Academia scientiarum, or, The academy of sciences being a short and easie introduction to the knowledge of the liberal arts and sciences, with the names of those famous authors that have written on every particular science : in English and Latine / by D. Abercromby ...

THE ACADEMY OF SCIENCES.

ACADEMIA SCIENTIARUM.

Section I. Algebra.

ALgebra, or the Analytical Doctrine, is the Art of find∣ing an unknown Magnitude, taking it as if it were known, and finding the equality between it and the given Magnitudes: It implieth then a dissolving of what is suppos'd to be compounded, which is meant by the Greek word 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, or Resolution:

This Name may upon this account be given to the common operations of Arith∣metick; as for instance, to what we call Substraction, Division, Extraction of Roots, &c. for Substraction is nothing else but a Dissolution or Resolution of what is suppos'd to be compounded, or made up by Addition; and Division a re∣solution of what is suppos'd to be made up by Multiplication; as likewise Ex∣traction of the square Root, is a reso∣lution of what is supposed to be made up by squaring: But such resolutions being easie, are not called Algebra, for the resolution of things, whereof the compo∣sition is more intricate, is more properly understood by this harsh word.

The Arabs call it Algibr Walmo∣kabala, from the first of these two words we call it Algebra, which taken together, imply the Art of Restitution and Resolution. Lucas de Burgo, the most ancient European Algebrist, calls it the Rule of Restauration and Opposi∣tion.

And indeed, this is its chief work; a quantity unknown, which they commonly call Root, is supposed by Additions, Substractions, Multiplications, Divi∣sions, and other like Operations, to be so chang'd, as to be made equal to a known quantity compared with it, or set over against it; which comparing is common∣ly called Equation, and by resolving such an Equation, the Root so changed, transformed or luxated, is in a manner put into joynt again, and its true value made known, for the word Giabara, from which the word Algebra is derived, does signifie, to restore or set a broken Bone or Joynt.

Theo says, that Algebra was inven∣ted by Plato; however the chief Wri∣ters of Algebra are those whose names I have set down here, to gratifie such as would learn this noble Art.

Lucas Pacciolus, or Lucas of Burgo, a Minorita Fryer, wrote an Italian Treatise of Algebra, in Venice, 1494. a little after the Invention of the Art of

Printing; there he mentions Pisanus, and several others that had written on the same Subject before him, but their Works are not Extant. Harriot, Oughtred, Descartes, Huddenius, Gelleus, Billius, and lately the fam'd Dr. Wallis has written a large Volume on this Subject.

Sectio Prima. Algebra.

ALgebra sive Doctrina Ana∣lytica est ars inveniendi magnitudinem incognitam eam accipiendo quasi cog∣nita foret, inveniendoque aequalita∣tem eam inter, datasque magnitudi∣nes. Sonat itaque Resolutionem ejus quod compositum supponitur, hicque Graecae vocis 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, sensus est: Hoc

proinde nomen tribui poterit commu∣nibus Arithmeticae operationibus, pu∣ta Substractioni, Divisioni, Extra∣ctioni radicum quadratarum, &c. Substractio enim nihil aliud est quam resolutio ejus quod ex Additione sup∣ponitur emersisse, compositi, Divisio quid? nisi resolutio ejus quod ex Mul∣tiplicatione supponitur emersisse, compositi, Extractioque radicis qua∣dratae nil aliud est quam resolutio ejus quod ex quadratione supponitur emer∣sisse, compositi: Sed hujuscemodi re∣solutiones utpote faciliores Algebrae nomine intelligendae non veniunt, dif∣ficilium enim compositionum resolu∣tio barbara hac voce, & magis pro∣prie intelligitur.

Arabibus dicitur Algiabr Walmoka∣bala, a priore voce nos Algebram dici mus, geminae eae voces simul sumptae artem restitutionis, ac resolutionis so∣nant. Lucas Burgensis antiquissimus inter Europaeos Algebrista Algebram Restaurationis & Oppositionis regulam vocat.

Et reipsa praecipuum hoc ejus opus est, quantitas adhuc incognita quam vulgo Radicem dicunt, quibusdam Additionibus, Subductionibus, Mul∣tiplicationibus, Divisionibus, aliisque ••d genus operationibus ita supponitur mutata, ut tandem aequalis fiat quan∣titati notae eidem comparatae, aut e regione ejusdem collocatae, quae com∣paratio aequatio dici solet: Hujus au∣tem aequationis resolutione radix hunc in modum mutata, aut quasi luxata, priori rursus, ut ita dicam, situi resti∣tuitur, verusque ejus valor innotescit, vox enim Giabara unde Algiabr desu∣mitur, fracti ossis restaurationem sonat. inventam asserit a Platone Algebram Theo; ut ut sit praecipui Algebrae Scrip∣tores hi sunt quorum nomina hic ap∣pono in eorum gratiam qui nobilem hanc artem discere voluerint.

Lucas Pacciolus, aut Burgensis, Ita∣licum de Algebra Tractatum scripsit Venetiis Anno nonagesimo quarto su∣pra millesimum quadringentesimum

••aulo post inventam Typographiam; ••bi commemorat Pisanum, aliosque ••on paucos qui de eodem argumento ••rius scripserant, at eorum opera jam ••on extant. Harriotus, Oughtredus, Cartesius, Huddenius, Gelleus, Billius, ••c nuperrime celeberrimus Vallisius ••oc super argumento amplum volu∣••en edidit.

Sect. II. Arithmetick.

ARithmetick is the Art of Num∣bering; 'tis either Practical or Speculative; the Speculative Arithme∣tick contains some general truths rela∣ting to Numbers: As for instance, Unity is the beginning of every Num∣ber; a Number is a Multitude com∣pounded of Unites. An even part of a Number is that which by Multiplica∣tion produceth that number. As 2 is an

even part of 10, because 2 multiplied by 5, give 10.

An uneven part of a number is that which by Multiplication produceth not that number. Thus 3 is an uneven part of 10, because however multiplied, it shall never produce this number 10.

The proportion of Numbers is either according to their excess, defect, or equality, for that thing has some pro∣portion to another that is either less, greater, or equal. A perfect number is that which is equal to all its even parts: The first perfect number is 6, for all its even parts are 1, 2, 3, which together give 6. The next perfect Number is 28, for all its even parts are 1, 2, 4, 7, 14, which by Addition give 28.

These ensuing notions likewise may be referr'd to the Speculative part of Arithmetick,

To Multiply one number by another, as 4 by 2, is to take the Multiplicand 4 as many times as the Unity may be taken

in the Multiplicator 2, and so 4 being multiplied by 2, the Product must be 8.

To divide one number by another; as for instance, 8 by 2, is to find out how many times 2 are contained in 8.

A plain number is the product of two numbers multiplied the one by the other; 12 then is a plain number, because it is the product of 6 multiplied by 2.

A Solid number is the product of three numbers multiplied, such is 24, because 'tis the product of those three numbers multiplied 2, 3, 4, for multiplying 2 by 3 I have 6, and 6 by 4 I have 24.

A Square number is the product of two equal numbers muitiplied by one another, or of the same number multi∣plied by itself. 4 Is a Square number, as being the product of 2 multiplied by 2, and 2 is called the Square Root.

A Cube is the product of three equal numbers, or of the same number thrice taken; for if you multiply 2 by 2, you

have 4; and if you multiply 4 by •• again, you have 8, and 8 is called th•• Cube Root.

That part of Arithmetick that relate•• to the Practice, contains, First Ad¦dition, which is the gathering of man•• numbers into one Sum; as if I add •• to 6, the whole is 8. Secondly Sub¦straction, as if I take 4 from 6, ther•• remains 2▪ Thirdly, Multiplication as if I enquire how many are four time•• six, and I find 24. Fourthly, Divi¦sion, as if I enquire how many times •• are contained in 24, and I find the•• to be contain'd four times in 24. Fifthly, the Fractions. Sixthly, th•• Decimal Fractions, invented to supply broken numbers, very troublesome to Practitioners. Seventhly, the Ex¦traction of Roots, Cubic and Square▪ Eighthly, the four Rules of Proportion, of Society, Alligation, Falshood, the Doctrine of Progressions.

We may reckon the ensuing Au∣thors among the best Arithmeticians. Simon Stevinius invented the Deci∣mal Fractions; Neper supplies trou∣blesome and intricate Divisions by his Rabdologick Plates, and his Loga∣rithms; and Tacquet has given us both the Theory, and the Practice of Arithmetick; Euclid in the 7, 8, 9, and 10 of his Elements of Geometry; Jordanus, Nemorantius, Francis Mau∣rolycus, Barlaamon, &c.

Sectio Secunda. Arithmetica.

ARithmetica est ars numerandi; est autem practica aut specula∣tiva; haec manifeste vera quaedam, & generalia de numeris pronunciata complectitur: Cujuscemodi ea sunt quae sequuntur. Omnis numeri prin∣cipium est unitas; numerus est multi∣tudo ex unitatibus composita. Pars aliquota numeriea est quae numerum me∣titur. Ita numerus hic 2 est pars

••iquota numeri hujus 10, quinquies ••im 2 sunt 10.

Pars aliquanta numeri est ea quae ••umerum non metitur. Ita numerus ••ic 3 est pars aliquanta numeri hujus ••o; ter enim sumptus dat 9, & qua∣••er dat 12.

Proportio numerorum est nume∣••orum consideratio juxta excessum, defectum aut aequalitatem: Illud ••nim ad aliud proportionem habet, quod aut minus, aut majus, aut aequale est.

Perfectus numerus dicitur qui om∣nibus suis partibus paribus aequalis est. Primus perfectus est 6, illius enim om∣nes partes pares seu aliquotae sunt 1, 2, 3, quae simul additae dant 6. Se∣cundus est 28; nam illius omnes par∣tes aliquotae seu pares sunt 1, 2, 4, 7, 14, quae simul additae 28 producunt.

Subsequentes pariter notiones ad Arithmeticam speculativam referri poterunt. Unum numerum per alium

••ultiplicare seu in alium ducere ut 4 ••n 2 est toties sumere multiplicandum •• quoties sumi potest in multiplicatore •• unitas: Quare si 4 ducas in 2, summa ••utura est 8. Unum numerum divi∣••ere per alium ut 8 per 2 nihil aliud est quam invenire quoties 2 conti∣••eantur in 8. Numerus planus a duo∣••us numeris in se invicem ductis pro∣ducitur, 12 igitur est numerus planus quia producitur a numero 6 in 2 ducto.

Solidus numerus a tribus numeris multiplicatis oritur: Ejusmodi est 24, ex tribus enim hisce numeris multipli∣catis emergit 2, 3, 4; si enim 2 duco in 3 habeo 6, & si duxero 6 in 4, ha∣••eo 24. Numerus quadratus produ∣citur a duobus aequalibus numeris inse invicem ductis, cujusmodi est 4: Oritur enim a numero 2 in 2 ducto, qui radix quadrata dicitur.

Cubus oritur ex multiplicatione trium numerorum aequalium, aut ejus∣dem numeri ter assumpti ita 8 cubus

primus ex multiplicatione numeri 2 ter assumpti, producitur, si enim 2 du∣cas in 2 habes 4, & si 4 rursus ducas in 2 habes 8, & 2 radix cubica dicitur.

Pars illa Arithmeticae quae spectat praxim complectitur primo Additio∣nem quae est plurium numerorum in unam summam collectio, ut si ad∣dam 2 huic numero 6 summa integra futura est 8. Secundo, Substractio∣nem ut si 4. subduco e numero 6, super∣sunt 2. Tertio, Multiplicationem, ut si inquiram quot constituant quater 6, comperiam 24. Quarto, Divisionem ut si inquiram quoties 6 contineantur in 24 comperioque in 24 quater con∣tineri. Quinto, Fractiones. Sexto, Fractiones Decimales ad supplemen∣tum Fractionum practicis permolesta∣rum excogitatas. Septimo, Extra∣ctionem radicum cubicarum, ac qua∣dratarum. Octavo, Regulas propor∣tionum, societatis: alligationis, fal∣si, & doctrinam progressionum.

Annumerare possumus sequentes Authores primis Arithmeticis. Simo∣••em Stevinium fractionum decemalium ••nventorem; Neperum Scotum qui divisionis molestiam laminis suis rab∣dologicis, & logarithmis omnem sustu∣••it; Tacquetum qui Arithmeticae, & Theoriam, & praxim tradidit; Eucli∣••em 7, 8, 9, 10, Elementorum, Jor∣••anum, Nemorantium, Franciscum Maurolicum, & Barlaamontium, &c.

Sect. III. Judiciary Astrology.

JUdiciary Astrology is that Science, by the help of which Men pretend to judge of things to come, and more especially of Mens Good and Bad For∣tunes. The Judiciary Astrologers do ascribe considerable vertues to the diffe∣rent Conjunctions amd Aspects of the Stars.

They distinguish five kinds of mu∣tual Aspects among the Planets: The first is called a Sextile, when one Pla∣net is distant from another the sixth part of the Circuit of the Heavens, that is to say, 60 degrees. The se∣cond is called a Quartile, when the distance is but the fourth part of the circle or 90 degrees. The third is cal∣led a Trine, when the distance is but the third part of the circle, or 120 de∣grees. The fourth is called an Oppo∣sition,

when the two Planets are in the two opposite points of the circle, and distant from one another 180 degrees. The fifth is called a Conjunction, when the two Planets are in the same Sign of the Zodiack.

Astrologers divide the Heavens into twelve equal parts, which they call Hou∣ses; they say that every Planet has eight dignities, viz. House, Exalta∣tion, Triplicity, Term, Chariot or Throne, Person, Joy, Face.

They say the Stars were not only made to give light: Hence 'tis they take the station, direction and retrogradation (as they speak) of a Planet to be a cer∣tain reeling, or spinning of Fates and Fortunes: They distinguish all the Constellations into so many Triangles or Trigones: The first is the fiery Trigone, comprehending Aries, Leo, Sagittarius; the second is the Earthly, comprehen∣ding those ensuing Constellations, Tau∣rus, Virgo, Capricornus; the third is the Aerial, comprehending Gemini,

Libra, Aquarius; the fourth Trigone is the Watery, comprehending Cancer, Scorpius, Pisces.

If you desire to know more particularly the Principles of this Science, you may consult these following Authors. Van∣nius, Butler, Cardan, Gadbury, Al∣bottazen, Haly, Julius Firmicus, Jo∣hannes Jovianus Pontanus, Peze∣lius, &c.

Secttio Tertia. Astrologia Judiciaria.

AStrologia Judiciaria ea est Scien∣tia cujus ope de rebus futuris homines pronunciant, ac praesertim de faelici aut infaelici cujusque fato. Astrologi Judiciarii insignes ascri∣bunt virtutes diversis conjunctioni∣bus, aspectibusque planetarum.

Quinos distinguunt aspectus plane∣tarum. Primus dicitur Sextilis cum distat planeta unus ab alio sexta par∣te circuli, hoc est 60 gradibus. Se∣cundus vocatur Quadratus cum di∣stant invicem quarta parte ejusdem circuli, hoc est 90 gradibus. Tertius dicitur Trigonus quando tertia tan∣tum parte, seu 120 gradibus. Quar∣••us Oppositionis cum uterque pla∣neta

sibi oppositi sunt, disjunctique 180 gradibus. Quintus est Conjun∣ctionis cum duo planetae sunt in eo∣dem signo Zodiaci.

Universum Coeli ambitum secant Astrologi in duodenas partes aequa∣les, quas vocant domos seu domi∣cilia.

Octonas planetarum dignitates nu∣merant, quae sunt domus, exaltatio, trigonus, terminus, carpentum, per∣sona, gaudium, facies.

Stellas dicunt non creatas tantum ad orbem illuminandum: Unde aiunt stationem, directionem & re∣trocessum planetae esse nescio quam fatorum revolutionem, ac quasi ne∣tionem: Constellationes omnes distin∣guunt tot in triangula seu trigona: Primum trigonum igneum dicitur, complectiturque Arietem, Leonem, Sagittarium; secundum terrestre ap∣pellatur, continetque Taurum, Virgi∣nem, Capricornum; tertium aerium est complexum Geminos, Libram, Aqua∣rium;

quartum appellatione aqueum, continet Cancrum, Scorpium, Pis∣ces.

Si propius hujus Scientiae prin∣cipia intueri volueris, consulere po∣teris hos sequentes Authores, Van∣nium, Butlerium, Cardanum, Gadbu∣rium, Justinum, Philippum Melancto∣num, Origanum, Ptolomaeum, Alboha∣zen, Haly, Julium Firmicum, Jo∣hannem Jovianum Pontanum, Peze∣lium, &c.

Sect▪ IV. Astronomy.

AStronomy gives us an account of the Motions of Coelestial Bodies, of of their distance, order, bulk, &c. The Ba∣bylonians will have Belus to have been the Inventor of it, the Aegyptians Mercury, the Moors Atlas and Hercu∣les, the Grecians Jupiter, Orpheus and Atreus, the Scythes Prometheus. We may divide it into two Parts, the one Spherical, and the other we may call Systematical The Spherical is that part of Astronomy which treateth of the Sphere, whether Artificial or Natural; the Artificial Sphere is made up of ten circles, whereof six are great ones, because they divide the whole Sphere into two equal parts, such we reckon the Horizon, the Meridian, the Equator, the two Colures, and the Zodiack. The little Circles are those that divide the Sphere

into two unequal parts, as the two Tro∣picks, and the two Polar Circles: Every circle is divided into sixty parts, which they call first minutes; and each Minute likewise into sixty parts, which we call second Minutes.

The Natural Sphere, or the Coelestial Globe, besides the foregoing Circles, of∣fers to our view divers Constellations: The Antients reckon'd eight and forty, comprehending in this number all the Stars to be seen in Greece, and all the known Parts of the World; 12 of those Constellations are contain'd in the Zo∣diack, 21 are to be seen toward the North, and 15 towards the South; but of late there are twelve other Constellations discovered towards the South.

The Systematical Astronomy, which others call the Theorical, is that part which by the help of some Engines and Orbs, offers to our view those Coelestial Motions which are not so obvious to every common understanding.

This part of. Astronomy comprehends several Hypotheses, as that of Anaxa∣goras and Democritus, who allowed a free motion to the Stars, but of no first Mover, or Primum mobile: Neither did they admit any second motion to∣wards ihe East, but a simple motion only towards the West; so in their Opinion, those Stars only could be said to move toward the East, that moved more slowly towards the West. There is another Hypothesis that considers the Stars as tied to solid Spheres; and who hold this Hypothesis, hold likewise the Earth to rest in the Centre of the World.

Copernicus allows motion to the Earth; he fixeth the Sun in the Centre of the World, though it turns round about its own Axis within seven and twenty days, as 'tis manifest by the mo∣tion of its spots. 1. In this System, the Orb of the sixed Stars is immoveable. 2. Mercury turns round the Sun in almost three months. 3. Venus in four months

and a half, and the Earth itself in twelve months, and round the Earth the Moon tarneth every month. 4. Mars's revolu∣tion round the Sun is ended in almost two years, as Jupiter's in twelve years, and Saturn's in thirty.

Tycobrahe orders his System thus: First the Firmament, or the Sphere of the fixed Stars, the Earth being the Centre of the World; then the Orbs of Saturn, Jupiter and Mars; Venus and Mercury turn round the Sun, and the Moon round the Earth.

The Old System was ordered thus: The Earth was the Centre of the World, a∣bove it were plac'd the Planets and Hea∣vens in this order; the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, the two Chrystalline Heavens, and the Primum mobile.

Authors.

Ptolomy, Aratus, Eudoxus, Calippe, Tycobrahe, Gassendy, de Billy, Cour∣cier, de Sacrobosco, Fracastorius, Ga∣lilaeus.

Sectio Quarta. Astronomia.

AStronomia describit corporum Coelestium motum, distantiam, ordinem, magnitudinem, &c. Illius inventorem Babylonii volunt esse Be∣lum, Aegyptii Mercurium, Mauri At∣lantem & Herculem, Graeci Jovem, Orpheum & Atreum, Scythae Prome∣theum. Eam dividere possumus ge∣minas in partes, alteram Sphaericam, alteram appellare possumus Systema∣ticam. Sphaerica est ea pars Astrono∣miae quae agit de Sphaera, sive arte facta, sive naturali: Sphaera arte facta con∣stat 10 circulis quorum 6 sunt majores quia dividunt Sphaeram in duas par∣tes aequales; cujusmodi numeramus horizontem & meridianum aequato∣rem, colurosque duos aequinoctii, & solstitii, & zodiacum. Minores cir∣culi sunt ii qui Sphaeram in duas partes

inaequales dividunt: Cujusmodi sunt duo tropici, totidemque polares: Quivis circulus dividitur in gradus 360, & quivis gradus in 60 particu∣las, quas prima minuta vocant; & mi∣nutum primum in sexaginta partes quas secunda minuta dicimus.

Sphaera naturalis, seu Globus coele∣stis praeter commemoratos circulos aspicientibus exhibet varias constella∣tiones: Antiqui octo supra quadra∣ginta constellationes numerabant: Quo numero comprehendebant om∣nes stellas in Graecia conspicuas, atque in omnibus cognitis tum mundi parti∣bus: 12 constellationes continebat zo∣diacus, 21 apparent ad boream, 15 ad austrum, versus hanc partem duo∣decim nuper aliae detectae sunt.

Astronomia Systematica quam alii Theoricam vocant est ea Astronomiae pars quae aspectui nostro exhibet ope quarundam Machinarum Orbiumque eos coelestes motus qui omnibus non aeque obvii sunt.

Haec Astronomiae pars varias com∣plectitur hypotheses cujusmodi est hypothesis Anaxagorae ac Democriti, qui motum astris liberum assignabant sed nullum admittebant Primum mo∣bile; neque ulla proinde solidis Sphae∣ris alligabant sydera: Nec ullum secundum in ortum concedebant mo∣tum, sed simplicem tantum in occa∣sum: Ita juxta eorum sententiam ea tantum sydera moveri dicuntur in or∣tum, quae lentius moventur in occa∣sum: Alia quaedam est hypothesis quae sydera, ut solidis alligata Sphae∣ris intuetur; quique hanc hypothe∣sim tenent terram in centro mundi quietam volunt.

Copernicus motum terrae attribuit; so∣lem constituit in centro mundi immo∣tum, licet proprium circa axem movea∣tur spatio viginti septem dierum ut pa∣tet e motu ejusdem macularum in hoc systemate. 1. Orbis fixarum immo∣tus est. 2. Mercurius spatio fere trium mensium circa solem vertitur. 3. Venus

intra quatuor menses, & semissem, terraque ipsa duodecim mensibus, cir∣caque terram quolibet mense gyrat Luna. 4. Martis periodus circa so∣lem absolvitur duobus fere annis, ut Jovis duodecim, Saturnique spatio triginta annorum.

Suum Tycobrahe systema ita con∣stituit. Firmamentum, seu coelum fixarum primo loco statuit: Mundi centrum terra est; fixarum coelo suc∣cedit coelum Saturni, tum Jovis, & Martis, Venus & Mercurius circa solem gyrant luna circa terram movetur.

Antiquum systema ita se habebat: Terra mundi centrum occupabat; su∣pra illam erant aqua, aer, & ignis, suc∣cedebant planetae coelique hoc ordine, Luna, Mercurius, Venus, Sol, Mars, Jupiter, Saturnus, Firmamentum, duo coeli chrystallini Primum mobile.

Authores.

Ptolomaeus, Aratus, Eudoxus, Calip∣pus, Tycobrahe, Gassendus, Billius, Courcierius, de Sacrobosco, Fracastorius, Galilaeus.

Sect. V. Military Architecture.

ARchitectonica Militaris, or Mili∣tary Architecture, is the Art of Fortifying. This Art teacheth us how to encline towards the Angles of a Po∣ligone, that is, a Figure of many An∣gles, certaines lines upon which the For∣tress is to be built in such a manner, that the Enemy by whatever side he makes his approach, may be beat back by the lesser number.

Every point of the circumference of the Fortress must be defended by some

other part of the same.

According to the Holland method of Fortifying, the Angle of the Bastion, or the Flanqued, and Defended Angle ex∣ceeds always by 15 degrees the half of the angle of the Polygone; upon this account 'tis that the angle of the Bastion is never streight, or of 90 degrees, unless in a place defended by 12 Bastions; but in places defended by more than 12, it is always streight.

According to tht French method, if the Polygone be a triangle, the angle of the Bastion contains 45 degrees; if it be a Pentagone, or of five angles, it contains 78 degrees; if the Polygone have more than five sides, the angle of the Bastion is streight, or is open 90 deg.

Authors.

Errard of Barleduc, Samuel Maro∣lois, Adam Fritach, Stevin in Italian, de Lorini, del Cavallero Francisco Tensimi, del Cavallero Alessandro Ba∣rone, de Groote, Herigone.

Sectio Quinta. Architectonica Militaris.

ARchitectonica Militaris est ars muniendi, ars autem muniendi docet qui inclinare debeamus ad an∣gulos polygoni hoc est figurae variis terminatae angulis lineas quasdam su∣per quibus propugnaculum aedifican∣dum est, ita ut hostis quacumque parte invadat, minoribus viribus re∣pelli possit.

Omne punctum in procinctu muni∣menti debet defendi ab alia parte.

Juxta methodum muniendi Hol∣landicam angulus propugnaculi, aut defensus excedit semper quindecim gradibus semissem polygoni, quamo∣brem angulus propugnaculi nunquam est rectus nisi locus duodecim pro∣pugnaculis defenditur, quoties autem locus pluribus, quam duodecim pro∣pugnaculis munitur, rectus semper est.

Juxta Gallicam muniendi metho∣dum si munitum polygonum triangu∣lum fuerit, angulus polygoni est gra∣duum 46, si pentagonum fuerit, an∣gulus propugnaculi est gradibus 78; si polygonum constet pluribus quam quinque lateribus, angulus propugna∣culi est rectus, aut 90 graduum.

Authores.

Errardus Barneto-duceus, Samuel Marolois, Adamus Fritachius, Stevi∣nius Italice, de Lorini, Franciscus Ten∣simi, Herigonius, &c.

Sect. VI. The Military Art.

THe Military Art of the Greeks and the Romans was on several accounts different from that of this Age.

Of old an ordinary Grecian Army did contain 28672, among whom we reckon not those that were upon the Ele∣phants, who were sometimes in greater numbers, sometimes in lesser. This Army was divided into Horse and Foot: The Foot was divided again into Oplites and Psiles, the Oplites were those that wore a heavy Armour, the Psiles were slightly Arm'd.

The number of the Oplites was always double of the number of the Psiles, and the Psiles double of the number of the Cavalry. All the Oplites of the Pha∣lange were put in one Battalion, whereof the Front contained 256 men, and the Wing 16.

Of all the Psiles of the Phalange, the Grecians made two Battalions, each ha∣ving 128 men on a breast, and 8 in the slanks; all the Cavalry of the Phalange was divided into 16 squar'd Turmes or Troops, whereof each did contain 64 men.

In a Grecian Army made up of four Phalanges, there were four Battalions of Oplites, 8 of Psiles, and 64 Troops of Horse.

In a Roman Legion there were four different sorts of men, not only as to Age, Riches, Warlick Science, but likewise on the account of their Arms, and way of Fighting; for of the younger and poorer sort (as Polybius assures us) they made their Velites; those that were somewhat above them upon the account of their age and riches, were Halbar∣deers, or Hasteries; such as were richer, and in the full vigour of their age, were Princes; and the oldest and most experi∣mented, were the Triaries.

The number of the Soldiers of every one of those different sorts, was diffe∣rent in different times, according as the Legion was less or more numerous. When the Legion did amount to 4200, as it did in Polybius his time, there were 600 Triaries in the Legion, and 1200 of every one of the three other sorts, to wit, of Princes, Hastaries, and Velites. When the Legion was more numerous, those three different sorts were likewise encreased, the Tria∣ries only excepted, who were always the same number.

In the Militia of this Age, there is no such repartition observed, the Armies being not always divided into parts made up of the samo numbers; for some Regi∣ments have 10 Companies, others 15, others 20, &c. Likewise the Compa∣panies have not always the same number, some being a hundred men strong, others one hundred and twenty, others one hun∣dred and fifty, &c.

In this Age an Army is drawn up in Battel, or three Lines, and the French divide sometimes every Line into seve∣ral little Bodies; the Turks give some∣times to their Army the figure of a Cer••sont.

The Camp, especially if the Enemy be near, ought to be in some place where there is a great abundance of Water, and Provisions: And if the Army is to make a long stay, 'tis to be observed if the Air be good.

Ye are not to Encamp near a Hill, which being taken by the Enemy, might incommode your Camp.

Authors.

Polybius, Stevin, Herigone.

Sectio Secta. Ars Bellica.

ARS Bellica, seu Militaris tum Graecorum, tum Romanorum varie discrepabat ab hodierna recen∣tiorum.

Communis Graecorum exercitus numerabat 28672, quibus non annu∣meramus qui Elephantis insidebant qui non eundem semper numerum conflabant, sed interdum majorem, minorem interdum. Hic exercitus dividebatur in equites, peditesque, pedites rursus in Oplitas & Psilos, Oplitae erant gravis armaturae mili∣tes, Psili levis armaturae.

Numerus Oplitarum duplus erat numeri Psilorum, & Psili equitum nu∣merum geminabant. Omnes Oplitae unius Phalangis uno colligebantur in agmine cujus frons constabat 256, & ala 16.

Ex omnibus Psilis Phalangis consti∣tuebant Graeci duo agmina, a fronte stabant viginti octo supra centum, a latere octo. Omnes equites Phalan∣gis distribuebantur in turmas quadra∣tas sedecim, quarum quaelibet qua∣tuor supra sexaginta milites contine∣bat.

In exercitu Graeco ex quadruplici Phalange conflato quatuor erant ag∣mina Oplitarum, octo Psilorum, & sexaginta quatuor turmae equitum.

Romana legio quatuor complecte∣batur hominum Genera diversa non aetate tantum, divitiis, scientiaque Bellica, sed & armis, modoque pug∣nandi: Ex junioribus enim, paupe∣rioribusque, ut testatur Polybius seli∣gebantur Velites, ex proximis hasta∣rii, ex aetate florentibus Principes, se∣nioresque, & magis experti seligeban∣tur in Triarios.

Numerus militum ex quibus di∣versi illi ordines constabant diversis temporibus diversus erat; prout legio magis, minusque numerosa erat. Cum legio constabat ducentis supra quatuor millia, ut temporibus Polybii constabat; sexcenti erant Triarii in legione, ducenti supra mille in quovis ordinum reliquorum, scilicet Princi∣pum, Hastariorum, & Velitum: At numerosiore jam legione tres varii or∣dines numerosiores omnes reddeban∣tur, exceptis tantum modo Triariis quorum numerus idem semper erat.

In Militia hujus saeculi nulla hujus∣modi distributio observatur, cum exer∣citus non dividatur in partes eodem semper numero constantes: Quaedam enim legiones constant 10 cohortibus quaedam 15, quaedam 20, pauciori∣bus aut pluribus; cohortes pariter non semper eodem constant numero: Quaedam enim constant 100 militibus, aliae 120, aliae 150 &c.

Hoc saeculo exercitus pugnaturus in tres ordines distribuitur; Galli unumquemque ordinem in varia ag∣mina quandoque distribuunt, Turcae exercitum interdum ordinant in for∣mam lunae crescentis.

Castra, maxime si in propinquo fue∣rit hostis debent figi in loco tuto ubi magna adsit aquarum copia, com∣meatusque, & si diuturnior esse de∣beat exercitus mora, videndum an au∣ra illic salubris sit.

Cavendum autem imprimis ne ca∣stra prope montem statuantur, qui ab hoste occupatus exercitui noxius esse posset.

Authores.

Polybius, Stevinius, Heregonius.

Sect. VII. Cosmography.

COsmography is a Description of the World, and its chief Parts..

The World is the Highest Heaven, and whatever it contains, it is divided into the Sublunary Region, and the Coe∣lestial: The Sublunary Region is ob∣noxious to divers Changes, and is con∣tained in the concave surface of the Orb of the Moon: It contains the four Ele∣ments, the Earth, the Water, the Air, the Fire.

The Semi-diametre of the Earth con∣tains about 3436 Italian miles.

The ordinary depth of the Sea is 500 Geometrical paces.

The Surface of the Earth is almost equal to the Surface of the Sea, and somewhat higher, because we see that Ri∣vers from their first rise to the Sea go always downwards.

The Divines think that the Earth was entirely round, and surrounded with Waters on all sides, but after God had commanded the Waters to retreat, so many Hills were made as there are Con∣cavities to receive the Seas.

The Coelestial Region is that part of the World which is extended from the concave surface of the Heaven of the Moon, to the convex surface of the Highest Heaven; which space compre∣hends the Heavens of all the Stars.

Astronomers distinguish three sorts of Spheres; the first is streight, when the Equator maketh streight angles with the Horizon; the second is oblique, when the Intersection of the Horizon and Equator makes oblique angles; the third is the Parallel Sphere, when the Equa∣tor and the Horizon are joyned together.

Astronomers conceive ten Points, and ten chief Circles in the concave superficies of the first Mobile: The Points are the two Poles of the World, the two Poles of the Zodiack, the two Equinoctial, and two Solsticial Points, Zenith and Nadir.

The Circles are the Horizon, Meri∣dian, Equator, Zodiack, the Colures of the Equinox, and the Colures of the Solstice. The Cancer and Capricorne, the Arctick and Antarctick circles; by Zenith and Nadir we understand two points, the first directly answering to our Heads, and the second to our Feet.

Astronomers fancy divers Motions in the Heavens: the Primum Mobile turns round with it all the other Orbs in 24 hours. They allow to the other Hea∣vens under the first Mobile a motion of Libration from the North to the South, and from the South to the North.

The Eclipse of the Moon is a real pri∣vation of its light, by the interposition of the Earth between it and the Sun. The Eclipse of the Sun is not a real pri∣vation of light, because the Sun E∣clips'd, is only hid from our eyes by the interposition of the Moon.

All the Eclipses of the Moon are uni∣versal, or seen by all such as see the Moon; all the Eclipses of the Sun are

Particular ones, or not seen by every one that sees the Sun.

There are five Zones, one Torrid, two Temperate, and two Cold ones. The torrid Zone is comprehended be∣tween the two Tropicks; its breadth is 47 degrees, if we reckon according to the common Calcul 23 ½ on each side of the Equator; the two tempe∣rate Zones are contain'd between the Tropicks and the Polar Circles, whereof one is South, and the other North; the breadth of both is 43 degrees. The cold Zones are contain'd within the Polar Circles, distant from the Poles of the World 23 degrees ½.

Authors.

Peter Aerte his World, in five Vol. Herigone, Garcy, Adrianus Metius.

Sectio Septima. Cosmographia.

COsmographia est descriptio mun∣di, praecipuarumque ejusdem partium.

Mundus est caelum altissimum, & quicquid eo comprehenditur, dividitur in regionem sublunarem, & coele∣stem, regio sublunaris variis est ob∣noxia mutationibus, contineturque concava caeli lunaris superficie, qua∣tuor complectitur elementa, terram, aquam, aerem, ignem.

Semi-diameter terrae quadringenta fere & triginta sex supra tria millia, milliaria Ilalica complectitur.

Communis marium altitudo est pas∣suum Geometricorum quingentorum. - Superficies terrae est fere aequalis su∣perficiei maris, atque aliquanto altior, quia animadvertimus flumina ab ipsa origine ad mare descendere, seu deor∣sum tendere.

Putant Theologi terram initio ro∣tundam fuisse, atque aquis undique circumcinctam: Sed postquam Deus aquas recedere jussisset, tot erupere montes, quot sunt concavitates aquis marinis recipiendis idoneae.

Regio coelestis est ea pars mundi quae porrigitur a superficie concava coeli lunaris ad superficiem convexam altissimi coeli, quod spatium coelos om∣nium stellarum comprehendit.

Astronomi triplicem sphaeram di∣stinguunt prima est sphaera recta quando aequator rectos cum horizonte angulos constituit; secunda est o∣bliqua cum intersectio aequatoris, & horizontis constituit obliquos, tertia est parallela cum aequator, & horizon sibi congruunt, aut conjunguntur.

Astronomi in concava primi mobi∣lis superficie concipiunt 10 puncta, totidemque primarios circulos: Pun∣cta sunt duo mundi poli, duo poli zo∣diaci, duo puncta aequinoctialia, duo puncta solsticialia, Zenith & Nadir.

Circuli sunt horizon, meridianus, aequator, zodiacus, colurus aequino∣ctiorum, colurus solstitiorum, Tro∣picus Cancri, & capricorni, duoque polares: His vocibus Zenith & Na∣dir intelligimus duo puncta ex dia∣metro opposita, alterum, scilicet ze∣nith vertici nostro imminens, alterum nempe nadir, pedibus oppositum.

Astronomi varios concipiunt in coe∣lis motus. Primum mobile reliquos se∣cum coelos 24 horarum spatio circum∣ducit: Reliquis sub primo mobili coe∣lis addunt motum librationis a sep∣tentrione in austrum & ab austro in septentrionem.

Eclipsis lunae est vera luminis pri∣vatio interjectu terrae lunam inter & solem: Eclipsis solis non est realis pri∣vatio luminis. Sol enim deficiens tegitur tantum ab oculis nostris inter∣positu lunae. Omnes Eclipses lunae sunt universales aut conspicuae omni∣bus corpus lunare eo tempore intu∣entibus; omnes Eclipses solis sunt

particulares, aut non conspicuae om∣nibus qui solem ipsum intueri possunt.

Quinque sunt Zonae, una torrida, duae temperatae, duaeque frigidae, tor∣rida Zona comprehenditur duobus Tropicis: Ipsius latitudo est vulgari calculo 47 graduum; nempe 23 ½ cis, ••ltraque aequatorem; duae temperatae comprehenduntur tropicis, & polari∣••us circulis quorum alter meridiona∣••is alter borealis est, utriusque latitudo est graduum 43; frigidae Zonae com∣prehenduntur polaribus circulis dissi∣••is a mundi polis grad. 23 ½.

Authores.

Petrus de Aerte, seu mundus ipsius •• voluminibus, Herigonius, Garcaeus, Adrianus Metius.

Sect. VIII. Catoptrick.

CAtoptrick is derived from 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, a Looking-glass, because it treats of the Rays, as being reflected by polish'd Bodies. This Science demonstrates these following Propositions.

• 1. If a Ray falling upon a glass, make equal angles, 'tis reflected into itself.
• 2. Rays reflected from plain and con∣vex glasses, do neither come together, nor are equi-distant.
• 3. Heights and Depths seem to be overturned in Convex glasses.
• 4. In Convex glasses, what is on the left hand, appears to be on the right; and what is on the right hand, appears to be on the left.
• 5. If the eye were in the centre of •• Concave-glass, it would see nothing but itself.

Authors.

Euclid and Peter Herigone have written on this Subject.

Sectio Octava. Catoptrica.

CAtoptrica derivatur a Graeca voce 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, quod speculum sonat, quia agit de radio ut reflexo a laeviga∣tis corporibus, sequentes propositiones demonstrat.

• 1. Si radius in qualecumque specu∣lum cadens aequales facit angulos ipse in seipsum reflectitur.
• 2. Radii a planis, convexisque spe∣culis reflexi neque mutuo concurrent, neque erunt paralleli.
• 3. Altitudines & profunditates in convexis speculis inversae apparent.
• 4. In speculis convexis sinistra vi∣dentur dextra, & dextra sinistra.
• 5. Si oculus ponatur in centro spe∣culi concavi seipsum tantum cernet.

Authores.

Euclides, & Petrus Herigonius hoc super argumento scripserunt.

Sect. IX. Chymistry.

CHymistry is the Art of Analysing, or Resolving Bodies by the opera∣tion of the fire into their compounding principles.

The Chymists do generally affirm Mer∣cury, Salt, and Sulphur to be the com∣pounding principles of all compounded things; which Doctrine is learnedly and solidly confuted by the English Philoso∣pher, I mean the Famous Robert Boyle in his Sceptical Chymist. Yet it can∣not be denied but that it is useful and necessary likewise to mankind, upon the account of those many excellent Medi∣cines

it prepares to the great advantage of Physicians, and ease of their Patients, whereof these ensuing are some of the most considerable.

• 1. Aurum fulminans, or thundering Gold; a very good Sudorifick; it may be taken in the Measles from 2 grains to 6 in any convenient Electuary; it stops Vomiting, and is a hindrance to the activity of Mercury, or Quick-silver.
• 2. Vitriolus Lunae taken inwardly, is prevalent against the Dropsie, and the Head-ach, of what sort soever; you may take it from 2 grains to 6 in any Speci∣fick water; it is likewise a moderate purger.
• 3. Sal Jovis, is a great drier.
• 4. Magisterium Bismuth, softeneth the skin, and is good against Scabs and Itch, if you mix a drachm of it with 4 ounces of water, because it is a great de∣stroyer of Salts and Acids, two general causes of most Distempers.
• 5. Sal Saturni taken inwardly, pre∣vaileth against the Squinancy, the over∣flowing

• of the Flowers, Piles, Dysentery; you may take it from 2 grains to 4 in Plantain-water.
• 6. Oleum Saturni cleanseth and dri∣eth up Ulcers.
• 7. Spiritus ardens Saturni resisteth powerfully putrefaction; it is beneficial to such as are troubled with too much Melancholy. You may take it from 8 to 16 drops, in any convenient liquor, a fortnight together.
• 8. Crocus aperitivus martis has a a peculiar vertue against all distempers occasioned by obstructions▪ You may take it from 2 grains to 2 scruples in Lozenges or Pills.
• 9. Crocus martis astringens is of a peculiar vertue against the glitting of the Yard, the overflowing of the monthly Flowers and Piles; you may take it from 15 grains to a drachm in Lozenges or Pills.
• 10. Mars Diaphoreticus cures effe∣ctually the most melancholy distempers, as likewise Quartan-Agues; you may

• take it from 10 to 20 grains in Pills, or any convenient Liquor.
• 11. Sublimatum corrosivum eats up superfluous flesh, and drieth up Ul∣cers.
• 12. Sublimatum dulce, or Aquila alba, is very good against all Venereal Distempers; 'tis a great Deobstruent, and killer of worms; it may be taken in Pills from 6 grains to 30: 'Tis a mild purger.
• 13. Praecipitatum rubrum drieth up wounds, and consumeth superfluous or proud flesh.
• 14. Turbith minerale, or The Yel∣low Praecipitate, is a strong purger, and worketh both upwards and downwards; 'tis good against Venereal Distempers; you may take it in Pills from 2 gr. to 6.
• 15. Crudum Antimonium is a Su∣dorifick, but if you boyl it in any acid liquor, it will provoke you to vomit.
• 16. Regulus Antimonii purgeth upwards and downwards, if mixed with any Cathartick or Purger.
• ...

• 17. Vitrum Antimonii is the stron∣gest Vomitory that is made of Anti∣mony.
• 18. Antimonium Diaphoreticum resisteth powerfully Poison, and is like∣wise good against contagious Distem∣pers, and against the Measlles.
• 19. Flores Antimonii provoke to Vomit; and Rubri flores Antimonii as yet more; you may take them both from 2 gr. to 14, taking every quarter of an hour a spoonful of Broth wherein you have boyl'd a competent quantity of the Cream of Tartar.
• 20. Sulphur Antimonii is prevalent against the Distempers of the Breast; you may take 6 grains of it in any appropri∣ated liquor.

Authors.

Paracelsus, Beguinus, Helmontius, and the deservedly Renowned Robert Boyle, &c.

Sectio Nona. Chymica.

CHymica est ars reducendi corpo∣ra vi ignis in ea ex quibus con∣stant principia. Fatentur Chymicorum plerique, asseruntque Mercurium, Sal, Sulphur, esse tria ut loquuntur, pri∣ma, seu constituentia omnium rerum compositarum principia: Quam do∣ctrinam erudite more suo, ingenioseque ac solidis argumentis confutat Philo∣sophus Britannicus celeberrimus me∣rito Boylius in Chymico suo Sceptico.

Nemo tamen inficias ierit Chy∣miam & utilem esse generi humano, & necessariam ob tot generosa quae

parat medicamenta non mediocri me∣dicorum emolumento, magnoque com∣missorum ipsis aegrorum levamine: Quae hic subjunguntur, quaedam sunt ••e praecipuis.

• 1. Aurum fulminans sudores pro∣vocat; adhiberi potest adversus mor∣billos, minima dosis sit gr. 2 maxima gr. 6 sistit vomitum, obstatque acti∣vitati Mercurii.
• 2. Vitriolus lunae interius sumptus praevalet contra Hydropem, & quem∣cumque capitis dolorem: dosis mini∣ma gr. 2 maxima 6 in quacumque aqua specifica; leniter quoque pur∣gat.
• 3. Sal Jovis valde desiccat.
• 4. Magisterium Bismuth, emollit carnem, valetque contra scabiem & pruriginem si illius drachmam qua∣tuor unciis aquae commisceas, quia salia, & acida, geminas plerumque morborum causas destruit.
• 5. Sal Saturni, si sumatur interius praevalet contra anginam, immode∣ratum

• menstruorum fluxum, Haemor∣rhoides, Dysenteriam; dosis minima gr. 2, summa 4, in aqua plantaginis.
• 6. Oleum Saturni purgat, exsic∣catque Ulcera.
• 7. Spiritus ardens Saturni potenter resistit putrefactioni; nimia melan∣cholia dejectis prodest: dosis 6, 8 aut 16 guttae in quovis conveniente liquo∣re per quatuordecim dies.
• 8. Crocus aperitivus martis peculi∣ari virtute pollet adversus morbos ab obstructionibus ortos: dosis minima gr. 2 summa scrupuli duo in trapeziis, aut pilulis.
• 9. Crocus martis astringens peculiari∣ter valet contra stillicidium penis, ni∣mium menstruorum fluxum, & hoe∣morrhoides; dosis ima gr. 15, summa, drachma in trapeziis, aut pilulis.
• 10. Mars Diaphoreticus reipsa cu∣rat plerosque morbos a melancholia ortos, atque febres etiam quartanas;

• dosis 10 aut 20 gr. in pilulis, aut con∣veniente quopiam liquore.
• 11. Sublimatum corrosivum exedit superfluam carnem, exsiccatque Ul∣cera.
• 12. Sublimatum dulce, aut Aquila alba pollet adversus omnem venere∣am intemperiem: insigniter Deob∣struit, vermiumque excidium est; si in pilulis sumitur; minima dosis gr. 6 summa gr. 30; leniter purgat.
• 13. Praecipitatum rubrum exsiccat vulnera, consumitque superfluam car∣nem.
• Turbith menerale, aut Praecipitatum flavum valide purgat superne & in∣ferne, valet adversus morbos venereos; dosis ima in pilulis gr. 2. summa gr. 6.
• 15. Crudum Antimonium est sudo∣rificum, sed si illud in acido quopiam liquore concoquas, vomitum provo∣cabit.
• Regulus Antimonii Cathartico cui∣piam immixtus superne, inferneque purgat.
• ...

• 17. Nihil ex Antimonio fit, quod po∣••entius Vitro Antimonii vomitum ex∣••itet.
• 18. Antimonium Diaphoreticum re∣••istit potenter veneno, valetque contra morbos contagiosos, & morbillos.
• 19. Flores Antimonii vomitum pro∣••ocant fortiusque, adhuc, Rubri flores Antimonii; amborum dosis ima gr. 2 ••umma 15, sume interim quovis qua∣••rante horae Cochleare jusculi in quo ••remoris tartari sufficiens mensura ••octa fuerit.
• 20. Sulphur Antimonii pollet ad∣versus omnes pectoris morbos; dosis ••r. 6 in quovis idoneo liquore.

Authores.

Paracelsus, Helmontius, Beguinus, meritoque celeberrimus ubique Boy∣••ius.

Sect. X. Dioptrick.

DIoptrick is that part of Astrology that searcheth out by Instruments the distance of the Sun, Moon, and other Planets. If you take it more generally, its chief end is to shew the apparent chan∣ges of our sight, and of visible objects look'd into through Prospective glasses.

It treats of the broken or refracted Rays of light, and this is its chief prin∣ciple: When a Ray passeth through a thin middle into a thicker, it breaks in the Superficies of the thicker towards the perpendicular line; and when it pas∣seth through a thick middle, or medium, to a thinner it deviates from the perpen∣dicular line, which this obvious experi∣ment demonstrates. Lay an Image, or any other visible object, in the bottom of a Vessel, and then go back till it vanish out of your sight; now if you fill this Ves∣sel

with water, it shall presently be vi∣sible again, because the Ray coming from your eye, breaks downwards in the superficies of the water, as the same going streight up to the superficies of the water deviates from the perpendicu∣lar, because of the thinner air towards the eye, which renders the object visible again.

This Science treats likewise of Con∣vex and Concave glasses, as they may work some change in the sight, and may help it. It gives▪ an account of those whom Aristotle calls 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, who see remote things distinctly, and nearer ob∣jects confusedly; and why those whom we call 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, see both the remote and nearer objects confusedly.

It teacheth likewise amongst other things, 1. That those whom we call 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 see distinctly some things that are represented by Convex glasses in a streight situation. 2. That they see not distinctly through a Convex glass any of those objects that are overturn'd.

3. It sheweth the influence of Glasses ap∣plied one to another upon our sight.

Authors.

Kepler, Maurolycus, Euclide, &c. have written of this curious Science.

Sectio Decima. Dioptrica.

DIoptrica ea Astrologiae pars est quae instrumentis quibusdam distantiam Solis & Lunae, aliorumque planetarum indagat. Eam in genere si spectes, praecipuus ejusdem scopus est indicare apparentes visus muta∣tiones, objectorumque per vitra op∣tica ut microscopia, megaloscopia in∣spectorum, agit de radio fracto; hocque primarium hujus scientiae principium est: Cum radius lucis progreditur a tenuiore medio ad dentius, frangitur versus perpendicularem in superficie spissioris; cumque progreditur a me∣dio spissiore ad tenuius, deviat a per∣pendiculari. Quod obvio hoc experi∣mento manifestum fit: Imaginem aut quodvis aliud conspicuum obje∣ctum infundo vasis cujuspiam colloca: tum recede donec objectum non am∣plius

appareat: Jam si vas hoc aqua impleas, oculis se mox imago ogge∣ret: Quia radius lucis ab oculo ad fundum vasis porrectus frangitur de∣orsum in superficie aquae versus Per∣pendicularem, ut idem ad superfi∣ciem ascendens ob tenuiorem aerem deviat a perpendiculari versus ocu∣lum, unde fit ut objectum rursus con∣spiciendum se praebeat.

Insuper haec Scientia agit de con∣vexis concavisque vitris, quatenus visum aut variare, aut juvare possunt. Redditque pariter rationem cur ii quos Aristoteles 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 vocat, remo∣ta distincte videant, propinqua con∣fuse; & cur ii quos 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 dicimus tum remota, tum propinqua objecta confuse videant.

Inter alia pariter docet, 1. Eos quos 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 dicimus, quaedam vi∣dere distincte quae a vitris convexis recto in situ exhibentur. 2. Mi∣nime eos videre distincte per vitra convexa ullùm eorum objectorum quae eversa sunt. 3. Ostendit vi∣trorum

sibi invicem junctorum in vi∣sum nostrum operationem.

Authores.

Keplerus, Maurolycus, Euclides, &c. de curiosa hac Scientia scripsere.

Sect. XI. Moral Philosophy.

EThica is that Art which directs us how to act always conformably to right reason: Its chief principle is this, Do as you would be done by.

It teacheth us that God is our last end, because he only is Bonum Suffi∣ciens, the Sufficient Good, nothing else being able to content us. It teacheth likewise that we can never love any thing but under the shew and appearance of Good, whereof it offereth three sorts, Honour Profit and Pleasure.

God alone is our Objective Beatitude or Happiness, (as they speak in the Schools,) our Formal Beatitude is that operation of the Mind by which we possess God, which is the Intuitive Vision or Contemplation of God.

This Art sheweth that the Internal Principles of Humane Actions are either Natural, as Powers; or Acquired, as Habits: That the Understanding moves the Will to act, and the Will our Un∣derstanding; that a Habit being gene∣rated by the repetition of Acts, giveth the Soul not the real power of acting, but only enables it to act more easily.

Authors.

Aristotle, Seneca, Plato, Cicero, &c.

〈1 page duplicate〉〈1 page duplicate〉

Sectio Undecima. Ethica seu Moralis Philosophia.

HAEC ea est ars quae nos ad agen∣dum in omnibus conformiter rectae rationi dirigit: Primarium ip∣sius principium hoc est, Quod tibi vis fieri, & alteri feceris.

Docet Deum esse ultimum nostrum finem quia ille solus est Bonum Suffi∣ciens, cum nihil aliud beatos nos effi∣cere queat: Docet pariter nihil nos amare posse nisi sub specie boni, cujus triplex genus proponit Jucundum, Utile Honestum.

Beatitudo nostra Objectiva, ut lo∣quuntur Scholae, solus Deus est, For∣malis nostra Beatitudo est ea mentis operatio qua Deum possidemus, In∣tuitiva scilicet Dei Visio.

Hic Habitus docet principia in∣terna actionum humanarum, aut esse nobis congenita, cujusmodi sunt Po∣tentiae; aut acquisita, cujusmodi sunt Habitus; docet intellectum movere vo∣luntatem ad agendum, & vice versa; habitum actuum repititione produ∣ctum, animae tribuere non ipsam qui∣dem agendi facultatem, seu poten∣tiam, sed majorem quamdam facili∣tatem.

Authores.

Aristoteles, Seneca, Plato, Cicero, &c.

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Sect. XII. Geography.

GEography is the Description of the Earth, and its chief Parts..

Because Geographers talk much of the Longitude and Latitude of a place, 'tis of some use to know what is meant by these two words.

The Longitude then of a place, or its distance from the East, is an Arch of the Equator intercepted between the Se∣micircle of the first Meridian, and the Meridian of the place, according to the order of the Signs. The Latitude of a place, or its distance from the Equi∣noctial line, is the arch of the Meridian, intercepted between the Equator and the place proposed, being always equal to the elevation of the Pole, which is the arch of the Meridian intercepted between the conspicuous Pole and the Horizon, be∣cause the latitude of a place, as likwise the

height of the Pole, together with the arch of the Meridian intercepted between the Pole & the Zenith, are equal to the fourth part of the Meridian or the Quadrant.

The whole World is now divided in∣to four Parts, Europe, Asia, Africa, and America: Europe is bounded to∣wards the North by the Hyperborean Sea, towards the West by the Atlantick Sea, and the Herculean by the Streights of Gibraltar and by the Ocean; towards the East by the Egean Sea, the Helles∣pont, Propontis, Bosphorus Thracius, the Streights of Caffa, the Meotide Lake, the River Tanais, &c. till you come to a little Town called ••uria, from whence 'tis bounded by a white line till you come to the White Sea.

The chief Parts of Europe are Ger∣many, Spain, France, Great Britain, Switzerland, the Low Countries, Ire∣land, Denmarck, Norway, Swede∣land, Poland, Italy, Croatia, Sclavo∣nia, Dalmatia, Albania, Grecia, Thra∣cia, Bulgaria, Servia, Bosnia, Russia, Hungaria, Transylvania.

Asia is bounded towards the North by the Scythian Sea, towards the East by the Sea called Eoum, towards the South by the Indian Sea or the Red Sea, to∣wards the West by the Arabick Sreights and the Interne Sea.

Africa is joyn'd to Asia by an Isthme, or a narrow piece of Ground dividing two Seas: 'Tis bounded by several Seas, towards the East by the Red Sea, to∣wards the South by the Ethiopian Sea, towards the West by the Atlantick Sea, towards the North by the Interne Sea.

The chief Parts of Africa we reckon to be those following, Barbary Biledul∣geride, Sarra, the Countrey of the Ne∣groes, Egypt, Ethiopia both superior and inferior, the Kingdom of the A∣byssins.

America was wholly unknown to the Antients till about the year 1492, it was discovered by Christopher Columbus, a Genoese, in the name of Ferdinand King of Castile. 'Tis called America from Americus Vespucius, a Floren∣tine,

who the first after Columbus, in the Year 1497, under the auspices of the King of Portugal, discover'd that Part of it that lyes beyond the Equinoctial line.

America is divided into two Parts, the one Norrhern, and the other Southern, or the Peruane America; they are both divided by an Isthme. The Northern America is called the Mexi∣can, from its chief City Mexico. We know only those Countreys that lye near the shore, as Canada, the Land of La∣brador, the adjacent Islands, New France or Norimbegra, Virginia or Apalchen, Florida, New Spain, New Grenade, California, Quivira, Ana∣nian, Jucatan, Guatimala, Hondura, Nicaragna.

In the Southern America you have Castile, the Golden Peru, Chili, Chica, the Countrey of the Pantagons, Brasilia, Caribana, Guiiana, Biquiri or the Coun∣trey of the Amazons, Paguan, Picoram, Moxos, Uram, Charchas.

Authors.

Ptolomy, the Great Atlas, the En∣glish Atlas, Ortelius, Strabo, Soli∣nus, Pomponius Mela, Philipp Clu∣vier, &c.

Sectio Duodecima. Geographia.

GEographia est descriptio terrae praecipuarumque ejus par∣tium.

Quia Geographi multum loquun∣tur de Longitudine ac Latitudine loci, utile fuerit scire quid reipsa sint.

Longitudo itaque loci, aut ipsius distantia ab ortu, est arcus aequatoris inter semicirculum primi meridiani, & meridianum loci secundum ordi∣nem signorum interceptus. Latitu∣do loci aut ejusdem distantia a linea aequinoctiali est arcus meridiani inter∣ceptus aequatorem inter, & locum propositum, estque semper aequalis ele∣vationi poli, quae est arcus meridia∣ni horizontem inter, & conspicuum polum interceptus, quod tam latitudo

loci, quam elevatio poli cum arcu meridiani inter polum & zenith in∣tercepto, aequent quadrantem meri∣diani.

Totus terrarum orbis nunc dividi∣tur in quatuor partes, Europam, Asiam, Africam, Americam: Europa termi∣nos habet a septentrione Mare Hyper∣boreum, aut septentrionale, ab occi∣dente Mare Atlanticum, fretum Her∣culeum, & Oceanum, ob ortu Mare Aegaeum, Hellespontum, Propontidem Bosphorum Thracium, Bosphorum Cimmerium, Lacum Maeotim, Ta∣nais fluenta usque ad oppidum Tuia, inde lineam rectam ad sinum usque Granduicum, seu Mare Album.

Praecipuae Europae partes sunt, Ger∣mania, Hispania, Gallia, Magna Britannia, Helvetia, Belgium, Dania, Suedia, Polonia, Italia, Croatia, Sclavonia, Dalmatia, Albania, Grae∣cia, Thracia, Bulgaria, Servia, Bosnia, Russia, Hungaria, Transyl∣vania.

Asia terminatur versus septentrio∣nem Mari Scythico, versus ortum Ma∣ri Eoo, versus meridiem Mari Indico, aut Rubro, versus occidentem sinu Arabico & Mari Interno.

Africa Isthmo jungitur Asiae, termi∣nos habet varias circum maria, ab ortu mare Rubrum, a Meridie Aethiopi∣cum, ab occasu Atlanticum, a sep∣tentrione internum.

Praecipuas Africae partes sequen∣tes numeramus, Barbariam, Biledul∣geridem, Sarram, Regionem Nigri∣tarum, Aegyptum Aethiopiam u∣tramque superiorem & inferiorem, Regnum Abyssinorum.

America antiquis prorsus incognita fuit, donec sub annum quadringen∣tesimum nonagesimum secundum su∣pra millesinum detecta fuit a Chri∣stophoro Columbo Genuensi nomine Ferdinandi Regis Castiliae. America dicitur ab Americo Vespucio Floren∣tino

qui primus post Columbum anno 1497. sub auspiciis Regis Lusitaniae eam partem continentis detexit quae ultra lineam aequinoctialem jacet.

America dividitur duas in partes alteram septentrionalem, meridiona∣lem alteram aut Peruanam; utraque Isthmo dividitur, septentrionalis A∣merica vocatur Mexicana a praecipua ejusdem civitate Mexico▪ Regiones tantum littoribus adjacentes novimus, nempe Canadam, terram Laboratoris, atque insulas adjacentes, Novam Fran∣ciam sive Norimbregram, Virginiam sive Apalchen, Floridam, Novam Hispaniam, Novam Granatam, Cali∣forniam, Quiviram, Ananian, Juca∣tan, Guatimalam, Honduram, Ni∣caragnem.

In meridionali America sunt Ca∣stilio Aurea, Peruvia, Chili, Regio Pentagonum, Brasilia, Caribana, Guiiana, Biquiri, Paguam, Picoram, Moxos, Uram, Charchas.

Authores.

Ptolomaeus, Magnus Atlas, Ortelius, Strabo, Solinus, Pomponius Mela, Philippus Cluverius.

Sect. XIII. Geometry.

THis Science teacheth us how to Measure the Earth, and to set limits to every Mans Lands; 'tis entire∣ly contain'd in the Fifteen Books of Euclid's Elements: The first thirteen are acknowledg'd by all to be undoubtedly of this Author; the two last are ascrib'd by some to Hipsicles of Alexandria.

Euclid's Elements may be divided into four Parts; the first Part, contain'd in the first six Books, treats of Plains; the second, consisting of the three other

following Books searcheth into the pro∣perties of Numbers; the third Part of Euclid's Elements, consisting of the tenth Book only, treats of commensura∣ble and incommensurable Lines; and lastly, the fourth Part comprehending the remaining Books, treats of Solids, or Bodies.

The first part of Euclid's Elements is again threefold; the first four Books treat of Plains absolutely considered, of their equality and inequality; the fifth treats of the proportion of Magnitudes in general; the sixth sheweth the propor∣tion of plain Figures.

Geometry may be divided into these three subordinate parts, Altimetry, Pla∣nimetry, and Stereometry; Altime∣try is the Art of measuring streight Lines, Planimetry is the Art of measu∣ring Surfaces, Stereometry is the Art of measuring Solids or Bodies.

A line is measured by a line of a known magnitude, and a superficies or surface by a square of a known magnitude, and

Solids are measured by a Cube of a known bulk.

Authors.

Euclid, Hero Mechanicus▪ Four∣nierius, Malapertius, Maginus, Cla∣vius, Nicolaus Tartalea in Italian, Adrianus Metius, Samuel Marolois, Simon Stevin, and Daniel Sant Bech.

Sectio Decima tertia. Geometria.

HAEC Scientia docet nos qui terram metiamur, atque unius cujusque praediis limites praescriba∣mus: Integra continetur quindecim Libris Elementorum Euclidis: Prio∣res tredecim sine ulla controversia Euclidi ascribuntur ab omnibus, po∣steriores vero duo, a quibusdam Hyp∣sicli Alexandrino tribuuntur.

Elementa Euclidis dividi possunt in quatuor partes; quorum prima pars sex prioribus libris contenta, agit de planis; secunda, quae ex tribus se∣quentibus

conflatur, affectiones nu∣merorum examinat; tertia pars Ele∣mentorum Euclidis, quae solo libro de∣cimo constat, de lineis commensura∣bilibus, ac incommensurabilibus agit; quarta denique pars, quam residui libri constituunt de solidis, aut corpo∣ribus disserit.

Prima pars Elementorum Euclidis rursus triplex est; priores enim qua∣••uor libri agunt de planis absolute spectatis, de eorum aequalitate, aut inaequalitate; quintus disserit de pro∣portionibus magnitudinum in genere; sextus planarum figurarum propor∣tiones exponit.

Geometria dividi potest in has tres partes subordinatas, in Altimetriam, Planimetriam, & Stereometriam; Altimetria est ars dimetiendi lineas rectas, Planimetria est ars dimetiendi superficies, Stereometria est ars dime∣tiendi solida, sive corpora.

Lineas metiuntur lineae notae mag∣nitudinis, superficiem metitur qua∣dratum

mensurae notae, solidaque me∣titur cubus notae molis.

Authores.

Euclides, Hero Mechanicus, Four∣nierius, Malapertius, Maginus, Cla∣vius, Nicolaus Tartalea Italice, Adri∣anus Metius, Samuel Marolois, Simon Stevinius, Daniel Sant Bechius.

Sect. XIV. The Art of Dialling.

GNomonica is the Art of Dialling, or of making Sun-dials.

Of Sun-dials there are two sorts, some are Pendulums, and others are Fix'd ones. The Pendulums are those that being hung up, or held up, shew the hours by the height of the Sun, as the Astrolabe, the Cylinder, the Quadrants, the Astronomical Rings, and others of the same kind.

The Fixed-dials require a certain situation, to shew the hours by the mo∣tion of the Sun from East to West, and upon this account they are more exact than the Pendulums.

The Centre of the Dial, is that point of the plane of the Dial in which the axis of the World is cut by the plane.

The perpendicular Style is a streight line drawn from the centre of the Earth to the plane of the Dial: The centre then of the World, or of the Earth in a Dial, is the top of the style, which is perpendicu∣lar to the plain of the Dial.

The Pole of the plane of the Dial, is the Pole of a great circle equi-distant from the plane of the Dial.

In all Astronomical Dials, that part of the style which by its shadow sheweth the hour, must be in the axis or axle-tree of the World.

The Italians reckon 24 hours, begin∣ning from the setting of the Sun; the Babylonians reckon as many from the rising of the Sun, to the going down of

the same; but in the old Dials, the hours of the day, and of the night, are reckon'd separately, viz. 12 from the rising of the Sun, till the going down of the same; and as many from the set∣ting of the Sun, till the rising of the same.

Authors.

Maurolycus, Ptolomaeus, Kircherus, &c.

Sectio Decima quarta. Gnomonica.

GNomonica est ars construendi horologia solaria.

Horologia solaria dividuntur in pendula, & fixa: Pendula sunt ea quae appensa, aut manu suspensa, ho∣ras indicant ope altitudinis solaris: Cujusmodi sunt Astrolabium, Cylin∣drus, Quadrans, Annuli Astronomici, aliaque ejusdem generis.

Horologia stabilia, seu fixa, requi∣runt situm quemdam ut ostendant ho∣ras ope motus solis ab ortu in occa∣sum, ideoque accuratiora sunt pen∣dulis.

Centrum horologii est punctum plani horologii, in quo axis mundi se∣catura plano.

Stylus perpendicularis est recta a centro terrae ad planum horologii du∣cta, unde centrum mundi, sive terrae in horologio est vertex styli plano ho∣rologii normalis.

Polus plani horologii, est polus magni circuli paralleli plano horo∣logii.

In omni horologio Astronomico ea pars styli quae umbra horam ostendit, debet esse in axe mundi.

Itali numerant horas 24 initio du∣cto ab occasu solis; Babylonii nu∣merant totidem initio ducto ab ortu

solis; sed in antiquis horologiis horae diei, noctisque separatim enumeran∣tur, duodecim scilicet enumerantur ab ortu solis ad occasum, totidemque ab occasu ad ortum.

Authores.

Maurolycus, Ptolomaeus, Kircherus, &c.

Sect. XV. Grammar.

GRammar is the Art of Writing and Speaking well; it treats of Words and the Construction of Words.

This Art considereth two things in Words, the Letters, and the Sylla∣bles; as likewise two sorts of Letters for some sound alone, and are called Vowels, as a, e, i, o, u,; others sound not alone, but together with some other letter, and they are called upon this account Conso∣nants, as these following, b, c, d g k, p, q, t, which letters are called Mutes, as f, l, m, n, r, s, x, z are called half Vowels.

A Syllable that has a full sound is made up either of a Vowel and a Conso∣nant, or of Vowels and Consonants.

In Words, Grammar considereth their accent or tone, whether acute, or

grave, or mean; their Derivation and Etymology, their Composition and Sim∣plicity; their numbers; if the word be a Noun, Plural, singular; their Cases, Nominative, Genitive, Dative, Accu∣sative, Vocative, Ablative: If the word be a Verb, it considereth the Tenses, as Present, Imperfect, Perfect, Future or to come.

It teacheth the Art of Construing words one with another, as the Adjective with the Substantive, in order to make a congruous Speech; either continued or interrupted: It distinguisheth the sen∣tences by three notes, which we commonly call Comma, Semicolon, Colon, or as the Latins speak, Punctum.

The first is a short pause of respira∣tion, which we express thus (,) the se∣cond is a longer pause, which we express thus (;) the third is a full pause, and finisheth the sense, which we mark thus (.)

Chief Authors.

Alvares and Despauter.

Sectio Decima quinta. Grammatica.

GRammatica est Ars recte loquen∣di, scribendique; agit de voci∣bus, vocumque constructione.

Duo contemplatur in vocibus lite∣ras & syllabas, ut pariter duo gene∣ra literarum quaedam enim solitarie sonant, & vocales dicuntur, ut a e, i, o, u,; quaedam solitarie non sonant, sed simul cum alia quapiam litera, & propterea consonantes dicuntur, cu∣jusmodi sunt hae literae oppositae b, c, d, g, p, q, t, quae literae dicuntur mu∣tae, ut f, l, m, n, r, s, x, z dicuntur se∣mivocales.

Syllaba quae integrum habet sonum, constat vel unica vocali, vel vocali addita consonante, vel vocalibus si∣mul & consonantibus.

In vocibus Grammatica considerat accentum, seu tonum, sive acutum,

sive gravem, sive medium, earum derivationem, originem, atque ety∣mologiam, compositionem, simplici∣tatem, Numeros, si quaestio de No∣mine sit, Singularem, Pluralem; Casus, Nominativum, Genitivum, Da∣tivum, Accusativum, Vocativum, Ab∣lativum; si quaestio de Verbo sit, con∣siderat Tempora, ut Praesens, Imper∣••ectum, Praeteritum, Futurum.

Docet qui voces simul construere debeamus, ut Adjectivum cum Sub∣stantivo, ut fiat oratio congrua, con∣tinua, aut interrupta; distinguit sen∣tentias tribus hisce notis, quas designa∣mus appellationibus hisce Comma, Se∣micolon, Colon, aut ut Latini loquun∣tur, punctum.

Prima nota indicat brevem a respi∣rando cessationem, quam exprimimus hunc in modum (,) secunda est diu∣turnior cessatio quam exprimimus hunc in modum (;) postrema est ple∣na cessatio, sensumque absolvit, quam ita notamus (.)

Authores primae notae.

Alvares, Despauterius, &c.

Section XVI. Hydrography.

HYdrography is a Description of the Waters, especially the Seas.

The Sea is the general Collection of Waters, 'tis divided into the Ocean and Mediterranean Sea: The Ocean is that Sea which surrounds the whole Earth, 'tis divided into the great Ocean, Gulfs and Streights.

The Ocean hath four different names, from the four opposite points of the World, from the East, 'tis called the Eastern Sea; from the South, the Southern; from the North, the Northern; 'tis divided into three vast Seas, Indian, or Red Sea; the Atlantick Sea, so called

from Atlas, a Hill in Mauritania; and the Pacifick Sea.

The Indian Sea reacheth from the Islands of Sumatra and Java to the Pro∣montory of Good Hope, its chief Gulfs are the Ganget••ck Gulf, or the Gulf of Bengala, whose longitude is 120 deg. latitude 16 deg. the Persick Gulf, or Elcatif Sea, whose longitude is 76 deg. latitude 26; the Arabick Gulph, or the Red Sea, commonly called Mar di Meca, whose longitude is 70 deg. latitude 20; the Barbarick Gulf, whose longitude is 70 deg. latitude 4.

These are the chief Islands of the Ocean, Lerne, or Madagascar, or the Island of St. Laurence, longit. 75 deg. lat 20. Discuriada, or Zocotara, longit. 48 deg. lat. 11. the Maldives, longit. 105. lat. 5. Nanigeris, commonly called Zeilan, longit. 113. lat. 6. Taprobana, Suma∣tra, longit. 130. lat 0. Java the Great, longit. 140. lat. 10.

We reckon among the chief Islands of the Atlantick Sea, Albion, or Great

Britain, longit. 22. lat. 52. Ireland, longit. 13. lat. 54. Hesperides, or the Islands of the Cap vert, longit. 353. lat. 17. Cuba, longit. 295. lat. 22. Ja∣maica, 298. lat. 18.

The Pacifick, or Southern Sea, lies between Asia, America, and the Ma∣gellanick Gulf; its chief Islands are Japan, longit. 170. lat. 36. The Mo∣lucs, longit. 157. lat. 1. Salomon's Islands, longit. 195. lat. 10.

Authors.

Herigone, Ortelius, Pomponius Mela, Joachim, Vadiam, Fournier.

Sectio Decima sexta. Hydrographia.

HYdrographia est descriptio A∣quarum, maxime Marium.

Mare est generalis aquarum col∣lectio, dividitur in Oceanum, & Mare Mediterraneum: Oceanus est mare quod universam terram ambit, divi∣ditur in vastum, sinuosum, & fre∣tum.

Oceanus quatuor sortitur appella∣tiones a quatuor cardinalibus mundi partibus, ab oriente Eous dicitur, ab occidente Occiduus, a meridie Australis, a septentrione Septentrio∣nalis; dividitur in tria vasta maria Indicum, sive Rubrum, Atlanticum a••

Atlante Mauritaniae monte sic dictum, & in Pacificum.

Oceanus Indicus porrigitur ab Insu∣lis Sumatra, & Java usque ad Ca∣put Bonae Spei: Ejus praecipui Sinus sunt Gangeticus, sive Bengalensis, cujus longitudo 120 graduum, latitudo 16 graduum. Sinus Persicus, cujus longit. 76 graduum, latitudo 20 graduum. Sinus Arabicus, aut Mare Rubrum, vulgo Mar di Meca, cujus longit. 70. lat. 20. Sinus Barbaricus, sive Mare Asperum, cujus longit. 70. lat. 4.

Primariae Oceani Insulae sunt Lerne, aut Madagascar, seu Insula Sancti Lau∣rentii, cujus long. 75. lat. 20. Discuria∣da aut Zocotara, cujus long. 48. lat. 11. Maldiviae, longit. 105. lat. 5. Nani∣geris, vulgo Zeilan, cujus longit. 113. lat. 6. Taprobana, Sumatra, longit. 130. lat. 0. Java Major, longit. 140. lat. 10.

Praecipuae Insulae Maris Atlantici sunt Albion, sive Magna Britannia,

••ujus longit. 22. lat 52. Hibernia, ••ujus longit. 13. lat. 54. Hesperides, ••ut Insulae Promontorii viridis, longit. ••arum Insularum 353. lat. 17. Cuba, ••ujus longit. 295. lat. 22. Jamaica, ••ujus longit. 298. lat. 18.

Mare Pacificum, sive Meridionale ••cet inter Asiam, Americamque, & ••retum Magellanicum; Praecipuae ejus ••nsulae sunt Japonia, cujus longit. 170. ••t. 36. Molucae, longit. 157. lat. 1. ••nsulae Salomonis longit. 195. lat. 10.

Authores.

Herigonius, Ortelius, Pomponius Me∣••, Joachimus, Vadiamus, Fournierius.

Sect. XVII. Logick.

LOgick is the Art of Disputing wel•• The three operations of the Min•• make up its whole object, which are Ap∣prehension, Judgement or Affirmation and Illation. It teacheth, that the truth of any of those three operations consist•• in their confirmity to their objects: S•• this compounded Apprehension, Go•• Almighty, is true, because I apprehen•• God to be, what he really is, that i•• Almighty; you may easily apply this t•• the other two Operations.

Its two chief Principles are these Dictum de omni, and Dictum de nul∣lo: The first signifieth, that whatever 〈◊〉〈◊〉 generally affirmed of any thing, m•…•… likewise be affirm'd of whatever is con∣tain'd under that thing, as if I s•…•… Every Animal is a living Creature, th•…•… it follows, that a Bird is a living Cre••∣tur••▪

The second signifieth, that what ever is generally denied of any thing is denied likewise of whatever is con∣tain'd under that thing; as if I say No Animal is a Stone, then I may, an cught likewise to say, No Bird is Stone, No Man is a Stone, &c.

Logick teacheth the Art of making Syllogism, which consisteth of three Pro∣positions, whereof the first two being gran∣ted, the Conclusion must necessarily b•• granted, because it was already impli∣citely admitted by him, who admitted of the Premises: As 'tis evident in this Syllogism, Every Man is a living Crea∣ture, Peter is a Man, ergo, Peter is a living Creature.

Logick is natural to all Mankind, be∣cause 'tis nothing else but the use of our Reasoning Faculty. Artificial Logick is made up of some Rules and Precepts that help our Reasoning Faculty.

Authors.

Aristotle, Arriaga, Ruvius, Guil∣minot, &c.

Sectio Decima septima. Logica.

LOgica est ars recte disserendi: Ipsius objectum sunt tres mentis ••perationes; Apprehensio, Judicium ••ut Affirmatio, & Illatio. Docet ••eritatem illarum operationum in ea∣••um cum ipsis objectis conformitate esse positam; ut composita haec ap∣prehensio, Deus Omnipotens, est vera, ••uia apprehendo Deum, ut reipsa est omnipotentem: Quod reliquis operationibus applicari facile potest.

Duo praecipua Logicae principia sunt ista, Dictum de omni, & Dictum ••e nullo: Prius significat quicquid ge∣neraliter affirmatur de re quapiam, affirmari idem posse de omnibus sub eadem contentis, ut si dicam, omne animal est vivens, licebit dicere om∣nis volucris est vivens. Posterius

••nnuit, quicquid generaliter negatur de quapiam re, negari posse idem de omnibus eadem comprehensis; ut si dicam, Nullum animal est lapis; lice∣bit etiam dicere, Nulla volucris est lapis; Nullus homo est lapis, &c.

Logica docet artem conficiendi Syl∣logismi, qui constat tribus propositio∣nibus: Quarum duae primae si semel admittantur, tertia necessario admitti debet, quia jam tacite admissa est ab eo qui duas primas admisit, ut patet in hoc Syllogismo, Omnis homo est animal, Petrus est homo, ergo, Pe∣trus est animal.

Logica congenita est humano gene∣ri, cum nihil aliud sit quam facultatis nostrae rationalis exercitium. Artifi∣cialis Logica sunt praecepta quaedam hanc facultatem juvantia.

Authores.

Aristoteles, Arriaga, Ruvius, Guil∣minotius, &c.

Sect. XVIII. Metaphysick.

THis Science considers Beings, as abstracted from all matter; and is so called, because it treats of things somewhat besides, above, or beyond Na∣ture. It considereth two things in a Being, 1. Its Essence, which seems to have a real Being, though it does not exist, as a Rose in the midst of Winter. 2. Its Existence, which is actually in being, or by which a thing is actually in being, as the existence of a Rose is that by which it now is.

It considereth three properties of every Being, its Unity, Goodness, and Truth; Unity is that by which a thing is one, and not many. Truth or Verity, is the conformity of any thing to its real or consistent Principles, as true Gold con∣sists in its conformity to the principles of

this Metal. The Metaphysical Goodness of things, is that essential perfection which is agreeable to them.

This Science treats likewise of Powers, Acts, Principles, and Causes, and proves, in opposition to Aristotle, and other an∣cient Philosophers, that the World was not eternal.

Authors.

Aristotle, Vasques, Suares, Va∣lentia, &c.

Sectio Decima octava. Metaphysica.

HAEC Scientia considerat Entia, ut abstracta ab omni materia, nomenque hoc trahit inde quod agat de rebus aliquatenus praeter, vel su∣pra, aut ultra naturam.

Duo in Ente contemplatur, 1. Es∣sentiam, quae videtur esse verum Ens licet non existat, ut Rosa media Hye∣me. 2. Existentiam quae actu in rerum natura est, aut vi cujus aliquid actu existit, ut existentia Rosae est id vi cu∣jus Rosa nunc existit.

Contemplatur tres in quovis Ente proprietates, Unitatem, Bonitatem, Veritatem: Unitas est id vi cujus quidpiam est unum, & non multa. Veritas est conformitas unius cujusque rei cum principiis veris, & constituen∣tibus, ut veritas Auri, aut Aurum verum est ejusdem conformitas cum consti∣tuentibus

hujusce Metalli principiis. Metaphysica Bonitas rerum est essen∣tialis illa perfectio quae rebus congruit.

Haec Scientia agit pariter de poten∣tiis, actibus, principiis, causis, con∣traque Aristotelem, aliosque antiquos Philosophos, probat mundum non fuisse aeternum.

Authores.

Aristoteles, Vasques, Suares, Va∣lentia, &c.

Sect. XIX. Musick.

MUsick is a Science which teacheth us what belongs to the Theory and Practice of Harmony.

Melody is that which has a certain order compounded of Sounds and Inter∣vals.

This Science treats of these seven ensuing things, of Sounds, of Intervals, of Genders, of Constitutions or Systems, of Tunes, of Changes, of the making of Melody.

The Sound is a gentle falling of the voice upon the Note.

The Interval is comprehended under two Sounds, the one sharper than the other.

Authors.

Guido Aretine, in the Year 1028, Invented these six Syllables, ut, re, mi, fal, sol, la, of which mi, fa, or fa, mi, imply a half Tune, and the others follow∣ing one another signifie a greater or lesser Tune; Euclid, Ptolomy, Aristoxenus, Faber Stapulensis, Boetius, John Ke∣pler, Salinas, Zarlins, and Vincentius Galilaeus in Italian.

Sectio Decima nona. Musica.

MUsica est Scientia quae Theo∣riam Praximque Harmoniae docet.

Concentus est id quod certum ha∣bet ordinem ex Sonis & Intervallis compositum.

Haec Scientia de septem hisce se∣quentibus agit, de Sonis, de Interval∣lis, de Generibus, de Constitutioni∣bus, de Tonis, de Mutatione, de Me∣lopaeia.

Sonus est concinnus vocis casus ad unam extensionem:

Intervallum est id quod continetur duobus sonis acumine, & gravitate differentibus.

Authores.

Guido Aretinus, anno salutis 1028, invenit has sex Syllabas, ut, re, mi, fa, sol, la, quarum mi, fa, vel fa, mi, dimidium Tonum significant, ac se∣quentes sese invicem aliae Tonum absque discrimine majorem aut mino∣rem; Euclides, Ptolomaeus, Aristoxe∣nus, Faber Stapulensis, Boetius, Joan∣nes Keplerus, Salinas, Zarlinus, Vin∣centius Galilaeus Italice.

Sect. XX. The Mechanicks.

THis Science considereth the quan∣tity of Moving forces, and of Duration of the time in which the Mo∣tion is performed.

The gravity of a Body, is a certain capacity of falling downwards; the cen∣ter of gravity, is that place or point from which if we conceive the Body to be suspended, whatever situation you may give it, it shall retain the same.

The Center of Magnitude, and of gra∣vity, are not always the same, as 'tis evi∣dent in a Bowl half Lead, half Wood.

The Pendula diameter of gravity, or the handle, is a streight line drawn through the center of gravity perpendicu∣larly to the Horizon.

No weight can rest, unless the pen∣dula diameter of gravity, or handle, pass through the place upon which it

leans, or from which the weight is sus∣pended.

In all Planes, the center of the figure, is likewise the center of gravity.

This Art teacheth in general, how to find out the ponderousness of every thing, and how to move things with little strength.

We must not forget in this place a sort of Mecbanism, the knowledge where∣of is of great concern for the good of Mankind; I mean that of Trusses, and Instruments fit for restoring by degrees, any part of the Body to its natural place and situation.

The burst Peritonaeum sometimes gives way to the Intestines, at other times to the Caul. and not seldom, to both, to get out of their natural place, into the Groins, or the Scrotum, there causing a Rupture, called Enterocele, or Her∣nia intestinalis; if the Bowels come out, an Epiplocele, or Hernia omen∣talis; if the Omentum or Caul be out. The Peritonaeum is made up of two

strong, but soft Membranes, which do so contain whatsoever is included in the Belly, that, when sound, nothing can fall out. In Women, the Os pubis is its utmost limit. In Men, its outermost Membrane reacheth further, and consti∣tutes the first proper coat of the Testi∣cles. In the Groin, it comprehends the seminal Vessels, as in a Sheath, called Processus, which being stretched or in∣larged, or coming to burst, is the im∣mediate cause of the lately mentioned Ruptures. We must not nevertheless imagine, that the Peritonaeum cannot be distended, and burst in other places, and therein to cause a Rupture.

The causes which make the Perito∣naeum to Burst or Dilate, are falling, leaping, beating, bearing of heavy bur∣thens, strong Vomitings or Coughing, Obstipation of the Belly, Winds pent in, and vehement motions of the Body.

But I can do no greater service to the Publick, than to inform the World of two of the best Artists I know of in this

kind, both living together in Black Fryers, in London, I mean the Famed Robert Smith, a Scotch Gentleman, and his Son-in-Law, Thomas Jewel, who give daily succesful proofs of their Skill in this kind of Mechanism, their Trusses of what kind soever being so light, so easie, and so fitted to all the motions of the Body, that they are not at all trou∣blesome.

They likewise cure effectually any De∣formity in humane Bodies, occasioned by the preternatural bending outwards, in∣wards, or downwards, of any part thereof, and by such ingenuously contrived En∣gines, as force Nature gently into its first place and situation.

Authors.

Aristotle, Henry Monenthole, Jo∣seph Blancan, Guid Ubald, Stevin, Hero, Robert Vulturius, Cedren, John Baptista Porta, Joseph Boillot, Ranelli, Barbette, Brown, &c.

Sectio Vigesima. Mechanica.

MEchanica est Scientia quae quantitates virium moven∣tium, & temporum in quibus fit mo∣tus considerat.

Gravitas corporis est quaedam po∣tentia ad descensum.

Centrum gravitatis est punctum ex quo vel sola cogitatione suspensum corpus, quemcumque situm dederis retinet.

Centrum gravitatis, & centrum magnitudinis non sunt semper idem, ut patet in Sphaera plumbo▪ lignea.

Pendula gravitatis diameter, aut ansa est linea recta ducta per centrum gravitatis acta Horizonti perpendicu∣laris.

Nullum pondus quiescere potest nisi pendula gravitatis diameter, aut ansa transeat per locum cui

innititur, aut e quo suspenditur corpus.

In omni Plano figurae centrum, cen∣trum quoque gravitatis est.

Haec ars docet in genere modum re∣periendae ponderationis, rerumque exiguis viribus movendarum metho∣dum.

Non est praetermittendum hoc lo∣co aliud genus mechanismi cujus no∣titia non parum humano generi pro∣fuerit; de mechanismo loquor, fas∣ciarum, instrumentorumque, aut ma∣chinarum quibus paulatim quaevis corporis pars ad debitum a natura si∣tum reducatur.

Rupto Peritonaeo interdum inte∣stina, omentum interdum, saepe & in∣testina, & omentum loco naturali ex∣cidunt in inguina, aut Scrotum, i∣bique Hernia producitur, dicta En∣terocele, aut Intestinalis, si prolaban∣tur Intestina, vel Epiplocele, aut Her∣nia Omentalis si Omentum excidat.

Peritonaeum gemina valida quidem

sed molli constat membrana, quae ita concludit quicquid imo ventre com∣prehenditur, ut cum sanum corpus est nihil procidere possit. Peritonaeum in mulieribus Osse pubis terminatur: In viris Tunica exterior ulterius pro∣cedit, ac Testiculorum involucrum primum proprium constituit. In In∣guine vasa seminalia comprehendit, instar vaginae, Processus dictae: Pro∣cessus hic laxatus, Dilatatus aut Rup∣tus est immediata herniarum mox commemoratarum causa: Non est tamen existimandum Peritonaeum non posse distendi, rumpique etiam aliis in locis ibique Herniam producere.

Causae Peritonaei Rupti, aut Dilatati hae fere sunt, lapsus, saltatio, percussio, gravium onerum gestatio, vomitus violentior, aut tussis, constipatio ven∣tris, flatus reclusi, vehementiorque omnis corporis motus.

Sed nihil forte utilius rei Publicae praestitero, quam si hic nominatim in∣dica vero duos peritissimos quos qui∣dem

norim hujusmodi mechanismi artifices simul conviventes Londini in ea regione urbis quae Black Fryers, dicitur; sunt autem ii celebris Rober∣tus Smith Scotus, ejusque gener Tho∣mas Jewel, qui quotidiana magnoque successu suae hoc in genere mecha∣nismi peritiae experimenta exhibent: Ipsorum enim fasciae cujuscumque ge∣neris, sive contra hernias Intestinales, sive Omentales, sive Umbilicales, sive Ventosas, aut contra aquosas, adeo leves sunt, gestatuque faciles, om∣nique corporis motui ita obsecundant, ut nihil omnino molestiae gestantibus secum afferant.

Reipsa quoque praenominati tollunt quamcumque humanorum corporum deformitatem a praeternaturali partis cujuspiam extrorsum, introrsum, aut deorsum distentione ortam, instrumen∣tisque ac machinis ingenii ejusmodi quibus natura suaviter ad pristinum situm reducatur.

Authores.

Aristoteles, Henricus Monentholus, Josephus Blancanus, Guidus Ubaldus' Stevinus, Hero, Robertus Vulturius, Cedrenus, Joannes Baptista Porta, Jo∣sephus Boillotus, Augustus Ranelli, Pau∣lus Barbettus, Johannes Brownius, &c.

Sect. XXI. Medica: Or the Art of Conserving and Curing Humane Bodies.

HErmes Trismegistus, a Fam'd Physician in Egypt, invented this necessary Art: 'Tis either Empirical, that is, grounded upon meer Experience; or Dogmatical, that is, grounded both upon Reason and Experience: Hippo∣crates and Galenus were the chief Ma∣sters of the Dogmatical part.

This Art is either Speculative or Pra∣ctical;

the former considereth, 1. The nature, and the outward causes of Di∣stempers, as the six things that are called not natural, because they are not the constituent parts of our Bodies, such we reckon the Air, Meat, Drink, Sleep, Watching, Motion and Rest, what we throw off, and what we retain, Excreta & Retenta; our Passions, Plethora, or fulness, Cacochymy, or an ill ha∣bit of our bloud. 2. It searcheth into the internal causes of our Distempers, as Wind, Worms, Acids.

The practical part of this noble and useful Art relates to the method of Cu∣ring, which is either performed by Alte∣ration or Evacuation. Whether this Evacuation be wrought by Bleeding, Vo∣miting, Stool, Urine, Sweat, or insen∣ble Transpiration; and upon this ac∣count, its true object is the whole Ma∣teria Medica, or whatever may be sub∣servient to the Physician's intention in either of the three Kingdoms, I mean, Animal, Vegitative, and Mineral.

The whole Materia Medica may be re∣duc'd to the ensuing Heads.

• 1. the Attenuating Remedies, as Eli∣campe Roots, Wormwood Leaves, Ca∣momile Flowers, the hot Seeds, Juniper, and Lawrel Berries, old Tallow, and Grease, especially that of a Wolf, and of a Bear, most Oyls, as of bitter Al∣monds, Walnuts, &c. the Plaisters of Betony, Diachylon, Oxycroceum, &c.
• 2. The Softening, as Marsh mallow Roots, Briony Roots, &c.
• 3. Such as dissolve Clots, as the Roots of round Birthwort.
• 4. The Deterging, as the Roots of Gentian, and Birthwort.
• 5 The Epicerasticks, that by a mode∣rate moisture take off the sharpness of the humour, as Mallow, and Marsh-mallow Roots.
• 6. Alexipharmaca, that resist Ve∣nome, as Angelica Root.
• 7. The Thickening, as the Roots of Bugloss and Plantain.
• ...

• 8. The Cathartick, which either purge the Bile, as Cassia, Manna, Tamarinds, &c. or the Phlegm, as Carthamy, wild Saf∣fron, Agarick, Turbith, Jalep, or the Melancholy, as Sena Oake-Fern, or the Watery Humours, as Dwarf Elder, El∣der-seed, Bark, Juice, Mechoaca.
• 9. The Vomitory, whether milder ones, as Sarabacca Leaves bruised in Dill Water, or stronger ones, as the Spirit of Tobacco, the Infusion of To∣bacco, Crocus Metallorum, &c.
• 10. Diureticks, as Radish Roots, Parseley Roots, &c.
• 11. The Sudorificks, as Harts horn, Diascordium, Angelica Roots, &c.
• 12. The Repelling Remedies, as the Sloe-tree Roots, Tormentil Roots, &c.
• 13. The Emplasticks that stop the passages of the Body, as Lilly Roots, wild Comphry Roots, &c.
• 14. The Absorbing Remedies, which by a great faculty of drying, consume the moisture, as all Cenders, Vineger, Brine, &c.
• ...

• 15. The Blistering, which raise Bli∣sters, as the Cantharides, Mustard, Gar∣lick, Water-cresses.
• 16. The Suppurating, that generate matter, as Marsh-mallow Roots, white Lilly Roots.
• 17. The Vulnerary, as Tormentil Roots, the Roots of both Comphreys.
• 18. The Sarcoticks, that remove what∣ever may hinder the breeding of Flesh, as the Roots of Birthwort, Tragacanth, Dragons Bloud, Sarcocolla, &c.
• 19. The Epuloticks, that generate a Callus, or Scarr, as Dragons Bloud, Myrtle Leaves.
• 20. The Anodines, as Marsh-mallows, and Lilly Roots.
• 21. The Narcoticks, which take away all feeling, as Oyl of Palm, Lau∣rel, Turpentine, Opium, &c.
• 22. The Hypnoticks, that cause Sleep, as Requies Nicolai, Diascordium, Lau∣danum opiatum, &c.
• 23. Such as stop Bleeding, as Corals, the Bolus, Seal'd Earth.
• ...

• 24. The Cephalicks, as the Roots of Birthwort, Betony Leaves, Galanga.
• 25. The Errhina, that purge the Brains and the Breast, by bringing down the superfluous pituite lying about the Meninges, as the Juice of Betony, the Powder of white and black Hellebore.
• 26. The Ophthalmicks for the Eyes, as Eye-bright, and Celadine water, and also their Juices.
• 27. Otica, that ease the pains of the Ears, as Laurel Leaves, Leeks, Ra∣dishes.
• 28. The Cardiacks, as the Roots of Zodoaria, Great Leopards Bane, Thistle, and Balm water.
• 29. The Bechick, that render the hu∣mours contained in the Lungs and the Breast, fit to be thrown up, as the Syrup of ground▪Ivy.
• 30. The Aromaticks, as Roots of Cy∣perus.
• 31. Splenica, such as cure the Spleen, as the Powder of Style, Valerian Roots.
• ...

• 32, The Nephritcks, that help the Reins, as Marsh-mallow Roots, Sal Pru∣nella, &c.
• 33. The Lithontripticks, that break the Stone, as Elecampane Roots, Galan∣ga, &c.
• 34. The Hystericks, that cure Hy∣sterical Fits, as Purslain Seed, the Seed of Agnus Castus, the Trochisques of Myrrh, &c.
• 35. The Arthriticks, that prevail against the Gout, as Elecampane Roots, Night-shade, Plaintain, Marsh-mallow Leaves.

Authors.

Hippocrates, Galen, Trallian, Ac∣tuarius, Cornelius Celsus, Avicenna, Sennertus, Riverius, Macasius, Re∣gius, Willis, Barbette, Harvey the Inventor of the Circulation of the Bloud.

Sectio Vigesima prima. Medica: Sive Ars Conservandi & re∣staurandi Humani Corporis.

HErmes Trismegistus celebris apud Aegyptios medicus necessariae hujusce artis inventor dicitur: Est au∣tem aut Empirica, hoc est quae me∣ra experientia, aut Dogmatica, quae ra∣tione & experientia nititur: Medici∣nae Dogmaticae praecipui magistri exti∣tere Hippocrates & Galenus.

Est aut speculativa aut practica;

prior considerat, 1. Naturam, cau∣sasque externas morborum, ut sex res dictas non naturales quia non sunt partes corporis humani constituentes, cujusmodi censemus aerem, cibum, potum, somnum, vigilias, motum, & quietem, excreta, & retenta, ani∣mi pathemata, plethoram, sive Ple∣nitudinem, Cacochymiam, sive pra∣vum sanguinis habitum. 2. Scruta∣tur internas morborum causas, puta flatus, vermes, acidum.

Practica pars nobilis hujus, uti∣lisque artis methodum medendi spe∣ctat, quae posita est in Evacuatione, & Alteratione, quocumque demum modo evacuatio contingat, sive venae sectione, sive vomitu, dejectione, su∣dore, urina, aut insensibili transpira∣tione; quocirca verum ipsius obje∣ctum est tota materia medica, aut quicquid in regno Animali, Vegeta∣bili, & Minerali, Medici scopo inservire poterit.

Porro totam materiam medicam ad sequentia capita reducere fere pos∣sumus.

• 1. Attenuantia, ut Radices Aenulae Campanae, Folia Absinthii, Flores Ca∣momillae, Semina Calida, Baccae Juniperi, Lauri, Axungiae vetustio∣res maxime Vulpina, & Ursina, Olea pleraque, ut amygdalarum Amara∣rum, Nucum, &c. Emplastra de Be∣tonica, Diachylon, Oxycroceum, &c.
• 2. Emollientia, ut Radices Altheae, Bryoniae.
• 3. Grumos dissolventia, ut Radices Aristolochiae rotundae.
• 4. Detergentia, ut Radices Gentia∣nae, Aristolochiae.
• 5. Epicerastica quae moderata hu∣midate Acrimoniam humorum ob∣tundunt, ut Radices Malvae, & Al∣theae.
• 6. Alexipharmaca quae resistunt Ve∣neno, ut Radix Angelicae.
• 7. Condensantia, ut Radices Buglos∣sae, & Plantaginis.
• ...

• 8. Cathartica que vel purgant Bi∣lem, ut Cassia, Manna, Tamarin∣di, &c. vel Phlegma, ut Carthamus, Crocus Sylvestris, Turbith, Jalap, vel Melancholiam, ut Sena, Polypo∣dium quercinum, vel Humores aquo∣sos, ut Sambuci, & Ebuli Semen, Cortex, Succus, Mechoaca.
• 9. Vomitoria, sive mitiora, ut asa∣ri folia, aut validiora, ut Spiritus Ni∣cotianae, Infusio Nicotianae, Crocus Metallorum., &c.
• 10. Diuretica. ut Radices Rapha∣ni, Apii.
• 11. Sudorifica, ut Cornu cervi, Di∣ascordium, Radices Angelicae.
• 12. Repellentia, ut Radices Pruni Sylvestris, Tormentillae, &c.
• 13. Emplastica quae corporis meatus obstruunt, ut Radices Symphiti, & Li∣liorum.
• 14. Absorbentia, quae valida exsic∣candi vi absumunt humorem, ut om∣nes Cineres, Acetum, Muria.
• ...

• 15. Vesicatoria, quae vesicas exci∣tant, ut Cantharides, Sinapi, Allium, Nasturtium.
• 16. Suppurantia, a quibus pus ge∣neratur, ut Radices Althaeae, Liliorum Alborum, &c.
• 17. Vulneraria, ut Radices Tor∣mentillae, Consolidae utriusque.
• 18. Sarcotica, quae removent quic∣quid Carnis generationem prohibet, ut Radices Aristolochiae, Tragacan∣tha, Sanguis Draconis, Sarcocolla.
• 19. Epulotica, quae callum gene∣rant, aut cicatricem, ut Sanguis Dra∣conis, Folia Myrthi.
• 20. Anodina, ut Radices Althaeae, Radices Liliorum.
• 21. Narcotica, quae omnem sen∣sum tollunt, ut Oleum Palmae, Lauri, Terebinthinae, &c.
• 22. Hypnotica, quae somnos conci∣liant, ut Requies Nicolai, Diascordi∣um, Laudanum opiatum, &c.
• 23. Sanguinem Sistentia, ut Co∣ralliae, Bolus, Terra Sigillata, &c.
• ...

• 24. Cephalica, ut Radices Aristo∣lochiae, Galangae, Folia Betonicae.
• 25. Errhina, quae cerebum pur∣gant & Thoracem, educta superflua circa meninges pituita, ut Succus Be∣tonicae Pulvis albi & nigri Hellebori.
• 26. Ophthalmica, ut aquae & succi Euphrasiae, & Chelidoniae.
• 27. Otica, quae levant aurium do∣lorem, ut Folia Lauri, Radices Porri, Raphani.
• 28. Cardiaca, ut Radices Zedoariae, Doronici, aquae Cardui Benedicti, & Melissae.
• 29. Bechica, quae humores in Tho∣race, & pulmone conclusos ad facilio∣rem Tussiendo ejectionem disponunt, ut Sirupus & succus hederae terrestris.
• 30. Aromatica, ut Sirupi Absin∣thii, & Betonicae.
• 31. Splenica, ut Pulvis ex Chalybe, Radices Valerianae.
• ...

• 32. Nephritica, ut Radices Althaeae, Sal Prunellae.
• 33. Lithontriptica, quae calculum frangunt, ut Radices Aenulae Campa∣nae, Galangae.
• 34. Hysterica, ut semen agni casti, Portulacae, Trochisci de Myrrha.
• 35. Arthritica, quae valent adver∣sus Podagram, & Chiragram, ut Ra∣dices Aenulae Campanae, Folia Solani, Plantaginis, Althaeae.

Authores.

Hippocrates, Galenus, Trallianus, Actuarius, Cornelius Celsus, Avicenna, Sennertus, Riverius, Macasius, Regi∣us, Willisius, Barbetius, Harveius circulationis Sanguinis Inventor, &c.

Sect. XXII. The Art of Sailing.

ARS Nautica, or Histiodromica, is that Art which teacheth how to direct a Ship through the Seas, to the propos'd Harbour.

This Art requireth the knowledge of the Mariners Compass, and the Lead, of the Sea-coasts, Capes, Rocks, Promonto∣ries, Harbours, of the distances of one place from another, of the ebbing and flowing of the Sea, of the latitude and longitude of every place. It requireth likewise the knowledge of several Instru∣ments fit to take the latitude of a place, as of the Cross-staff, of the Quadrant, of the Nocturnal, of the Plane Scale, of Gunter's Scale, &c.

The Mariners Compass is a round Plane, whose circumference is divided into 32 equal parts, by streight lines, called Rhombs, passing through the center.

The height of the Pole, of so great benefit to Sailers, is found out thus: Observe first the height of the Sun at Noon-day, with an Astrolabe, or some other Instrument of that kind; then take the declination of the Sun, from the height, if the Sun declines from the E∣quator towards the Northern Pole; or add the declination of the Sun, to the ob∣served height, if the Sun declines to∣wards the Southern Pole; the remaining number, or the sum made up by Additi∣on, gives you the height of the Equator, whose Complement to 90 degrees (as they speak) is always the height of the Pole. Thus if the height of the Equator above our Horizon be 60 deg. the height of the Pole is 30 deg. because 30 added to 60, make up 90; and if the Pole be eleva∣ted but 10 deg. the height of the Equator is 80, because this number is the Com∣plement of that.

If their could be an Hour Glass, or •• Clock, so contriv'd, as to fall but very little short of the Measure of Time▪

with the help of this Clock, to the great advantage of Sailers, the differences of the longitudes might be found after this manner: When the Ship sets off, let the Clock shew the hour in the place from whence you sail'd, without discontinu∣ing: If then we would know the longi∣tude of the place in which we now are, let us, by observation of the Sun, find the hour in that place we chance to be in; which if it be the same pointed at by the Clock, or shewn by the Glass, 'tis cer∣tain we are in the same Meridian we were in at our first setting out; but if we find by observation, more hours than the Clock pointeth at, we have made a progress towards the East; if we find fewer hours, we are gone towards the West; and the differences of the longi∣tudes may easily be known, if the diffe∣rences of the hours be converted into de∣grees, and minutes of degrees.

Authors.

Seller, Everard, Wright, &c.

Sectio Vigesima secunda. Ars Nautica.

ARS Nautica, sive Histiodromica ea est quae docet qui dirigi de∣beat navis per maria ad propositum portum.

Haec ars requirit notitiam pyxidis Nauticae, & Bolidis, orae Maritimae, Promontoriorum, Rupium, Portuum distantiarum inter loca, aestuum Ma∣ritimorum, latitudinis & longitudinis cujusque loci, instrumentorum pari∣ter variorum ad investigandam syde∣rum altitudinem, ut Baculi decussati, Quadrantis, Nocturnalis, Scalarum planarum, Scalarum Gunteri, &c.

Pyxis Nautica est planum rotun∣dum, cujus circumferentia in 32 par∣tes aequales dividitur rectis lineis per centrum transeuntibus quae Rhombi dicuntur.

Altitudo poli Navigantibus adeo utilis sic invenitur: Observa primo Meridianam solis altitudinem ope astrolabii, aut alterius cujuspiam in∣strumenti, tum substrahe declinatio∣nem solis ex altitudine jam inventa so∣lis, ope instrumenti, si declinatio solis versus polum conspicuum sit, aut adde declinationem solis observatae altitudi∣ni si sol declinaverit versus polum me∣ridionalem, residuum aut summa fu∣tura est altitudo aequatoris, cujus complementum est semper altitudo poli: Itaque si altitudo aequatoris su∣pra horizontem nostrum sit graduum sexaginta, altitudi poli futura est gra∣duum triginta: Quia si addas 30 ipsis 60, summa futura est 90; & si polus 10 tantum supra horizontem gradibus extet, aequator supra eundem extabit 80, quia hic numerus est complemen∣tum illius.

Si posset construi Clepsydra, aut ho∣rologium quod ab accurata mensura temporis parum aberraret: Illius ope

inveniri possent hoc modo longitudi∣num differentiae: Aptetur horologium ita ut dum solvit navis ostendat horas loci unde discedimus, deinde inter navigandum nunquam cesset: Cumque libuerit scire longitudinem loci in quo sumus, ex observatione coelesti inqui∣ratur illius loci hora, quae si omnino convenerit cum hora quam horologi∣um indicat, certum erit nos esse sub eo unde discessimus meridiano, si vero plures horas observatione invenimus, quam horologium indicet, progressi sumus versus ortum, si pauciores de∣fleximus versus occidentem, dignos∣ceturque differentia longitudinum, si reducantur differentiae horarum in gradus, & minuta graduum.

Authores.

Sellerius, Everardus, Wrightius, &c.

Sect. XXIII. Opticks.

THE Opticks, or Optica, gives us an account of various appea∣rances of Objects. This Science treats of the streight Ray, as the Catoptrick of the reflected, and the Dioptrick of the refracted or broken Ray. These follow∣ing Definitions belong to the Opticks. The proper Objects of Sense, are those that can be known but by one sense; and the common Objects, such as may be known by more than one sense. Light and Colour, are the proper Objects of our sight; the Light, upon its own ac∣count; and the Colour, by the help of Light. These following things, are the common Objects of our Senses, Bulk, Figure, Place, Situation, Distance, Continuity, Discontinuity, Motion, and Rest. The visuel Rays, are the streight lines, by which the frame of the visible Object is in a manner carried to the eye.

We may reckon among the chief prin∣ciples of this Science, these following.

The visible object radiates from all its least parts, to all the least parts of the Medium, to which one may draw a streight line.

That is seen, and that only, from which to the eye the visuel Ray may be eztended.

The more bodies there appear between the eye and the object, the more remote the objects appear to be.

The Convergent Rays, are those that departing from the object, come to∣gether: Such are, the Rays of diverse parts of the object, which cut one another in the Chrystalline humor. The Divergent Rays, departing from the object towards the eye, recede from one another: The Rays of every point of the object, are divergent, till they come to the Chrystalline humour, beyond which they come together again towards the Retina.

We may reckon these following Pro∣positoins amongst the most considerable of the Opticks.

No visible object is seen at first alto∣gether, and perfectly.

Magnitudes being in the same streight line, the remoter seem to be the lesser.

Parallel intervals seem to be nearer one another, the farther they are from the eye.

Rectangle Magnitudes being seen at a distance, seem to be round.

Equal Magnitudes being under the eye, those that are farthest from the eye, seem to be highest.

Authors.

You may reckon amongst the best Ma∣sters of the Opticks, Euclid, Aquilo∣nius, Scheiner, Vitellio, Alhazane, Herigone, &c.

Sectio Vigesima tertia. Optica.

OPtica variae objectorum apparen∣tiae causas demonstrat. Agit de radio recto, ut Catoptrica de re∣flexo, & Dioptrica de refracto. Ad Opticam spectant sequentes definitio∣nes. Propria objecta sunt ea quae ab uno tantum sensu percipi possunt. Communia sunt ea quae a pluribus sensibus percipiuntur. Lumen & co∣lor sunt propria visus nostri objecta, lumen quidem ratione sui, color ope lucis. Communia visus objecta sunt ea quae sequuntur, quantitas, figura, locus, situs, distantia, continuitas, discontinuitas, motus, & quies. Ra∣dii visorii rectae lineae sunt, quibus forma aspectabilis objecti ad visum porrigitur.

Inter praecipua hujus Scientiae prin∣cipia sequentia numerare licet.

Visibile radiat e quolibet sui puncto ad quodlibet punctum medii ad quod recta duci potest.

Id omne & solum videtur a quo ad oculum radius Opticus extendi po∣test.

Quo plura corpora oculum inter, & objectum apparent, eo remotius exi∣stimatur objectum.

Convergentes radii sunt ii qui rece∣dendo ab objecto simul coeunt. E∣jusmodi sunt radii variorum puncto∣rum objecti qui se mutuo in humore Chrystallino secant.

Divergentes radii progrediendo ab objecto versus oculum recedunt a se invicem donec ad humorem Chry∣stallinum pervenerint ultra quem ver∣sus retinam coeunt.

Annumerare possumus praecipuis Opticae; propositiones sequentes.

Nullum visibile objectum simul to∣tum, & perfecte videtur.

Magnitudinum in eadem recta quae remotiores videntur, minores appa∣rent.

Parallela intervalla eo magis ad se in∣vicem accedere videntur quo sunt re∣motoria ab oculo.

Rectangulae magnitudines procul visae apparent rotundae.

Aequalium magnitudinum sub ocu∣lo quae remotiores, videntur altiores.

Authores.

Inter praecipuos Opticae doctores censere possumus Euclidem, Aquiloni∣um, Alhazenum, Scheinerum, Vitellio∣nem Herigonium, &c.

Sect. XXIV. Perspective.

PErspective representeth every object seen in some Diaphane, or trans∣parent Medium, through which the vi∣sual Rays are terminated or bounded on the object; and generally what▪ is seen through something, as through the Air, Water, Clouds, Glass, and the like, may be said to be seen in Perspective.

The chief Contents of this Science, may be referred to these following Heads.

The Ray is a streight line drawn from the Eye to the Glass perpendicularly.

That point is called Primary, on which falls a perpendicular line drawn from the Eye to the Glass.

The projection of a line, is not a crooked line.

The object being a Point, there is but

one visual Ray drawn from the Object to the center of the Eye, and this Ray is called the Axis, or Centrical, as being the most vivid, and the strongest of all.

If the Object be a streight line, the visual Rays make a triangle. If the Ob∣ject be a Surface, plane or spherical, the visual Rays represent a Pyramide.

Ichonography is the Pourtraiture of the Platform or Plane upon which we would raise any thing.

Orthography is the Pourtraiture of the fore part of the Object.

Scenography representeth the Object wholly elevated and perfect, with all its Dimensions and Umbrages on all sides.

The Horizontal line in Perspective, is taken from the height of our eye: This is the chief piece of the Picture, and which ought to be the rule of the di∣mensions and height of the Figure.

The point of Perspective, or sight, is made by the centrical Ray above the Horizon.

Authors.

Amongst the chief Writers of Per∣spective, you have Roger Bacon, John Baptist Porta, Stevin, Marole, John Cousin, Daniel Barbaro, Vignola, Serlio, du Cereau, Salomon de Caus, Guidus Ubaldus, Niceronius, &c.

Sectio Vigesima quarta. Perspectiva.

PErspectiva quodlibet objectum exhibet conspectum permedium quodpiam diaphanum, per quod radii visorii transeuntes terminantur ad objectum, & generaliter loquendo quicquid per aliud quidpiam videtur, ut per aerem, per aquam, per nubes, per vitrum, & quaecumque alia sunt ejusmodi, dici possunt videri in Per∣spectiva.

Quae praecipui momenti haec Scien∣tia continet ad sequentia Capita redu∣ci queunt. Radius primarius est rec∣ta ab oculo in vitrum ad angulos rec∣tos ducta.

Primarium punctum dicitur id in quod cadit perpendicularis ab oculo in vitrum ducta.

Projectio lineae non est linea curva.

Cum objectum est punctum uni∣cus

tantum est radius visorius ab ob∣jecto ad centrum oculi ductus, hicque radius dicitur Axis, aut radius Cen∣tricus, estque omnium vivacissimus, ac fortissimus.

Si objectum recta sit linea, radii visiorii conflant triangulum.

Si objectum sit superficies plana, aut sphaerica, radii visiorii conficiunt pyramidem.

Ichonographia est delineatio plani su∣per quod erigere quidpiam volumus.

Orthographia est delineatio anterio∣••is objecti partis.

Scenographia exhibet objectum om∣nino elevatum, perfectumque una cum omnibus ejusdem dimensionibus, um∣••risque undique.

Linea horizontalis in Perspectiva ••ucitur ab altitudine oculi: Haec prae∣••pui in pictura momenti est, regu∣••que esse debet dimensionum, altitu∣••numque figurae.

Punctum Perspectivae, aut visus fit ••entrico supra horizontem radio.

Authores.

Inter praecipuos Perspectivae scrip∣tores hi censentur Rogerius Bacco, Jo∣hannes Baptista Porta, Stevinius, Ma∣rolus, Johannes Cousinus, Daniel Bar∣baro, Vignola, Serlio, du Cereau, Salo∣mon de Caus, Guidus Ubaldus, Nicero∣nius, &c.

Sect. XXV. Poetry.

POetry is the Art of making Verse and Poems: In order to this, 〈…〉〈…〉 teacheth the quantity of Syllables, whe¦ther they be short or long, doubtful 〈…〉〈…〉 common, I mean, either short or long 〈…〉〈…〉 pleasure.

It teacheth what feet every Verse compounded of, that feet are made Syllables of different quantities, as Spondee consists of two long syllables;

for instance, Doctos, and Pyrrichius; of two short, as Rota; a Dactyle con∣sists of one long, and two short, as Pec∣tora.

A Poem implieth a Fiction: Upon this account, Verses that contain no Fiction, are not strictly considered▪ a Poem; and he that gives a meer Mat∣ter of Fact, without any ingenious Fic∣tion adapted to the Subject, is rather styl'd a Versificator, than a Poet.

Verses are either denominated from their Inventors, as Sapphick Verses, from the Greek Poetress Sappho, the first Inventress; as Pindarick, from Pindarus, or from the feet whereof they consist; as Iambick, from the Iambick•• of which they are compos'd, or from th•• matter they express; as Heroick, from the Praises of Great Men; as Elegiack from sad Narratives, or from the num∣ber of feet, as Hexameter, and Pent•• meter, the first having six, and the othe•• five.

The Scansion of a Verse, is the measu∣ring of a Verse by its feet. The Cesure is the making of a short syllable long at the end of a foot.

Authors.

Aristotle, Horace, Alvares, Despau∣ter, Waller, Cowley, Dryden, &.

Sectio Vigesima quinta. Poetica.

POetica est ars pangendorum car∣minum quem in scopum docet quantitatem syllabarum an scilicet sint longae, breves, dubiae, aut com∣munes, hoc est pro arbitrio, breves aut longae.

Docet ex quibus pedibus quilibet versus constet, pedesque constare ex syllabis variae quantitatis, Spondaeum

puta, duabus longis, ut Doctos, Pyr∣richium; ex duabus brevibus, ut Ro∣ta; Dactylum ex una longa & duabus brevibus, ut Pectora.

Poema fictionem necessario requi∣rit: Quare versus nullam fictionem complexi stricte loquendo Poema dici nequeunt: Qui rem absque ingenioso ullo commento, ut reipsa contigit, carmine describit, Versificator potius quam Poeta dicendus est.

Versus denominantur aut ab inven∣toribus, ut Sapphici versus a puella Graeca quae Sappho dicebatur, prima inventrice, ut Pindarici a Pindaro; aut a pedibus ex quibus constant, ut Iambici ab Iambis, ex quibus fiunt; aut a materia quam exprimunt, ut Heroici a laudibus Heroum, Ele∣giaci a maestis narrationibus; aut a numero pedum, ut Hexameter, & Pentameter a numero pedum sex, & quinque.

Scansio versus est ejusdem ope pe∣dum dimensio. Caesuta est productio syllabae brevis sub finem pedis.

Authores.

Aristoteles, Horatius, Alvares, Des∣pauterius, &c.

Sect. XXVI. Philosophy.

PHilosophy, if we take it generally, is the love of Wisdom; if more particularly, the knowledge of Natural Bodies, or of the Natural Causes of Things: The Aristotelian Philosophy acknowledgeth three Principles of every thing, Matter, Form, and Privation; for we can conceive nothing to be genera∣ted without these three; for if I con∣ceive the generation of fire in wood, I

must of necessity apprehend the Wood as the Matter, as likewise the Privation of the Fire in the Wood, and also the Form of Fire taking place of that of Wood.

This Philosophy resolveth all difficul∣ties relating to Bodies, by Matter, Pri∣vation, and Form, Occult Qualities, and such like pretences to humane Igno∣rance: So every Mixt, according to Aristotles Principle, is compounded of Matter and Form: This Matter, the Peripateticks call the Subject of all Forms; and this Form, the Act of Mat∣ter; and both together, the two com∣pounding Principles of all compounded Things

Aristotles Followers teach, that Na∣ture is such an Enemy to a Vacuum, that to shun it, she forceth heavy things up∣wards, and light things downwards.

The New Philosophy holds but two simple Principles of all things, Matter, and Motion; that, as the Material Cause; this, as the Efficient. The For∣mal

Cause of things, which School-men call a Substantial or Accidental Form, being nothing else, according to the Mo∣dern Philosophers, but a certain Tex∣ture of the compounding Particles; and by the variety of Textures every where obvious, or by the various Modifications of Matter, they give us a rational ac∣count of all the differences we observe among Corporeal Beings.

Authors of the School Philosophy.

Aristotle, and all his Commentators, as Averroes, Alexander Aphrodi∣saeus, &c.

Authors of the New Philosophy.

Descartes, Verulam, the Honoura∣ble Robert Boyle, who in not a few things, has out-done them both, and is deservedly styl'd abroad, The English Philosopher; he being indeed, the Honour of his Nation, as well as of his Family.

Sectio Vigesima sexta. Philosophia.

PHilosophia si latius sumatur, amorem sapientiae sonat, si pro∣pius & specialius, est corporum natu∣ralium, aut naturalium causarum cog∣nitio. Philosophia Aristotelica agnos∣cit tria rerum dum generantur prin∣cipia, Materiam, Formam, & Priva∣tionem. Nihil enim generari conci∣pimus nisi haec tria concipiamus: Si enim concipio generationem ignis in

ligno, necessario concipio lignum, ut materiam, & privationem pariter ip∣sius in ligno, formamque ignis formae ligni succedentem.

Haec Philosophia omnes fere diffi∣cultates ad corpora spectantes ope ma∣teriae, privationis, & formae resolvit, atque occultarum qualitatum bene∣ficio, aliisque humanae ignorantiae ve∣lamentis; unumquodque igitur mix∣tum juxta Aristotelica principia com∣ponitur ex materia, & forma: Hanc materiam vocant Peripatetici Subjec∣tum omnium formarum, & hanc for∣mam Actum materiae, componentiaque duo principia si simul sumantur, om∣nium rerum compositarum.

Aristotelis Sectatores docent Natu∣ram Vacuo adeo esse inimicam, ut illius vitandi gratia gravia sursum co∣gat, & levia deorsum.

Nova Philosophia duo admittit sim∣plicia omnium rerum principia Mate∣riam, & Motum, illam ceu causam Materialem hanc ut Efficientem. For∣malis

enim rerum causa, quam Scho∣lastici formam Substantialem vocant, aut Accidentalem, nihil aliud est jux∣ta Philosophos recentiores, quam tex∣tura quaedam partium componentium. Hacque contextus varietate ubique obvia, aut variis materiae Modificatio∣nibus, rationalem, facilem, obviamque nobis reddunt rationem omnium quae observamus, corporea inter entia dis∣criminum.

Authores Philosophiae Scholasticae.

Aristoteles ejusque Commentatores, ut Averroes, Alexander Aphrodi∣saeus, &c.

Authores novae Philosophiae.

Gassendus, Cartesius, Verulamius, il∣lustrissimus Robertus Boylius, qui in multis his omnibus palmam praeripuit, meritoque Philosophus Britannicus cognominatur; est que reipsa Nationis suae, & nobilissimae Familiae ornamen∣tum & decus.

Sect. XXVII. Rhetorick.

RHetorick is the Art of Speaking well; the duty of a Rhetorician, is to speak pertinently to the Subject, in order to perswade, and his chief scope must be to perswade by his discourse.

Rhetorick consists of four parts, In∣vention, Disposition, Elocution, and Pronounciation: Invention is the con∣triving of an Argument fit to perswade, and those Arguments are always taken from some of these ensuing Heads.

• 1. From the Definition, when we de∣clare what the thing is.
• 2. From the Division, when we distri∣bute a thing into all its parts.
• 3. From the Etymology, when we shew its Origine and signification.
• ...

• 4. From the Species, when we frame an Argument from that particular kind of thing the Subject we treat of, belongs to.
• 5. From the Genus, when we bring some proof from that general thing the Subject we treat of, is contain'd un∣der.
• 6. From the Similitude.
• 7. From the Dissimilitude.
• 8. From Contraries.
• 9. From Opposites, that can never concur together.
• 10. From Comparison.
• 11. From the four Causes, Efficient, Material, Formal, and Final.
• 12. From the Antecedents and Con∣sequents of a thing.

Disposition is the orderly placing of the things invented: This orderly pla∣cing consists of five things; Exordium, by which the Speaker prepares the minds of his Auditors, to what he is to say. Pro∣position, when the Orator declares what he intends to make out. Narration,

when he relates the Matter of Fact, with all its circumstances. Confirmation, when he proves his Proposition. Pero∣ration, when the Orator endeavours to move the affections of the Hearers, by a fit Elocution.

Elocution, made up of Tropes, as they speak in the Schools, by which Words change their signification; and of figures, which are an Elegant, and not Vulgar manner of speaking, is the ornament of Speech.

Pronunciation relates to the Voice, and the Gesture; by the first, we please the Ear; by the second, the Sight. These forementioned things (necessary to the compleating of an Orator) being seldom found together in any Eminency, gave occasion to Cicero to say, that We scarce find a good Orator in a whole Age.

Authors.

Aristole, Cicero, Suarez.

Sectio Vigesima septima. Rhetorica.

RHetorica est ars bene dicendi; officium Rhetoris est loqui ap∣posite ad scopum hoc est ad persua∣dendum; praecipuus enim ipsius sco∣pus est persuadere dictione.

Rhetorica quatuor constat partibus, Inventione, Dispositione, Elocutione, Pronunciatione: Inventio est exco∣gitatio argumenti ad persuadendum idonei; haec autem argumenta ducun∣tur semper ab aliquo sequentium ca∣pitum.

• 1. A Definitione, cum declaramus quid res sint.
• 2. A Divisione, cum rem distribui∣mus in omnes partes.
• 3, Ab Etymologia, cum indica∣mus ejusdem originem & significatio∣nem.
• ...

• 4. A Specie, cum argumentum quodpiam ducimus a particulari illa rerum specie, ad quam res, de qua agimus spectat.
• 5. A Genere, cum probationem de sumimus a generali illa re, sub qua id quod sub litem cadit, continetur.
• 6. A Similitudine.
• 7. A Dissimilitudine.
• 8. A Contrario.
• 9. Ab Oppositis, quae nunquam concurrere queunt.
• 10. A Comparatione.
• 11. A Quatuor causis, Efficiente, Materiali, Formali, & Finali.
• 12. Ab Antecedentibus & Conse∣quentibus.

Dispositio est ordinata rerum inven∣tarum collocatio: Haec ordinata col∣locatio his quinque constat, Exordio, quo parat Orator auditorum animos ad ea quae dicturus est. Propositione, cum Orator quid probaturus sit exponit. Narra∣tione,

cum materiam facti omnibus vestitam appendicibus enarrat. Con∣firmatione, cum propositionem suam probat. Peroratione, qua conatur Orator auditorum animos apta Elocu∣tione movere.

Elocutio, composita ex Tropis, quibus voces ad alienam significatio∣nem traducuntur, & figuris quae sunt elegantes, & non vulgares loquendi formulae, est totius Orationis orna∣mentum.

Pronunciatio spectat vocem, & ges∣tum, ista recreamus aurem, hac ocu∣lum: Praememorata haec quae in per∣fecto Oratore requirimus cum vix uspiam simul summo in gradu concur∣rant, impulerunt Ciceronem ut dicere•• vix singulis aetatibus singulos tolerabi∣les Oratores extisse.

Authores.

Aristoteles, Cicero, Suares.

Sect. XXVIII. The Doctrine of the Sphere.

SPhaerica is a Science which treats of the Sphere, whether Artificial or Natural.

The Sphere is a solid figure compre∣hended under one surface, to which all the streight lines drawn from one of those points that are within the figure, are equal one to another.

The Center of the Sphere, is the fore∣mentioned point.

The Axis of the Sphere, is a streight line drawn through the Center, and ter∣minated on each side in the surface of the Sphere; about which the Sphere turneth round.

The Poles of the Sphere, are the two extreme points of the Axis.

This Science demonstrates these fol∣lowing Propositions.

• 1. The Sphere toucheth but in one point the Plane by which it is not cut.
• 2. In the Sphere, great Circles cut one another into equal parts; and if they divide one another into equal parts, they are great Circles.
• 3. In the Sphere, the Pole of a great Circle is distant from the circumference of the same Circle, a full Quadrant, or a fourth part of the great Circle.
• 4. In the Sphere, Parallel Circles are about the same Poles; and Circles that are about the same Poles, are Parallel.
• 5. In the Sphere, there are no more than two Circles, both equal-distant and equal.

This Science teacheth how to find the Center, and the Pole of any Sphere, and sheweth likewise all the properties of the Circles of the Sphere.

Authors.

Theodosius, Maurolycus, Sacrobosco, Clavius, Mestlinus, Blancanus.

Sectio Vigesima octava. Sphaerica.

SPhaerica est Scientia quae agit de Sphaera, sive arte facta, sive na∣turali.

Sphaerica est figura solida compre∣hensa una superficie, ad quam ab uno eorum punctorum quae intra figuram sunt, omnes rectae lineae ductae sunt aequales inter se.

Centrum Sphaerae est punctum prae∣memoratum.

Axis Sphaerae est recta per centrum ducta & utrimque terminata in su∣perficie Sphaerae circa quam volvitur Sphaera.

Poli Sphaerae, sunt duo extrema puncta axis.

Haec Scientia sequentes propositio∣nes demonstrat.

• 1. Sphaera Planum a quo non secatur, non tangit in pluribus punctis uno.
• 2. In Sphaera, maximi circuli sese mutuo bifariam secant, & qui sese mutuo bifariam secant, sunt maximi.
• 3. In Sphaera, polus maximi circuli abest a circumferentia ejusdem cir∣culi quadrante maximi circuli.
• 4. In Sphaera, paralleli circuli circa eosdem polos sunt, & qui circa eosdem polos in Sphaera sunt, sunt paralleli.
• 5. In Sphaera non sunt plures circuli aequales, & paralleli quam duo.

Haec Scientia praeterea docet qui cen∣trum, polumque cujuscumque Sphaerae invenire possimus, indicatque pariter proprietates circulorum Sphaerae.

Authores.

Theodosius, Maurolycus, Sacrobosco, Clavius, Mestlinus, Blancanus.

Sect. XXIX. Divinity.

THeology, or Divity, is wholly di∣rected to the Glory of God, and Salvation of Mankind. The Specula∣tive part of it, proposeth to us things that we are to believe, as whatever con∣cerns Gods Attributes and Perfections, the Immortality of our Souls, and what∣ever is contain'd in the Apostolick Creed. The Practical part, proposeth to us things that we are to do, viz. whatever is contain'd in the Decalogue.

The immediate object of Divinity, as it relates to Christians, we reckon whatever concerns Christ, directly, or indirectly; as in general, the Old and New Testament. And in particular, the Prophecies relating to his Coming, his Miracles, his Doctrine, and the Con∣version of the World by his Apostles: If then, a Man knew no other Divinity,

but that which gives an account of Gods Attributes, he is not upon this account a Christian Divine, but a Philosopher, or Deist.

Christian Divinity, besides the afore∣said things, teacheth all kind of Vertues, as Charity, Humility, Patience, Chastity, Adoration, Prayer to, and Praise of God, Faith, Obedience, Repentance, &c. It will have us moreover to pardon and love our very Enemies; which no other Religion Commands: It offers to us the fundamental points of Christian Religi∣on, Christs Godhead, Passion, Death, Resurrection, &c. and (as I was saying) whatever is contained in the Creed.

Authors.

The Master of Sentences, Thomas Aquinas, Scotus, Hammond, Light∣foot, and several other Doctors of the Church of England.

Sectio Vigesima nona. Theologia.

THologia ad Dei gloriam, salu∣temque animarum tota dirigi∣tur. Speculativa pars proponit nobis credenda, ut quae spectant ad attri∣buta divina, immortalitatem animae, quaeque in symbolo Apostolorum con∣tinentur. Pars practica facienda no∣bis proponit, quaecumque scilicet De∣calogus nobis exhibet.

Theologia prout spectat Christianos, immediatum habet objectum quicquid refertur ad Christum directe, aut indi∣recte ut in genere tum Antiquum, tum novum Testamentum; & magis specia∣tim Prophetias ad ipsius adventum spectantes, miracula, doctrinam, homi∣numque ab Apostolis conversionem: Quocirca si nullum quis aliam nove∣rit Theologiam quam quae divinorum

attributorum reddit rationem non hoc nomine Christianus Theologus, sed Philosophus potius, aut Deista merus dici debet.

Theologia Christiana praeter supe∣rius commemorata docet omnia virtu∣tum genera, humilitatem, patientiam, castitatem, adorationem, orationem, laudem Dei, fidem, obedientiam, pae∣nitentiam, &c. Vult insuper nos non tantum remittere injuriam, sed & di∣ligere inimicos: Quod nulla nisi Chri∣stiana religio injungit. Proponit nobis religionis Christianae fundamenta, Christi Deitatem, passionem, mortem, resurrectionem, &c. atque ut superius dicebam quicquid in symbolo conti∣netur.

Authores.

Majister Sententiarum, Thomas A∣quinas, Johannes Duns Scotus a patria, Hamm••ndius, Lightfootius, aliique quam plurimi Ecclesiae Anglicanae Doctores.

Sect. XXX. Spherical Trigonometry.

SPherical Trigonometry teacheth us to measure Spherical Triangles, that is Triangles in the surface of the Sphere, made by the Arches of great Cir∣cles.

Those sides of a Spherical Triangle are of the same kind that both exceed, or both fall short of 90 degrees; but they are of a different sort, if the one ex∣ceed, and the other fall short of 90 de∣grees.

This Science demonstrates these fol∣lowing Propositions.

• 1. In all Spherical Triangles, any side whatsoever, is less than a Semi-circle.
• 2. In all Spherical Triangles, any two sides, howsoever they be consider'd, are greater than the third.
• ...

• 3. Of a Spherical triangle equilateral, if each side be a quadrant, or of 90 deg. all the angles are streight; and if each side be less than the quadrant, all the an∣gles are obtuse.
• 4. In all Spherical triangles, when the angles are all acute, all the arches are less than the quadrant.
• 5. In all Spherical triangles, the three angles are greater than two streight angles, and lesser than six.

Authors.

Kepler, Afraganius, Julius Higi∣nus, Garcaeus, Robert Hues, Adrianus Metius.

Sectio Trigesima. Trigonometria Sphaerica.

TRigonometria Sphaerica docet nos modum dimetiendi triangula Sphaerica, hoc est triangula ex tribus arcubus maximorum circulorum, in superficie Sphaerae composita.

Latera ea trianguli Sphaerici ejus∣dem sunt affectionis quae simul exce∣dunt, aut deficiunt a quadrante, aut nonaginta gradibus, sed non sunt e∣jusdem generis si unum latus exce∣dat, & alterum sit infra nonaginta gradus.

Haec Scientia sequentes hasce pro∣positiones demonstrat.

• 1. In omni triangulo Sphaerico quodvis latus quomodocumque sump∣tum est minus semi-circulo.
• 2. In omni triangulo Sphaerico duo latera reliquo sunt majora quomodo∣cumque sumpta.
• ...

• 3. Omne triangulum Sphaericum aequilaterum, si singula latera sunt quadrantes, habet singulos angulos rectos, si vero quadrante minora, ob, tusos.
• 4. In omni triangulo Sphaerico cujus omnes anguli sunt acuti arcus singuli quadrante minores sunt
• 5. Omnis trianguli Sphaerici tres an∣guli duobus quidem rectis sunt majo∣res, sex vero rectis minores.

Authores.

Keplerus, Afraganius, Julius Higi∣nus, Garcaeus, Robertus Hues, Adrianus Metius.

Sect. XXXI. The Rectiline Trigonometry.

THe Rectiline Trigonometry teach∣eth us how to measure Triangles made of streight lines.

A streight line, is the shortest way be∣tween two extremes.

Between two extremes, there can be but one streight line.

Two streight lines can not cut one ano∣ther, but in one point.

An angle is measured by degrees, so a streight angle is an angle of 90 degrees, an acute angle is an angle of fewer than 90, as an obtuse angle contains more than 90 degrees.

A line falling even down upon ano∣ther line, without inclining either to the one side, or to the other, is called a Per∣pendicular line, and makes two streight angles.

Parallel lines, are those that are equi∣distant one from another.

This Science demonstrates this Propo∣sition, of great use in Mathematicks, that the three angles of all Rectiline triangles, are equal to two streight ones.

All the angles of a triangle, may be acute, but there can be but one streight, or obtuse.

If one of the three angles of a triangle be streight, the two others are equal to a streight angle.

Who knows the degrees of two angles, knows the degrees of the third, because all three make up 180 degrees.

All the angles of a triangle being equal, all the sides are likewise equal.

Authors.

Euclid, Clavius, Arnauld; Mala∣pertius, Fournier, &c.

Sectio Trigesima prima. Trigonometria Rectilinea.

TRigonometria Rectilinea docet qui triangula ex rectis lineis composita metiri oporteat.

Linea recta est brevissima duo inter extrema via.

Duo inter extrema unica tantum duci potest recta.

Duae rectae nequeunt se invicem ni∣si in puncto secare.

Angulum metiuntur gradus, angu∣lus rectus est angulus 90 graduum, acutus angulus graduum pauciorum, angulus obtusus plures nonaginta gra∣dibus gradus continet.

Linea in aliam utrimque incidens ex aequo Perpendicularis dicitur, duosque utrimque rectos angulos constituit.

Lineae parallelae, sunt lineae aequo a se invicem intervallo dissitae.

Haec Scientia non exiguae Mathema∣ticis in disciplinis utilitatis hanc pro∣positionem demonstrat, omnis trian∣guli Rectilinei tres anguli duobus rec∣tis sunt aequales.

Omnes anguli trianguli rectilinei possunt esse acuti, sed unus tantum rectus esse potest, aut obtusus.

Si unus trium angulorum trianguli sit rectus, duo reliqui recto aequales sunt.

Qui novit duorum angulorum gra∣dus tertii anguli gradus novit, si∣mul enim tres anguli conficiunt nu∣merum 180.

Quoties omnes anguli trianguli sunt aequales, omnia latera quoque aequalia sunt.

Authores.

Euclides, Cicero, Clavius, Arnauld, Malapertius, Fournierius, &c.