The mathematical ievvel shewing the making, and most excellent vse of a singuler instrument so called: in that it performeth with wonderfull dexteritie, whatsoeuer is to be done, either by quadrant, ship, circle, cylinder, ring, dyall, horoscope, astrolabe, sphere, globe, or any such like heretofore deuised: ... The vse of which iewel, is so aboundant and ample, that it leadeth any man practising thereon, the direct pathway ... through the whole artes of astronomy, cosmography, ... and briefely of whatsoeuer concerneth the globe or sphere: ... The most part newly founde out by the author, compiled and published ... by Iohn Blagraue of Reading gentleman and well willer to the mathematickes, who hath cut all the prints or pictures of the whole worke with his owne hands. 1585.

Chapter 63. Of the Eclipse of the moone, the greatnesse and duration of the same.

Gemma Frisius 71.

THe Eclipse of the moone hath an easie calculation, the cause whereof is, that it dependeth not vppon the difference of seeing it in any respect (as before in the sunne.) For as oft as there happeneth an E∣clipse of the moone, because that she beyng opposite to the Sunne, lighteth into the shadow of the earth, which extendeth it selfe farre beyond the speere of the moone, and taketh away the light which she had of the Sunne: she by this meanes eclipseth in like bignesse and manner to all places of the world: and continueth like time, and is seene euery where at one moment, although that it be accounted at diuers houres in dyuers places, according to the distaunce and difference of the meridians, as hereafter I will shew in the longitude of places.

Blagraue. It appeareth here that Gemma Frisius had a meaning to intreate of the longitude of places whi∣che Oh would God he had liued to haue performed, that it might haue beene my good happe to haue seen his vttermost, in that behalfe, by which meanes I should haue eyther spared altogether the greate endeuour which I of necessitie must now for the credites sake of my Iewell employ in that behalfe, or at the least haue receyued such light from his doynges, that I might with ease haue gone through, with it. But now Gemma Frisius is gone, lamenting will not helpe: he left his sonne Cornel. Gemma behynde, who published his Fa∣thers woorke of the Catholicon, and stryued to augment it by his owne industrye: but God knowes, against the streame. For a man may easily knowe by the very matter and manner of it, his doyngs (of whi∣che I haue omitted the most part) from his fathers.

Gemma Frisius.

But now to come againe to the matter, as the Eclipse of the moone is vniuersall at one instaunt, it is farre otherwise in the Sunne: for one selfe same Eclipse of the Sunne to some appeareth great, and lasting: to other some little and gone in a moment: to some the North part, to some the South part of the Sunne is seene to be darkened: and that in infinit diuersities.

[illustration] cosmographical chart

Those on this side see no Eclipse.

The Sunne eclipsed.

Those that dwel on this side of the earth do see the Sun eclipsed.

The cause of so great variety, is the diuersity of the places whence the sun is beholdē: bicause that in the eclipse of the Sunne he looseth not his light, as the common sort do imagine: but only that the moone commeth betweene vs and the sun. VVhereby all countries see not the Eclipse in one maner. Insomuch that some doe see the sunne in his ful light, when that others see him almost wholly eclipsed. For the see∣ing of it, according to the scituation in sun∣drye places, is the greatest cause of the diuersity of the Eclipse of the sunne. But in the Eclipse of the moone, the view euery where doth vary it nothing, neyther in lō∣gitude nor latitude, for the moone is darke∣ned indeede, where there the sun is not (as is already said:) and therfore are we forced to seek so many variations of aspect in the sunne which in the moone needeth not. It shalbe sufficient here to take the time of the true opposition of the sun and moone for your meridian, either out of their proper ta¦bles, or out of Ephimerides, rightly calcula∣ted: & for that time to get the true place of the sun in the eclipticke, whose opposite is the iust place of the moon: & then seek the latit. of the mooue very diligently, as is shewed in the 58. chapter. Lastly you must gette the diameter or se∣midiameter of the moone: and likewise the semidiameter of the shadowe of the earth, of what quantity it is in the place of the moones passage. The same is somtime greater, somtime lesse, for two causes: for when the ☽ is neere her perig. she findeth the shade of the earth greater then in other places: the shadow of the earth runneth out taperwise vnto a point at the last, & becommeth lesser by so much the further as it extendeth frō the earth. Secondly, the shadow of the earth may be greater in the selfsame place of the moons passage, by rea∣son of the distance of the sun from the earth. For the neerer the sun commeth toward the centre of the earth, so much the shadow of the earth groweth the narrower & shorter, contrarywise, by the sunnes bearing backe from the Earth, it is extended and enlarged in the same place of the speere of the moone, in which it was nar∣rower before, as by these figures you may see.

Therfore to our purpose you must know by tables the time of the true opposition of the sun & the moone in the Eclipse: and the place of the sun & the moon for the same time, together with the latitude of the moon. And then the semidiameter of the moon, & of the shadow, through which the moons passage is. And here wil I shew in brief as much as shal suffice the learner to get the semidiamet. of the sun, the moon, & of the shade by the motus horarii, or diurnall motions of the Sunne and the moone. It is found out by the industry of ar∣tificial men, that what proportion 20. beareth to 11. the same doth the suns diurnal motion vnto his diamet, appering. Therfore multiply the suns diurnal motiō gottē out of any tables into 11. & deuide the product by 20. so haue you the diam. of the sun. The cause is, for that both the greatnes of the diamet. apparens of the ☉, & y^e swiftnes of the suns motiō are increased & diminished in like proportion, according to y^e site of the ☉ in his excentricke.

[illustration] cosmographical chart

The sunne in his Apogeon or farthest distance from the earth.

The sun in his perigion or nearest to the earth.

The figure of the Eclipse of the Moone.

The diametres also of the Moone do likewise keepe a proportion with her motion, so that the diametre Apparens of the Moone is almost equall to her Motus Horarius: Puruacchius saith, what proportion 48. beareth vnto 47. the same hath the mot. horarius of the moone vnto her Diameter apparens: therefore if a man take the motus horarius, or houre motion of y^e ☽ for her diametre, he shal not misse a minute. But to haue it ex∣actly, multiply the motus horarius of the Moone into 47. & deuide the product by 48. & therof shal come the moones diametre. Lastly the diametre of the shadow of the earth you shal thus get. Multiplie the diametre of the moone founde as before into 13. the product deuide by 5. and so shall you haue the greatest quantitie of the shadowe in that passage of the Moone, that is to say, the sunne being in the Apogeon: but the sunne being in other places, the shadow abateth in the same constitu∣tion of the ☽, as is said, by so much the more as the sun commeth neare to the earth: and how much the diametre of the shade is in another place, that is found by the motus horarius of the sunne, for by how much greater it waxeth in other places, the shade of the earth is made lesse, by so much ten times told: These rules are both generall, exact, & most excellent, which by a familiar ex∣ample I will manifest.

In the yeare 1555. the 4. of Iune the 24. houre, and 42. min. there is like to be a great eclipse of the Moone, which is to be knowne in that the place of the ☽, at the time of the true opposition is not farre from Cauda Draconis. For the place of the sunne is according to com∣mon tables ♓ 22. deg. 46. minutes, whereby the Moones place is ♐ 22. 46. also the Caput Draconis is in ♓ 23. deg. 8. minutes, therefore Caeuda is in ♐ 23. 8. so that the true place of the Moone is but 21. minutes from Cau∣da Draconis, wherby there is not onely knowne that an Eclipse shall be, but also a verie great one: for as oft as the Moone is aboue one deg. 8. min. in latitude any way, then shall the Moone auoide the shadow in her race. But heere the latitude of the Moone is scarce two min. which is a token that the Moone shalbe verie neere the centre of the shadow of the earth in this Eclipse. Now to know the quantitie & continuance of the same, we must know the semidiametre of the Moone, & of the shade of the earth by the rules before shewed. The Motus Diurnus of the ☽ in that place is 13. deg. 5. therefore her Motus horarius shalbe 32. min. 40. sec. and somwhat lesse: then this shalbe the diametre of the moone: but if you wil know it exquisitly, multiply 32. min. 40. sec. by 47. & deuide the product by 48. & so shal you haue 32. min. 20. sec. almost, & the same is the iust diametre of the Moone: halfe that vz. 16. min. 10. sec. is her semidiameter: which multiplie by 13. and the product deuide by fiue, you haue the diametre of the shade of the earth in the place of the Moones passage in her sphere, the sun being in his apogeon, the multiplication of the diametre maketh 25 220. sec. the diuision produceth 5044. sec. that is 84. min. 4. sec. so that the semid. of the shade is 42. min. 2 sec. And because the sun is neare his apoge∣on, the shadow of the earth cannot be diminished any quantity, to be accounted of by reason of the suns com∣ming neare vnto the earth, otherwise you should heere seeke the motus horarius of the ☉ being in his apogeon and also for the place where he now is, and the difference of these motions decuplied, that is multiplied by 10. should be taken from the greatnesse of the shade here found, & so shall you haue the exquisite bignesse of the shade of the earth, but here for methodes sake we thinke not good to prosecute euery least matter, but leaue such curiositie to those that haue more leisure, or who are whollie addicted to these studies. By these things found, you may onely by drawing of a figure knowe the greatnes and duration of theclipse, draw therefore the streight line AB, which shall be the 22. deg. of ♐ deuided into 60. min. Then in the 46. min. in which shall be the centre of the shadow of the earth, that is to say, opposite to the ☉ at the time of the true opposition, place the one foote of your compasse, and there according to the quantitie of the semidiametre of the earth now founde videlizet 42. minutes, make a circle for the shadow of the earth, the centre being C, whereon draw the line DE perpendiculer to AB, which is the circle of the latitude of the Moone, and because the latitude of the ☽ is found 2. min. northwards, take in your compas 2. of the 60. parts of AB, & place the same from C. towards D in the point E. & that is the centre of the Moone: in this centre according to the semidia∣metre of the ☽ vz. 16. min. 10. sec. make the circle of the moone, which being done you shal streight see before

[illustration] geometrical diagram

your eyes that the whole moone is drenched in the shadow of the whole earth without any calculation. And if you deuide the whole diametre of the moone into 12. digits, you shall apparantly see how many digits or points theclipse of the moone shall be. For looke how many digits of the moones diametre DF. shall con∣taine (with the distance from the vttermost shade of the earth vnto the edge of the moone farthest drenched within the darknesse) so many digits or points as they now call them shall theclipse be said to be. For D is the point of the shadow of the earth, most bending from thecliptick towards the which the moone departeth, but by numbers we shall thus proceed. Because EF is 16. min. & 10. sec. and the latit. of the Moone EC. 2. min. therfore CF shalbe 14. min. 10. sec. to which there being added CD, being 42. min. 2. sec. the whole DF shal be 56. min. 12. sec. Now by the rule of proportion, if 16. min. 10. sec. be worth 6. digits, what shall 56. min. 12. sec. be worth: & so following on the rule, you shal get 19. digits & 41. min. of a digit such as the whole dia∣metre of the moone maketh 12. To be short the whole moone containing 12. dig. shalbe wholly drenched in the shadow: & that so deepely that the shadow shal exceed the moone 8. dig. almost, which is as much to say, as that theclipse of the moone shalbe almost 20. digits. The moone her selfe conteineth not aboue 12. points, but the depth of the moone within the shadow of the earth shalbe almost 20. dig. wherby you shal vnderstād that when as the greatnes of theclipse exceedeth 12. digits, then shal there be an eclipse with tarriance, as they call it, that is, the moone shal tary a certaine space in the darknes before she shal receiue her light againe of the sun: & how many the more digits there shalbe found, by so much the longer shall the tariance of the moone be in the darknesse, & the whole eclipse endure: both which exactly to descrie, thus must you do. Open your com∣passe to the quantitie of the semidiam. of the earth and the ☽ ioyned togither as in this example, vnto 58. min. 12. sec. and on the centre of the shadow of the earth vz. C. describe a hidden or blind circle, and note wel the touching of this circle with the way of the Moone. I cal the way of the moone a line drawne by the centre of the moone vz. E, parallel if you list to the line AB. or if you be disposed to prosecute these matters more nar∣rowly: let this line make with DF the blunt angle DEM. of 95. deg. as heere the line LEHM. is, for this is the true way of the Moone whereby H is the place of the next knot. This line is cut of the blind circle in the points L & M, in which points the Moone being, maketh the beginning and end of theclipse. Lastly, from the 2. intersections of the shadow of the earth, and the way of the moone, set the semid. of the moone by helpe of your compasse in the way of the Moone vz. in N and O. For in the one of these places the Moone is altoge∣ther entred into the shadow of the earth and in the other, beginneth to get out thereof. Therefore you haue 5. moones if you list, the first on the centre L. where the ☽ begins to eclipse: the next on the centre o, when she is wholly darkned: the third on the centre E, when she is in the middle of theclipse, the fourth on the centre N. when she beginneth to get light againe: the last on M. where theclipse endeth, so that LO is the space, that the moone goeth from the beginning vntill she be all darkned, and ON of her whole darkning, which they call the tariance in Latin Mora: therefore OE is halfe her tariance called (Dimidia mora.) All which parts you may measure with your compasse by the parts of theclipticke before made: and deuiding ech of them by the Supe∣ratio horaria of the moone you shall haue all the times sought for, or the whole taken togither vz. LM. And by numbers may thus be performed. For that EC is 2. min. in latitude, and standeth almost perpendiculer on LM. the way of the ☽, therfore the square of LC shal be equal to the squares of LE, and EC. therfore taking the square of EC out of the square of LC, there shal remaine the square of LE by the last proposition sauing one, of the first booke of Euclide: For LC is the sum gathered of the semidiametres of the moone, and the shade vz. 5. 8. minutes, 12. seconds, but letting passe the seconds, the square of LC shall be equall to 3364- herehence taking the square of CE, vz. 4. there is left 3360. the square of LE, whose side is somwhat lesse then 58. and that is the line LE, so much also is EM. Let no man carpe heere because we saide that CE was perpendicular to the Moones way, when as before we drew him perpendiculer to theclipticke, the best learned men will neglect so much, because it bringeth no perceiueable error. Therefore the line LE be∣ing knowne to bee fiue 58. minutes almost, take out of that the semidiametre of the Moone vz. 16. minutes 12. seconds, the line LO shalbe 41. min. 48. almost, which they call minuta incidentiae, and NM is almost equal vnto it, called minuta repletionis. Lastly subduct LO being the minuts of theclipse waxing out of LE, there shal be left OE halfe the tarriance vz. 17. min. 12. seconds almost. Now because the Motus horarius of the Moone

was 32. min. 40. seconds, and the sunnes Motus horarius 2. min. 22. sec. take the one out of the other there re∣steth 30. min. 18. sec. the superation of the moones gate aboue the sunne in one houre. By this deuide all the parts of the Moones way before founde and you shall haue the tymes correspondent vnto them. As be∣cause the Mynuts of the waxing of the Eclips were 41. mynuts 48. so deuide those by 30. mynuts 18. seconds by reducing each number vnto secondes, so shal amount one howre 22. mynuts, the time of the waxing and likewise of the wearing of theclips. Likewise deuide the minuts of Dimedia mora vz. 17. my. 12. by 30. min. 18. seconds there commeth 33. my. of an howre, wherby the whole darckning is 1. howre 6. my. the whole time of the Eclips 3. howres 50. mynutes.