter AC, and here marke out a point with the letter K: This done, take with your Compasse the distance betwixt K and H; which distance you must set downe vpon the Diameter AC, placing the one foote of your compasse vpon K, and the other towards the center D, and there marke out a point with the let∣ter L: Then with your compasse take the shorter perpendicular line GH, and apply that widenesse vpon the longer perpendicu∣lar line IK, placing the one foot of your compasse at I, which is the bounds of the great latitude, and extend the other towards K, and there make a point at M. Then with your compasse take the distance betwixt L and M, and apply the same to the semi∣circle, placing the one foot of your compasse in A, and the other towards B, and there marke out a point with the letter N. Now the number of degrees comprehended betwixt A and N, will expresse the true distance of the two places, which will be found to be 39▪ degrees: which being multiplyed by 60, and so con∣uerted into miles according to our former Rules, will produce 2340, which is the distance of the said places.

17 The expression of the Distance of two places may be performed either by the Globe or Map according to these Rules.

1 The distance betwixt two places in the Globe, be∣ing obserued by the quadrant of Altitude, and ap∣plied to the degrees of the Equatour, or any great circle, will shew how many miles such places are distant.

The practise hereof is very easie, as shall be taught in this ex∣ample: we wil for instance take Tolledo in the middest of Spaine, and the Cape of Good Hope in the South Promontory of all Afri∣ca: The space taken by a quadrant of Altitude, or any threed ap∣plyed to the Equatour, will be found to bee about 82 degrees, which being multiplyed by 60, and so conuerted into miles, will render 4920, the true distance betwixt these two places.

2 The distance betwixt any two places in the Chart, obserued by a compasse, and applyed to the degrees of a greater Circle, will shew how many miles such places are distant one from the other.

For an example, we will take the city Seuill on the Southmo•••• part of Spaine, and Bilbao on the North-side: the space betwixt those places being taken with a thre••d or a compasse, and apply∣ed to one of the greater Circles, will containe about 6 degrees; which being multiplyed by 60, and so conuerted into Italian-miles, will produce 360: and so many miles those Cities are to be esteemed distant the one from the other.

The end of the first Booke.

Notes

• * 1.1

  Ptolom. ge∣ogr. l. 1. sec. 1.
• * 1.2

  Seneca in Medeâ. Act. 2.
• * 1.3

  De gen. & cor.
• * 1.4

  〈◊〉〈◊〉 de caelo cap. 4.
• * 1.5

  L. de Sphaer.
• * 1.6

  Lib. 1 geog. cap. 4.
• * 1.7

  Lib. 2. c. 72.
• * 1.8

  Lib. 1.
• * 1.9

  De Mundi fabr. part. 3. cap. 2.
• * 1.10

  Psal. 104.
• * 1.11

  Fundauit Terram su∣per bases su∣as, ne dimo∣ueatur in saeculum. vers. 5.
• * 1.12

  Ptol. dict. 1. cap. 5. Alph. 6. diff. 6.
• * 1.13

  Prop. 11. lib. 1.
• * 1.14

  Pag. 149.