THE Theoriques' of the seven Planets, showing all their diverse motions, and all other Accidents, called Passions, thereunto belonging. Now more plainly set forth in our mother tongue by M. Blundevile, than ever they have been heretofore in any other tongue whatsoever, and that with such pleasant demonstrative figures, as every man that hath any skill in Arithmetic, may easily understand the same. A Book most necessary for all Gentlemen that are desirous to be skilful in Astronomy, and for all Pilots and Seamen, or any others that love to serve the Prince on the Sea, or by the Sea to travel into foreign Countries. Whereunto is added by the said Master Blundevile, a brief Extract by him made, of Maginus his Theoriques', for the better understanding of the Prutenicall Tables, to calculate thereby the diverse motions of the seven Planets. There is also hereto added, The making, description, and use, of two most ingenious and necessary Instruments for Seamen, to find out thereby the latitude of any Place upon the Sea or Land, in the darkest night that is, without the help of Sun, Moon, or Starr●. First invented by M. Doctor Gilbert, a most excellent Philosopher, and one of the ordinary Physicians to her Majesty: and now here plainly set down in our mother tongue by Master Blundevile. LONDON, Printed by Adam Islip. 1602. A Table, showing all the principal points contained in the Theoriques' of the seven Planets. A Table showing the diverse shapes of the Moon. Page. 43. A comparison, showing in what things the Moon and Mercury do agree or differ, in describing their Ouale Figures. 125. Of the Passions of the seven Planets. 145. When and how these Passions do chance. 158. How to know whether the Moon be in the 90 degree, or not. 173. Of the Eclipses of the Moon. 174. How to know the bounds or limits, whereby is easily known what kind of Eclipse of the Moon will happen, when she is at the Full. 186. Of the twelve digits, whereinto the body of the Moon is wont to be divided, to know thereby how much at any Full she is eclipsed. 187. Of the continuance of the moons Eclipse, what it is, and how many things are wont by the Astronomers to be considered therein. 190. Of the Eclipse of the Sun, how & when it chanceth. 194. Of the variety of the Solar Eclipses, and why they be not always like, but do differ as well in magnitude as in time of continuance. 200. Of the two special kinds of Solar Eclipses, that is, total and Partial. 202. Of the Partial Eclipse of the Sun. 204. Of the bounds or limits of the Solar Eclipses. 206. Of the elliptical digits belonging to the Solar Eclipses. 208. What things are to be considered touching the continuance of the Solar Eclipse. 209. How to find out the quantities, increasing, decreasing, beginning, and ending of the suns Eclipses, without any offence of your eyesight. 210. The Methodical doctrine of the Eclipses, set down by Reinoldus in his commentary upon Purbachius. 211. A Table of all the Chapters contained in Maginus his Theoriques'. Chap. Page. 1. THe description of the eleventh heaven or first movable, together with such definitions as are contained therein. 216. 2. Of the tenth Heaven. 217. 3. Of the ninth Heaven. 220. 4. Of the eight Heaven. 223. 5. Of the seventh Heaven, that is, the heaven of Saturn. 226. 6. Of the sixth Heaven, or heaven of jupiter. 239. 7. Of the fift Heaven, or heaven of Mars. 240. 8. Of the fourth Heaven, or heaven of the Sun. 242. 9 Of the third Heaven, or heaven of Venus. 255. 10. Of the second Heaven, or heaven of Mercury. 258. 11. Of the first Heaven, or haven of the Moon. 263. The making, description, and use, of two most ingenious & necessary Instruments for Seamen, the one whereof is described in Pag. 280. And the other in 287. To the Reader. BEing advertised by divers of my good friends, how favourably it hath pleased the Gentlemen, both of the Court and Country, and specially the Gentlemen of the Inns of Court, to accept of my poor Pamphlets, entitled Blundeviles Exercises; yea, and that many have earnestly studied the same, because they plainly teach the first Principles, as well of Geography as of Astronomy: I thought I could not show myself any way more thankful unto them, than by setting forth the Theoriques' of the Planets, which I have collected, partly out of Ptolomey, and partly out of Purbachius, and of his Commentator Reinholdus, also out of Copernicus, but most out of Mestelyn, whom I have chiefly followed, because his method and order of writing greatly contenteth my humour. I have also in many things followed Maginus, a later writer, who came not unto my hands, before that I had almost ended the first part of my book, neither should I have had him at all, if my good friend M. Doctor Browne, one of the ordinary Physicians to her Majesty, had not gotten him for me, with which good Doctor I have had in times passed at Norwiche many learned conferences, and have received at his hands many good documents, whom I take to be so universally learned in all manner of good and liberal Sciences, as any other that I know in these days: and besides his great learning, I know him to be very wise and honest, which two virtues I wish to reign in all learned men, because they be the greatest ornaments that belong to learning. I have divided this my book into two parts, whereof the first part treateth of the divers motions of the Planets; and the second part, of their Passions; and that so plainly, and with such facility, as I hope that every man of a mean capacity may understand the same. For I thought good to collect out of the foresaid Authors no more but that which only was meet and fit for that purpose, praying all those that be learned, hereafter to add to this my book any necessary thing, that I through age and want of clear sight, have negligently omitted. And so I leave to trouble you, praying you to take this my labour in good part, so shall I have just cause to think the same well bestowed. Vale. THE THEORIQVES of the seven Planets, showing all their diverse motions, and all other accidents (called passions) thereunto belonging. Sigh every art hath his proper terms, without the knowledge whereof, no art is easily learned: Minding therefore here to treat of the Theoriques' of the Planets, I think it best first to set down all the terms together with the true significations thereof: which terms, though they be manifold, yet they may be all reduced into seven. For whatsoever term it be, it signifieth either a point, a centre, a line, a circle, a semicircle, a portion of a circle otherwise called an arch, or an orb, called in Latin Orbis, which is as much to say, as a round hoop or sphere, having breadth and thickness, and sometime it is taken for a circle. And you see here, that I make a difference betwixt a point and a centre; for though every centre is a point, yet every point is not a centre. Again, I make a difference betwixt a circle and an orb; for though they be like, in that they both have round shape, yet they differ, in that the orb hath both breadth and thickness, and the circle hath neither. But before I define the terms belonging to the Theoric of any Planet, I think it best, according to the method and order used by Michael Mestlyn, to set down four principal intentions, meet to be used in describing the Theoric of every Planet: of which four intentions, 1. The first is to show of how many particular orbs every Theoric consisteth. 2. The second is to show towards what part such orbs are moved, and in what time they make their revolutions, and also upon what centres or poles they make their regular movings. 3. The third intention, is plainly to describe all such points, lines, arches, semicircles, and such like things as are needful to be known for the calculating of the movings of any Planet. 4. The fourth intention, is to show how much latitude every Planet (having latitude) hath: for every Planet hath latitude, more or less, the Sun only excepted, which hath no latitude, because he never departeth from the Ecliptic line, with whose Theoric I mind here first to deal. Why deal you first with the Theoric of the Sun? FOr four causes. First, because his Theoric is more easy than all the rest. Secondly, as well for that he excelleth in dignity all the other Planets, as also for that the moving of all the other Planets dependeth upon his moving: which unless it be known, none of the others can be thoroughly known. Thirdly, for that the movings & revolutions of all the rest of the Planets are counted by his yearly revolutions. Fourthly, by the authority of Ptolomey, and other ancient writers, which in treating of the Theoriques', do first begin with the Theoric of the Sun. NOw here followeth the first Intention, showing by certain figures, of how many orbs the Theoric of the Sun consisteth, that is, of three orbs, hereafter described, & are contained in this figure next following. The first figure belonging to the Theoric of the Sun, showing his three orbs, and their centres, and also the two points called Auges, hereafter defined. THough the Theoric of the Sun consisteth but of three orbs, yet you see here, that in this figure there be four orbs or circles, that is, two black, and two white: whereof the upper black circle, marked with the letter D is called the upper deferent of the Auges; and the lower black circle, marked with the letter E. is called the inferior or lower deferent of the Auges; and the largest and greatest white circle, marked with the letter C. is called the Excentricke or deferent of the Sun, having the body of the Sun fixed therein: and in the middle white roundle are set down two pricks or centres, whereof that which is marked with the letter A. is the centre of the world; and the other next above that, marked with the letter B. is the centre of the deferent of the Sun, otherwise called the Excentricke; and the point which is in the upper limb of the deferent of the Sun, marked with the letter F. is called in the Arabike tongue Aux, in Greek Apogaeon, in Latin Absis summa, that is to say, the highest point, which I mean to call in our tongue in the singular number, Auge, and in the plural number, Auges: the opposite point whereof, marked with the letter G. is called in Greek Perigaeon, and in Latin Absis ima, that is to say, the lowest Auge. It is also called Oppositum Augis, that is, the point opposite to the Auge: so as by this figure you may perceive, that the point Auge is a point in the deferent of the Sun, farthest distant from the centre of the earth, and therefore is called of some Longior longitudo, that is, the farthest longitude, marked in the former figure with the letter F; and the opposite point to that, is called Propior longitude, that is, the nigher longitude, because it is nigher to the centre of the earth, and is marked in the said figure with the letter G. There be also in the said deferent, two other points of the mean longitude, whereof we shall speak hereafter. You see also, that the prick, marked with the letter A. is the centre of the world; & that the other prick, marked with the letter B. is the centre of the deferent of the Sun, which, because it is out of the centre of the world, and distant from the same, it is called the centre of the excentricke: and the distance betwixt these two centres, is called in Latin excentricita●; and I likewise from henceforth will call such distance the excentricity. Now describe the three foresaid circles or orbs, and show whereto they serve? THe first, called the orb excentricke, which in the former figure is made white, and marked with the letter C. is that which carrieth the body of the Sun, and therefore is called in Latin Deferens Solis, and I will also call it the deferent of the Sun: in the uttermost circumference whereof, are set the foresaid two Auges, the one right opposite to the other, marked with the letters F. G. as before is said. The other two black orbs, marked with the letters D. E. are those which carry the Auges, & therefore are called the deferents of the Auges, which be two several orbs; and yet to avoid Vacuum, do enclose one another in such sort, as the slenderest or narrowest part of the uppermost orb, marked with the letter D. doth join close to the thickest or fullest part of the neither orb, marked with the letter E. and the slenderest or narrowest part of the neither orb, joineth close to the thickest or fullest part of the upper orb: and these two orbs do contain within them the orb excentrique, or deferent of the Sun, and also do make the whole sphere of the Sun to be concentrique, that is to say, to have all one centre with the centre of the world: and yet in certain respects, these two orbs are also excentrique, that is to say, having a centre distant from the centre of the world: for the concave superficies of the uppermost black orb, and the convex superficies of the nethermost black orb, being severally taken, have the self same centre which the deferent of the Sun hath, which is the centre excentricke, marked with the letter B. All which things the former figure doth plainly show. Wherefore was the deferent of the Sun supposed to be excentrique? FOr three principal causes. First, for that the moving of the Sun is unequal, now slower, now swifter. Secondly, for that the body of the Sun, by his unequal distance from the earth, seemeth to our sight sometime greater, and sometime lesser, the grossness or thinness of the air being no cause thereof. Thirdly, for that the Sun being in this or that part of the Zodiac, the eclipse of the Moon continueth longer or shorter time, so as she abideth under the shadow of the earth more one time than another. All which things are salved by supposing an excentricke. Is the deferent of the Sun, and the circle excentrique, one self thing? NO, for though they have both one self centre, called the centre of the excentrique, yet the circle excentricke is the circumference of a circle imagined to be in the middle of the deferent, & is described by the centre of the suns body, dividing the deferent into two equal parts or hemispheres, as you may see in the second figure next following. The second Intention showeth what moving these orbs and circles before mentioned have, and upon what poles and axletrees they are turned about. BEfore I come to the declaration thereof, it shall be necessary to set down one other figure, containing the most part of such lines, points, centres, circles, semicircles, and arches, as do belong to the Theoric of the Sun, and to show what they signify. I say here fore the most part, because both these & all the rest shall be more fully declared, when we come to the third Intention, whose office is to show all such things at the full. ¶ The second figure belonging to the Theoric of the Sun. IN this figure, the outermost white orb signifieth the Zodiac, in which are described the characters of the twelve signs. And the next white orb within that, is the deferent of the Sun, in which is a little circle, representing the body of the Sun, whose centre is marked with the letter H. and the two black orbs are the two deferents of the Auges of the Sun before described; and in the middle white rundle are set down the two centres before described, that is, the centre of the world, marked with the letter A. and the centre of the deferent of the Sun marked with the letter B. Moreover, in this figure are drawn certain right lines, whereof the long perpendicular line passing through both the foresaid centres, marked with the letters C. D. is called the line of the Auges, and the overthwart line passing through the centre of the world to the Zodiac, marked with the letters E. F. signifieth the Axe tree of the Zodiac, whose outermost ends are the poles of the ecliptic. Then there is another overthwart right line parallel to the foresaid line E. F. which passing through the centre excentrique extendeth unto the deferent of the Sun, from the one side to the other side thereof, whose outermost ends are the poles of the said deferent, marked with the letters K. L. Besides these three lines, there are three other lines, whereof that which passeth from the centre of the world to the Zodiac, marked with the letters A. G. is called the line of the Suns mean moving. Then there is another line parallel to that, which passeth from the centre of the deferent to the centre or midst of the Sun's body, marked with the letters B. H. And the third line passing from the centre of the world through the midst of the suns body, even to the Zodiac, is called the line of the suns true moving, marked with the letters A. H. I. There are also in this figure certain portions of circles called arches, which have their proper significations, as the arch of the Zodiac, contained betwixt the first point of Aries, and the line of the Auges, marked with the letters E. C. is called the Auge of the Sun in his second signification, and the arch contained betwixt E. and G. is called the mean moving of the Sun, and the arch contained betwixt E. and I. is called the true moving of the Sun, and the arch contained betwixt G. and I. is called the equation of the Sun, and the arch contained betwixt the line of the mean moving of the Sun, and the line of the Auges marked with the letters C. G. is called of some Argumentum, and of some Anomalia, that is, the inequality of the suns moving. All which arches shall be more fully showed and declared in the third figure next following. There be also in this figure three little semicircles, whereof the two, marked with the letters K. P. and L. M. do signify those circles which the poles of the excentrique do describe by the moving of the two deferents of the Auges; and the third semicircle marked with the letters B. N. signifieth that circle which the centre of the excentrique describeth by the moving of the said deferents of the Auges about the centre of the world, the semidiameters of all which circles are equal. Doth the Theoric of the Sun only consist of the three orbs about mentioned, that is, of the deferent of the Sun, and of the two deferents of the Auges? THough the ancient Astronomers do appoint no more but those three, yet Copernicus having found by many observations made by himself and others since their time, that the Auges of the Sun do move unequally, and that the excentricity doth alter: he therefore to salve that appearance, doth add another orb called the excentor of the excentrique; which indeed are two shadowed orbs, enclosing one another like as the two black orbs do, the shape whereof you may see plainly expressed in the sphere of Mercury, hereafter following. Now show how the foresaid three orbs are moved, and first how the excentrique of the Sun is moved, and in what time he maketh his revolution? THe excentrique or deferent of the Sun is regularly moved upon his own centre, according to the succession of the signs right under the ecliptic, and maketh his revolution in the space of one whole year, that is in 365 days, and almost six hours, and by the revolution of this orb is described or limited the Sun's year. And you have to note, that the tables of Alphonsus and the Prutenicall tables do in a manner agree, touching the daily moving of this orb, which is i/59 ii/8 iii/19 iiii/37 and v. 24· so as his yearly revolution containeth 365 days, 5. hours. i/49 ii/15 iii/46 saving that the tables of Alphonsus do fail in the daily moving, v. 5· and thereby in the yearly revolution do exceed the Prutenicall tables by iii/13 and so much is the equal tropical year, according to Copernicus, counting the same from the very equinoctial point: but the daily moving of the Sun being counted from the first star of the Ram's horn, is i/59 ii/8 iii/11 iiii/22 v. 10· so as his yearly revolution containeth 365 days, 6 hours, i/9 and ii/39 and this is called the syderall year. The poles of this orb do equally observe the poles of the ecliptic, and therefore the centre of the suns body doth never serve from the ecliptic line. Why doth not this Orb also carry the Sun equally about the centre of the world? BEcause that every circular moving that is equal, maketh in equal time in his circumference both equal arches and also equal angles, upon the centre of equation; which centre in this Theoric, is all one with the centre of the excentrique marked with B. though in other Planets the centre of equation is a several centre by itself. And this kind of moving is only regular upon one centre, and not upon many or diverse centres, as you may perceive by the third figure next following: in which figure the Sun being in his excentrique, and turning about the centre B. is said to be equal, for whilst he descendeth from F. to H. on the left hand of the figure, he maketh the arch of his excentrique to be F. H. and the angle to be F. B. H. upon his own centre B. which is an obtuse or blunt angle: but upon the centre A. he maketh a lesser angle, which is F. A. H. for that is a right angle; and so by this means the angle F. B. H. should be equal to the angle F. A. H. that is to say, the greater to the lesser, which is unpossible. Wherefore the angles made upon A. the centre of the world, are not equal to the angles made upon the centre of the equal moving, marked with B. and therefore the moving of the Sun about the centre of the world, appeareth to be unequal, sometime slower and sometime swifter, according to the unequal arches of the excentrique, subtending equal angles in the centre of the world. How are the deferents of the Auges moved? THey are moved about the centre of the world, and upon the poles of the Ecliptic, according to the succession of the signs, making by virtue of the eight sphere, one revolution together with the said sphere, according to Alphonsus, in 49000 years, and by this moving they put forward the Auge of the excentrique by little and little into the next following degrees of the Ecliptic, and by reason of the incredible slowness of these orbs in their moving, the Astronomers do not agree in the quantity of their revolution. For Ptolomey thought them to be immoovable, and the followers of Alphonsus thought their revolution to be unequal, and to be made in 49000 years, as before. But Copernicus being helped by the observations of many ages, doth show that these orbs do pass through the Zodiac in 17108 Egyptian years, and that they pass through the orb of the fixed stars almost in 50718 Egyptian years; and that the other orb called the excentor of the excentor, which he himself addeth to the other orbs, doth make his revolution upon his own centre, which is the centre of a little circle, contrary to the succession of the signs, in 3434 Egyptian years: and by the moving of this orb, he showeth that the true Auge of the Sun creepeth on unequally, & that the excentricity doth alter and change. The dimension or measure of the suns sphere. THe greatest excentricity of the Sun, according to the demonstrations of Copernicus, containeth two degrees, i/50 and ii/7 such like parts or degrees I say, as the semidiameter B. F. of the excentrique containeth sixty degrees. And the least excentricity containeth but one such part, i/55 and ii/53 And by the demonstrations of the said Copernicus, the foresaid semidiameter B. F. doth contain 1142 semidiameters of the earth. And A. B. in his greatest excentricity containeth almost 48 semidiameters of the earth. And the said A. B. in his least excentricity containeth almost 37 semidiameters of the earth, so as when the excentricity was greatest, and that the Sun was in his Auge, according to the line A. F. set down in the third next figure, he was then distant from the centre of the earth 1190 semidiameters of the earth, which distance Ptolomey thought to be 1210 semidiameters of the earth. And when the Sun was in the point opposite to the Auge, he was then distant from the centre of the earth, according to the line A. G. set down in the said third figure, 1094 semidiameters of the earth. But when the excentricity is least, as it is in this our age, than the Sun being in his Auge, is distant from the centre of the earth 1179 semidiameters of the earth, but in these days the point opposite to the Auge, approacheth not so nigh to the earth, as it hath done in times past, for his distance now containeth 1105 semidiameters of the earth, which is further off than the former distance was, by eleven semidiameters of the earth. And you have to note, that one semidiameter of the earth containeth 3436 Italian miles, and 8/21· of a mile. The third Intention, showing what points, lines, and arches are necessary to be known touching the Theoric of the Sun. THough I have heretofore partly described such things in the first and second figures, yet I mind once again to declare the same again according to Mestlyn, who describeth every thing, and setteth down a third figure, expressing the same in such order as followeth. Seeing the moving of the Sun, by reason of the orb excentrique, is unequal, and that the true moving doth differ from the mean moving, for that cause it is necessary to know what the point Auge and his opposite point is, and their moving: Also which are the lines of the mean moving and true moving of the Sun, and what is the yearly inequality of such moving, called of Alphonsus, argumentum, and what the mean moving and true moving of the Sun is, and finally, what the Equation is. What is the moving of the point Auge, and of his opposite point? IT is an arch of the Ecliptic, contained betwixt the beginning of Aries, and the line of the Auges, which arch is called of Purbachius and others the Auge of the Sun, in his second signification: for Auge in the first signification, is only a point before described in both the former figures. ¶ The third figure belonging to the Theoric of the Sun. ALl the circles of this figure are like in signification to the circles before set down in the second figure, and in this figure betwixt the letter E. signifying here the beginning of Aries, and the letter C. signifying the point Auge, is contained the arch E. C. limiting the moving of the point Auge, counting from the beginning of Aries: but Ptolomey found in his time, that the said point was in the fift degree i/30 of Gemini, which point in these days, according to Copernicus his calculation, is almost in the ninth degree of Cancer. The maintainers of Alphonsus his tables have over boldly, as well here as else where, swerved from Ptolomey: in affirming the Auge of the Sun to have been in his time contrary to his own observations, in the 13 degree i/30 of Gemini, so as in these days that point ought to be in the first degree of Cancer: to whom no credit in this matter is to be given, because it is contrary to all the modern observations. What is the line of the mean moving of the Sun? IT is a right line drawn from the centre of the world to the Ecliptic, and equally distant from another line drawn from the centre of the excentrique to the centre or midst of the Sun, which other line in the Theoriques' of the other Planets ought to be drawn from the centre of equation: but because in the Theoric of the Sun the centre of the excentrique, and that of the equation is all one, the one therefore may be indifferently taken for the other: and this line of the mean moving is marked in the third figure with the letters A. I. being parallel to the line B. K. What is the line of the true moving of the Sun? IT is a right line drawn from the centre of the world, through the centre of the Sun to the very ecliptic, represented here in the third figure by the letters A. K. What is the arch of the mean moving of the Sun, and also what is the arch of his true moving? THe arch of his mean moving is an arch of the ecliptic contained betwixt the first point of Aries, marked with the letter E. and the line of the mean moving before described, and this arch is marked with the letters E. F. And the arch of the true moving of the Sun, is an arch of the Ecliptic, contained betwixt the beginning of Aries, and the line of the true moving of the Sun, which arch is marked with the letters E. K. And both these arches are always to be counted from the equinoctial point, according to the succession of the signs. Copernicus maketh two kinds of this true moving of the Sun, that is, simple, and compound, counting the simple moving from the first start of the Ram's horn, as from a beginning which is unmovable: but he counteth the compound moving from the beginning of the vernal equinox, which is movable. What is the yearly Anomalia or Inequality of the suns moving? IT is an arch of the Ecliptic, contained betwixt the line of the Auges and the line of the Suns moving, according to the succession of the signs, and this Inequality is twofold, that is, mean and true: the mean, is that which endeth at the line of the mean moving, and is marked with the letters C. I. And the true Inequality is that which endeth at the line of the true moving of the Sun, and is marked with the letters C. K. And this yearly Inequality is called the Inequality or Anomaly of the excentrique: but the followers of Alphonsus do call it Argumentum Solis. What is the equation of the suns moving? THat is an arch of the Ecliptic, contained betwixt the line of the true moving, and the line of the mean moving of the Sun, marked in the third figure with the letters I K. and this arch doth make with the centre of the world the angle K. A. I. equal to the angle A. H. B: Which angle the line of the true moving together, with the line drawn from the centre of the excentrique to the centre of the Sun, doth comprehend. And you have to note, that when the Sun is either in his Auge, or in the opposite point thereof, then there is no such arch at all, by reason that the two foresaid lines of the true and mean moving do at that time meet and concur in one, making one self line, but the said arch is greatest when the Sun is in his mean longitude, hereafter defined. When the Sun therefore descendeth from his Auge towards the point opposite of the Auge, this arch to show his true place, taketh away the equation from the mean moving. But when the Sun ascendeth from the opposite point towards the Auge, than this arch addeth so much to the mean moving. Wherefore sith this arch doth increase towards the mean longitude, and going again from thence, is diminished; it falleth out, that the moving of the Sun, which is equal in his own excentrique, appeareth in the centre of the world to be unequal, and to be most slow, the Sun being in his Auge: and the more that he descendeth from thence, his moving waxeth by little and little the swifter. But it is equal to the mean moving, when the Sun is in the mean longitude, but if he be in the point opposite to the Auge, than his moving is most swift, and it observeth the same course, though by a contrary way, that is, by decreasing, whilst the Sun ascendeth from the opposite point of the Auge towards the Auge. What call you the mean longitude? THe mean longitude may be taken two manner of ways. For first the point of the orb excentrique, in which his equation is greatest, is called the mean longitude, of which points there be in the excentrique, two: and that mean longitude is bounded in the third figure with the right line A. H. K. which line maketh right angles with the line of the Auge in the centre A. and in that place is found the angle A. H. B. or the arch marked in the said figure with the letters I K. on the left hand of the figure, which is the equation in the greatest excentricity of the Sun, and that is two degrees, i/323 ii/24 but in the least excentricity the equation is no more than one degree, i/55 ii/41 Secondly, the mean longitude is a point of the excentrique, in which the Sun or any other Planet hath a mean distance from the centre of the world, that is to say, it is in the midst betwixt the greatest and least distance. For this word longitude is generally taken for the distance of any Planet from the earth, which distance is greatest, when the Planet is in his Auge, and is least when he is in the opposite point of the Auge: so likewise the mean longitude is taken for that distance which exceedeth the least so much as it is exceeded of the greatest, and is equal to the semidiameter of the excentrique. Here now should follow the fourth Intention, showing the mou●ng of the Sun, according to latitude: which fourth Intention, in this Theoric only hath no place, for the Sun never swerveth one jot from the Ecliptic line, and therefore that line is called the way of the Sun, by which line all the latitudes and wander of the other Planets are to be measured and examined. And thus I end with the Theoric of the Sun. ¶ The Theoric of the Moon. Why do you deal with the Moon next after the Sun, sith she is the lowest Planet of all? FOr three causes. First, for that the Moon though she hath some more variety in her moving than the Sun, yet her Theoric is not so intricate as those of the rest of the Planets. Secondly, sith the Sun giveth light to the world by day, describing the years and days, it is meet therefore, that the Theoric of the Moon, which giveth light in the night, and describeth the months of the year, should follow next after that of the Sun. Thirdly, because all the ancient Astronomers treating of the Planets, do place the Theoric of the Moon next unto the Sun, whom it becometh us very well to follow therein. The first Intention, showing of how many orbs the Theoric of the Moon consisteth. IT consisteth of these five, whereof the first is the Excentrique, carrying the Epicicle: Then the two deferents of the Auges: and the fourth is the Epicicle, carrying the body of the Moon: (but both Copernicus and Maginus do appoint to the Moon, two Epicicles, that is, the first and second Epicicle, as shall be declared and demonstrated hereafter in my extract out of Maginu● his Theoriques':) and the fift is the Orb equant, environing all the rest of the Orbs. All which Orbs you may see plainly set down in the figure next following, and also the two Centres, the one of the world, & the other of the excentrique, by help of eight letters, set down also in the said figure, that is, A. B. C. D. E. F. G. H. ¶ The first figure belonging to the Theoric of the Moon. IN this figure the letter A. signifieth the centre of the world. And B. the centre of the excentrique: which centre, in going about the centre of the world, describeth a little circle marked with the letters B. H. And C. signifieth the orb excentrique, whose middle line being described by the centre of the Epicicle, is specially to be observed in demonstrating the motion of the Moon. D. signifieth the upper deferent of the Auges. E. signifieth the neither deferent of the Auges. F. signifieth the Epicicle, whereunto the body of the Moon is fixed. G. signifieth the orb equant, which is the outermost white orb, and is otherwise called the circle or deferent of the two nods or sections, signifying the head and tail of the Dragon. Why do the Astronomers appoint unto the Theoric of the Moon an orb excentrique? BEcause the equations of the Epicicle which the excentrique carrieth, are observed to be somewhere greater, and somewhere lesser, as shall be declared hereafter in the fift Figure belonging to the Theoric of the Moon. And this appearance is to be salved by supposing an excentrique. Wherefore are the deferents of the Auges added to the Theoric of the Moon? FOr the self-same causes which are before set down in the Theoric of the Sun. Why is the Epicicle supposed to be needful in this Theoric? FOr two causes: First, because the Moon hath another inequality in her moving, whereunto one only excentrique cannot supply: for in like and self-same places the motion of the Moon is found to be sometime swifter, and sometime flower. Secondly, because the Moon (other things being like) is observed to be sometime higher from the earth, and sometime lower, which is to be seen as well by the apparent magnitude of her body, as also by the continuance and quantity of her Eclipses. Why was it needful to add to this Theoric the Orb equant? FOr two causes: First, that the varieties of the Moon's latitude might be salved thereby. Secondly, that the moving of the excentrique, which is found to be irregular about his own centre, might be equated or made equal by the centre of this circle, being as it were the very point of equation, and thereof it is called the circle equant. Wherefore is this circle made to environ all the rest of the orbs? THough as touching the demonstration of the movings, it maketh no great matter whether this orb be without or within the rest of the orbs, yet sith that by carrying about the nodes and limits of the two latitudes of the sphere of the Moon, and that by this motion the whole composition of the moons sphere doth alter: it is more meet that this orb should compass in all the rest, than to be compassed of them. For it is more likely, that the inferior orb is moved and turned about of his superior, than the superior of the inferior. The second Intention, showing towards what part such orbs are moved, and in what time such orbs make their revolutions, and also upon what centres or poles they make their regular movings: and first, how and in what manner the excentrique of the Moon, carrying the Epicicle, is moved. THe excentrique of the Moon is equally moved about the centre of the world, according to the succession of the signs, and about his own poles, which are distant on both sides from the poles of the Ecliptic five degrees, making his revolution in the space of one month, and by this moving it carrieth about the centre of the Epicicle equally through the Zodiac. And the daily moving of this excentrique, or of the centre of the Epicicle under the Zodiac, is 13 degrees, i/10 ii/35 iii/1 iiii/7 v. 22· so as his whole revolution is made in 27 days, seven hours, i/43 ii/5 iii/8 and so much is the periodical month, which is otherwise called of john de Sacro Busto the month of peragration, whereof I have spoken in my Treatise of the sphere, in the 46 chapter of the first book thereof. What followeth of this inequality of the excentrique? TWo things. First, sith that the Astronomers by often observation have found, that the orb eccentric or centre of the Epicicle doth equally turn about the centre of the world, it must needs follow, that the moving of the said excentrique is unequal, as well about his own centre, as about any other point, clean contrary to that which hath been said touching the moving of the excentrique, or deferent of the Sun. Secondly, the moving of this excentrique is swifter, when the centre of the epicicle is in the upper part, nigh unto the Auge; for a greater portion thereof doth belong to the equal arches of the Zodiac, when she is nigh to the Auge, than when she is nigh to the opposite point of the Auge. Which things do plainly appear in the third and last figure belonging to the Theoric of the Sun before described. In which figure suppose the letters F. H. G. to represent the excentrique of the Moon, whose moving because it is equal about the centre A. must needs be unequal about the centre B. Moreover, because the medieties or halves of the Zodiac, divided by the right line E. A. H. K. are turned about in equal time, so as the greater portion of the excentrique is answerable to the upper half, & the lesser portion to the neither half, it easily appeareth, that the centre of the Epicicle maketh in his moving a greater bent or bout upward, and a lesser downward, that is to say, it goeth faster being in the upper half, than when it is in the neither half. How are the deferents of the Auges of the Moon moved? THey are equally moved, contrary to the succession of the signs about the centre of the world, & about the same poles that the excentrique is, and do make their revolution almost in 32 days. And by this moving they carry about the point Auge, or the whole line of the Auge, equally through the Zodiac, contrary to the succession of the signs. And they also cause the centre of the excentrique to describe a little circle about the centre of the world, whose semidiameter is equal to the excentricity, which little circle you may see in the first figure of the moons Theoric, marked with the letters B. H enuironning the centre of the Zodiac, marked with the letter A. And the daily moving of these deferents of the Auge, contrary to the succession of the signs is eleven degrees, i/12 ii/18 iii/21 iiii/52 v. 33· making one whole revolution in 32 days, three hours, i/4 ii/38 iii●° How and in what manner is the Epicicle moved or turned about? THis Epicicle being placed in the excentrique, and elevated above the centre of the Zodiac, is moved in the upper part of the excentrique, contrary to the succession of the signs, and in the neither part of the said excentrique, according to the succession of the signs upon his proper axle-tree, standing perpendicularly upon the plane of the excentrique, and being moved equally from the mean Auge, maketh his revolution in 27 days and almost in 13 hours, by which moving the body of the Moon is carried round about the centre of the Epicicle. And the daily moving of this Epicicle from the mean Auge, is 13 degrees, i/3 ii/53 iii/56 iiii/23 v/58· so as it maketh his whole revolution in 27 days, 13 hours, i/18 ii/34 iii/52 But for the better understanding of the motion of the Epicicle, you have to note, that there be three special points belonging to the Epicicle, that is, the mean Auge, the true Auge, and the Touch-point, otherwise called the point of concavity. How are these three points described? THe mean Auge is described by a right line, which being drawn from that point in the little circle, which is opposite to the centre of the excentrique, passeth through the centre of the Epicicle, even to the circumference thereof, marked in the figure next following with the letter M. The true Auge of the Epicicle is described by a right line, which being drawn from the centre of the world, passeth also through the centre of the Epicicle, even to the circumference thereof, and is marked with the letter V The point of concavity or Touch-point is described by a right line, which being drawn from the centre of the excentrique, passeth also through the centre of the Epicicle, even to the circumference thereof, marked in the figure following with the letter P. which point is called the point of concavity, because you must imagine, that in the plane of the excentrique there is a certain concavity, wherein the plane superficies of the Epicicle is turned about, which concavity of itself is immovable, because it is moved only according unto the motion of the excentrique: to the plane of which excentrique, if you attribute so much thickness or depth towards the centre thereof, as is the diameter of the Epicicle, it must needs fall out, that the circumference of the Epicicle will touch the concave superficies of the upper deferent of the Auges in one only point. And therefore this point of the Epicicle may be as well called the Touch-point, as the point of concavity: and this point is said to be immoovable, because it never changeth his place, as the other two points, that is, the mean and true Auge of the Epicicle do; which are sometime more or less distant one from another, the centre of the Epicicle being out of the line of the Auge of the excentrique; for being in that line, those three point are united, and do meet all three in one. And the differing distance of the mean and true Ange of the Epicicle, in any place out of the foresaid line, is always to be measured by the Touch-point, because it is immovable, & not wandering as the other two points are, as you shall more plainly perceive by the figure next following, and by that which shall be said hereafter. ¶ The second figure belonging to the Theoric of the Moon. THe outermost circle in this figure signifieth the Zodiac, whose centre is marked with the letter A. and the next inner great circle signifieth the excentrique of the Moon, whose centre is marked with the letter B. which centre by going about the centre A. describeth the little circle B. C. which point C. is the opposite point to B. And the five little circles placed severally upon the excentrique, do signify every where the Epicicle of the Moon, whose centres are marked with these five letters, D. E. F. G. H. Again the right lines, marked with the letters B. P. passing through the centres of all the five Epicicles do show in the circumference of the said Epicicles, the point of concavity, otherwise called the touch point, marked with the letter P. And the right lines, marked with A. V do show the true Auge of the Epicicle, marked with the letter V and the right lines, marked with the letter C. M. do show the mean Auge of the Epicicle, marked with the letter M. What conclusions are to be gathered out of this Inequality of the Epicicle? THese four here following. 1 First, for so much as it is found by observation, that the motion of the mean Auge of the Epicicle, marked with the letter M. is regular and equal, going every day 13 degrees and almost i/4 it must needs follow that the motion of the other two points, that is, the true Auge of the Epicicle, marked with the letter V and the touch point marked with P. is irregular and unequal, because the mean Auge of the Epicicle is a vagrant point, so called, because it keepeth not always one certain place in the Epicicle, and yet is the beginning of the motion of the Epicicle. 2 Secondly, if the centre of the Epicicle be in the Auge or opposite Auge of the excentrique, than these three points, that is, the Touch-point, the true Auge, and the mean Auge of the Epicicle be all one, that is to say, do concur or meet all in one self line. But if the centre of the Epicicle be out of any of the said points, viz. out of the Auge or opposite Auge of the excentrique, than they are so separated, as the true Auge of the Epicicle marked with the letter V is in the midst betwixt the mean Auge, marked with M, and the Touch-point marked with P, because the centre of the world is always in the midst betwixt the centre of the excentrique and the point C, which point C in the little circle, is opposite to the centre of the said excentrique, marked with B. And the greatest distance of these points is beneath the mean longitudes of the Excentrique. What those mean longitudes are, shall be declared hereafter. 3 Thirdly, in that half of the excentrique, which descendeth from the Auge of the said excentrique unto the opposite Auge of the same, the two Auges of the Epicicle, both true and mean, marked with the letters V and M, do go before the Touch●point, in respect of the motion of the Epicicle, which is contrary to the succession of the signs. But in respect of the motion of the excentrique, which is always according to the succession of the signs, the two points M and V do follow the Touch-point P, as you may easily perceive by the former figure last set down: for the centre of the Epicicle being in the Auge of the excentrique, marked with D, or in the opposite Auge of the same, marked with G, the three foresaid points are all joined together in one self line. But when the Epicicle descendeth from D to E, then P V and M are separated, and P goeth before V and M: and the letter V being the true Auge of the Epicicle, is in the midst betwixt P and M. And such digression or separation is encrased by little and littl● until the centre of the Epicicle do come to the letter F, for from thence they begin again to approach and to grow nigher together, until they fall into the point G, whereas they join again, and are all one. But the contrary happeneth when those points are in the other ascending half of the excentrique, for then M and V do go before P, proceeding according to the succession of the signs. 4 Fourthly, the moving of the Epicicle is swifter in the upper part of the excentrique, than in the neither part thereof, for there the mean Auge of the Epicicle proceedeth contrary to the succession of the ●ignes, that is to say, towards that part into the which the Epicicle is moved: but the contrary happeneth in the lower part of the excentrique. And you have to note, that the Touch-point P is the measure of the digression or separation of both the Auges of the Epicicle, as well true as mean, because the Touch-point doth at no time wander from his place but remaineth immoovable. The demonstration of this fourth conclusion is plainly set forth in the former second figure of the Moon, whereby you may perceive, that when the Epicicle is come to the letter H, nigh unto the mean longitude of the Excentrique, whereas the distance of the foresaid points M V and P is always greatest; then immediately both the Auges, M and V, begin again to approach unto the Touch-point P, wherefore M proceedeth towards P, contrary to the succession of the signs, until it meeteth with P in the Auge of the excentrique, marked with the letter D. And from thence M departeth again from P, contrary to the succession of the signs, until it arriveth to the other mean longitude of the excentrique, whereas it is furthest distant from P. And by reason that the Epicicle is also moved into that part, it falleth out, that the two movings meeting in one self part, the moving of the Moon in the Epicicle, or rather the Epicicle itself by following the wandering mean Auge, is swifter in his gate. But contrariwise, in the neither part of the excentrique, from the place nigh unto F (whereas the distance of M P is greatest) unto the other place of the greatest distance of the said points nigh unto H, the mean Auge of the Epicicle is moved according to the succession of the signs: and there, according to the quantity of his moving, it taketh so much away from the swiftness of the Epicicle, as thereby the Epicicle in that place is much more slower in his gate. How is the circle equant of the Moon moved, which is otherwise called the circle of the two nodes or intersections, signifying the head and tail of the Dragon? THis circle is equally moved, contrary to the succession of the signs, about the centre and poles of the Ecliptic, making his revolution almost in 19 years: and by the moving of this circle, the poles of the deferents of the Auge are carried about the poles of the ecliptic: and the daily moving of this orb under the ecliptic, is but i/3 ii/10 iii/38 iiii/23 and v. 24· so as it maketh his whole revolution in 6798 days, that is to say, in 18 Egyptian years, 228 days, 3 hours, i/49 ii/40 and iii/16 of an hour. How is the moving or departing of the Moon from these Intersections called? IT is called the moving, or rather the Anomaly of the moons latitude: and the Moon, or rather the centre of her Epicicle, maketh one return to these Intersections in 27 days and 5 hours, for in that time the Moon accomplisheth all the varieties and changes of her latitude both North and South, and in one day she is separated from these Intersections 13 degrees, i/1 ii/45 iii/39 iiii/30 and v/46· and maketh her return to the said Intersections in 27 days, 5 hours, and ii/36 of an hour. You said before that the motions of all the other Planets were governed by the Sun: Tell therefore, in what moving of any Orb belonging to the sphere of the Moon, there appeareth any harmony or agreement of the Moon with the Sun. THeir harmony consisteth in the moving of the deferents of the Auge of the Moon, and in those things which depend of those deferents. For the deferents of the Moon Auge do keep such proportion with the excentrique of the Moon, as look how much the line of her mean moving by the moving of the eccentric is moved forward from the line of the mean moving of the Sun, according to the succession of the signs, beginning at the conjunction or opposition of the said lines of the mean moving, as well of the Sun as of the Moon: so much do those deferents carry backward the Auge of the excentrique from the same line of the mean moving of the Sun, contrary to the succession of the signs, as you shall more easily perceive by this figure or instrument next following, used by Reinholdus in his Commentaries made upon the Theoriqes of Purbachius, the description and use whereof here followeth. ¶ The third figure belonging to the Theoric of the Moon. THis figure consisteth of certain Orbs and Circles, whereof some are movable, and some immovable. The first lowest and greatest immovable circle being divided into 180 parts, every one containing two degrees, which maketh in all 360 degrees, signifieth the Zodiac. And the limb of this circle is divided into two spaces, in the outermost whereof are set down the characters of the twelve signs: and in the innermost space are first set down above on the left hand nine little stars, each one representing the body of the Sun, And right under them are set down the first five aspects: the first whereof standing right under the letter A, signifieth the Conjunction of the Sun and Moon, marked thus ☌. and next to that on the left hand, is the Sextile aspect, marked thus ⚹. and then the Quadrat aspect, marked thus □. and next to that the Trine aspect marked thus △. and then the Opposition, marked thus ☍. and these are called the first aspects, because they go before the Full of the Moon: and then followeth again the Trine aspect, the Quadrat, the Sextile aspect, and the Conjunction, which are called the second aspects, because they chance after the Full. And the first Conjunction is placed right under the letter A, which standing in the very top of the figure in the outermost space of the limb, signifieth the beginning of Aries. Moreover, in the innermost space of the limb are set down these letters, viz. BRCQDPEOFNGMH, which letters do serve to show the motion as well of the Excentrique, as of the Auge of the Moon. And next to the foresaid Zodiac are placed 2 movable black orbs, which are the deferents of the Moons Auge, & opposite Auge, signified by the 2 little tapes fastened to the uppermost black orb; whereof the one tape is marked with the letter X, signifying the Moons Auge, & the other tape being unmarked, signifieth her opposite Auge. Next betwixt the said two black orbs, is a movable white orb, signifying the excentrique or deferent of the moons Epicicle, to which is put a little tape to show the place of the centre of the Epicicle, which centre is marked with the letter Y, and in the circumference of the said Epicicle is fixed the body of the Moon. And within the Orb excentrique is another immoovable white orb or roundel, the centre whereof is the centre of the world, marked with the letter T, about which is a little circle described by the centre of the excentrique of the Moon, by turning round about the centre of the world, which centre of the excentrique is marked with the letter S, and the opposite point to that, is marked with the letter V, and the circumference of the said little circle is divided into nine equal parts, marked with Arithmetical figures, as 1. 2. 3. and so forth to nine, to show the place of the centre of the excentrique, marked with S, in every aspect. For the centre of the moons Epicicle being in conjunction with the Sun, the centre S is found to be in the upper point of the little circle, marked with the figure 1, and being in the first Sextile aspect, the centre S is in the point marked with the figure 2, and so proceedeth from point to point, according to the order of the nine aspects, before set down. The use of this Figure or Instrument is plainly showed by this one example here following. SVppose therefore the Conjunction of the Sun and Moon to be under the letter A. wherefore you must place in one self line both the Auge of the excentrique, marked with the letter X, and also the centre of the Epicicle, marked with the letter Y, right under the letter A. And because the centre of the Epicicle doth move towards the left hand, according to the succession of the signs, and that the Auge of the Moon doth move towards the right hand, contrary to the succession of the signs, you must bring the centre Y to the letter B, for there will his place be within four days next after the Conjunction, and there having stayed the centre Y, turn the Auge X towards the right hand, even to the letter M, & stay it there, so shall you find the mid body of the Sun, who then followeth the Moon, to be in the midst betwixt the two letters B and M, right over the Sextile aspect; and at that time the Moon is said to be in a Sextile aspect to the Sun, for than she is nigh to the mean longitudes, signified here in this figure by a white right line, always crossing the line of the Auges (which is also white) in the centre of the world with right angles, and the shape of the moons light is then horned, like a sycle, called in Greek Minoides, and in Latin Falcata. But at the seventh day after the Conjunction, her light will increase somewhat more, wherefore by turning the centre Y to the letter C, and the Auge X to the letter N, you shall find the centre of the Sun to be in the very midst betwixt those two letters, right over the Quadrat aspect, and the Moon to be right in the opposite Auge, and thereby to be in a Quadrat aspect to the Sun, at which time the shape of her light is said to be halfed, which may be called the half Moon, in Greek Diochotomos, and in Latin Dimidia or Dimidiata. But the eleventh day after the Conjunction, she will seem round bodied, though not at the full: wherefore you must bring the centre Y to the letter D, and the Auge X to the letter O, so shall you find the centre of the Sun to be in the midst betwixt those two letters, right over the mark of the Trine aspect; for then the Moon being again in the mean longitude, is said to be in a Trine aspect to the Sun, and the shape of her light is round like a bowl, and may be called the whole Moon, though not the full Moon, and in Greek it is called A●●phichyrtos, in Latin Vtrinque gibbosa. Again, when the Moon is fifteen days old, then bring both the centre Y, and also the Auge X to the letter E, for than you shall find the Sun to be right over the mark of Opposition, so as the Moon is then opposite to the Sun, and then she is at the full, called in Latin Pleni Lunium, and in Greek Panselmos. But the nineteenth day of her age the centre Y will be in the letter F, and the Auge X in the letter H, and then the Moon is the third time in the mean longitude, and then she is again in a Trine aspect to the Sun, as she was before at the eleventh of her age. And when the Moon is two and twenty days old, than the centre Y shall be in G, and the Auge X in Q, and then the Moon shall be again in a Quadrat aspect to the Sun, as she was before when she was seven days old. And when she is six and twenty days old, than the centre Y shall be in H, and the Auge X in R, and then the Moon being the fourth time in the mean longitude, shall be in a Sextile aspect, as she was before, being but four days old. And when she shall be thirty days old, than the centre Y and the Auge X shall meet together under A, and so the Moon shall be again in Conjunction with the Sun. All which things are briefly set down by Reinholdus in this Table following, consisting of seven Collums: In the first whereof are set down the days of the moons age during her increase, that is to say, from the Conjunction to the full, containing fifteen days, descending downward: in the second Collum are set the first five Aspects: and in the third Collum the places or points of the Excentrique. In the fourth Collum the names of the moons divers shapes of lights, serving as well to her increase as decrease. In the fift Collum are set again the places of the Excentrique. In the sixth Collum the second Aspects, like to the first. And in the last Collum, the days of the moons age after the full, during her decrease or wane, that is, from 15 to 30, ascending upward. The Table followeth in the next Page. A TABLE SHOWING THE DIVERS SHAPES OF THE MOON. 1. 2. 3. 4. 5. 6. 7. The days or age of the Moon. The first five Aspects of the Moon. The places of the Excentrique The divers shapes and names of the lights of the Moon The places of the Excentrique. The second five Aspects of the Moon. The dates. 1. ☌ In the Auge. Coniunctio, the new Moon. In the Auge. ☌ 30. 4. ⚹. In the mean longitude of the Excentrique. Falcata, the horned Moon. In the mean longitude of the Excentrique. ⚹. 26. 7. □. In the opposite Auge. Demidiata, the half Moon. In the opposite Auge. □. 22. 11. △. In the mean longitude of the Excentrique. Vtrinquegihbosa, almost round. In the mean longitude of the Excentrique. △. 19 15. ☍. In the Auge. Pleni lunius, the full Moon. In the Auge. ☍. 15. How is this digression or departing of the Moon from the Sun, called? IT is commonly called the longitude or moving of the Moon from the Sun: and the Moon returneth again to the Sun, or rather overtaketh him in 29 days and one half day, in which time she accomplisheth all her divers illuminations or shapes of light, that is to say, she sustaineth all her aspects to the Sun, and showeth to the earth all the diversities of her lights and appearances. And this month is called the month synodical: for there are two kinds of Lunar months, the one periodical, in which she goeth through the whole Zodiac, and the other synodical, in which she overtaketh the Sun; which Sacrobust● calleth the month of Consecution, who maketh four Lunar months, that is, the month of Peragration, the month of Apparition, the month Medicinal, and the month of Consecution, which are all declared in the six and fortieth Chapter of my first book of the Sphere. And you have to understand, that the daily moving of the Moon from the Sun, containeth 12 degrees, i/11 ii/26 iii/41 iiii/29 u58· and the synodical month consisteth of 29 days, 12 hours, i/44 ii/3 iii/11 What conclusions do accompany this harmony of the Sun and Moon? THese four here following. First, in every mean Conjunction or Opposition of the Sun and Moon (which mean Conjunction or Opposition is said to be when the centre of the moons Epicicle is either in Conjunction or in Opposition to the centre of the Sun) the centre of the Epicicle is found to be in the Auge of the Excentrique, but in every Quadrat aspect the centre of the Epicicle is in the opposite Auge of the Excentrique. Secondly, by this means, in every Conjunction and Opposition, as well the Excentrique as the Epicicle, are most swift in their motions; but in the quarters they are slowest, because their Anomaly or Inequality is thereby altered, as hath been said a little before. Thirdly, the Moon in one synodical month passeth twice through the orb Excentrique. Fourthly, the centre of her Epicicle in one synodical month describeth about the centre of the world a certain Ovale figure, like to this here following: ¶ The fourth figure belonging to the Theoric of the Moon. IN which Figure, the letter A signifieth the centre of the world, or of the whole sphere of the Moon, and therefore at the new Moon the centre of the excentrique is in B, which centre B, by turning round about the centre A, describeth a little circle in the midst of this figure, marked with the letters DFNKMOR: and the four little circles placed upon the Ovale circle, do signify the Epicicle of the Moon, the four centres whereof are marked with these four letters, CIPE: and the letter C signifieth here also the Auge of the excentrique, and so doth the letter P, but the letters IE do each of them signify the opposite point of the Auge. Moreover, the line AC signifieth here the line of the mean moving of the Sun, from which line when the centre B departeth towards the right hand, and cometh to the point D, which is in the little circle, than the centre of the Epicicle marked with C, descendeth on the left hand to the point E, which is in the Ovale circle, and then the angles BAD, and BAE are equal through the equality of their movings. Likewise, when the centre of the excentrique cometh to the point in the little circle, marked with F, the centre of the Epicicle is in the point G. And when the centre of the excentrique falleth into the point H, and there hath described a quarter of the little circle, than the centre of the Epicicle hath likewise made a quarter of the Zodiac, which is 90 degrees, counting from the line of the mean moving of the Sun, whereof such distance of the Moon from the Sun is called a quarter, and is found to be in the point 1, being then in the opposite Auge of the excentrique, and so the Moon giveth light with half her body, and is then nighest to the earth. Again, when the centre of the excentrique cometh down into K, than the centre of the Epicicle departing from the earth, cometh to the point L: and when the centre of the excentrique cometh to the point M, then the centre of the Epicicle is in the point N. Lastly, when the centre of the excentrique falleth into O, the centre of the Epicicle shall be in P, so as OPEN shall be both in one right line, and thereby the centre of the Epicicle and the centre of the excentrique shall be distant from the Sun half a circle, which is a hundred and eighty degrees, and then the Moon shining with her whole body, is opposite to the Sun. And look what course the Epicicle hath kept in the first half of the Ovale circle during the moons increase, the like course it observeth in the other half of the said circle, whilst the Moon decreaseth. How are the Orbs belonging to the sphere of the Moon, to be measured? AS the line of the Auge marked with the letters AC, or AP, in the former fourth figure, containeth 60 degrees or parts, even so the opposite Auge, marked with the letters AI, or AQ, containeth according to Ptolomey of the like degrees or parts, 39 degrees and i/22 and the semidiameter of the excentrique, containeth 49 degrees, i/41 and the excentricity AB containeth 10 degrees, i/19 and the semidiameter of the Epicicle containeth 5 degrees, i/13 But if the degrees be such, as the semidiameter of the earth containeth but one degree or one part thereof, than he proveth by demonstration, that the line of the Auge containeth but 59 such degrees; and the line of the opposite Auge to contain no more but 38 degrees and i/43 and the semidiameter of the excentrique to contain 48 degrees, i/51 ii/30 and the excentricity to contain 10 degrees, i●●° ii/30 and the semidiameter of the Epicicle to contain 5 degrees, i/10 And hereof it cometh to pass, that the altitudes of the Moon are measured by the semidiameters of the earth. For the greatest altitude of the new of full Moon, being then in the Auge of the excentrique, is 64 degrees, i/10 and her least altitude when she is in the said Ange, is 53 degrees, i/50 but the greatest altitude of the Moon, being in the beginning of any of her quarters, and in the opposite Auge of the excentrique, is 43 degrees, i/53 and her least altitude is then 33 degrees, i●●° of the semidiameter of the earth, whereof every such part is equal to the semidiameter of the earth. And note, that by the altitude of the Moon is meant here a right line, extending from the centre of the earth to the centre of the Moon, in what part of heaven soever she be. But Copernicus correcting these things, in his suppositions or particular propositions, proveth the greatest altitude of the Moon, being either new or full, to contain 65 degrees, i●0· and her least altitude to contain 55 degrees, i/8 and being in the beginning of any of her quarters, her greatest altitude to contain 68 degrees, i/20 and her least altitude to contain 52 degrees, i/17 Such degrees, I say, whereof the semidiameter of the earth is but one. The third Intention, showing what points, lines, and arches are requisite to be known in the Theoric of the Moon, which are these here following. 1. THe line of the mean, and also the line of the true moving of the Moon. 2. The mean and true moving of the Moon. 3. The longitude or distance of the Moon from the Sun. 4. The doubled longitude or centre. 5. The centre of the equality. 6. The Auge and opposite Auge of the excentrique. 7. The Auge and opposite Auge, both mean and true, and also the Touch-point, or point of concavity, all three belonging to the Epicicle of the Moon. 8. The Equation of the Centre. 9 The argument equal or mean. 10. The argument equated. 11. The Equation of the Epicicle. 12. The diversity of the Diameter. 13. The proportional minutes: and to these may be added the Intersections, called the head and tail of the Dragon. Also the North and South limit, and the mean and true moving of the same. And finally, the mean & true Anomaly or Inequality of the Moon's latitude. What is the line of the mean moving of the Moon? IT is a right line, which being drawn from the centre of the world, passeth through the centre of the Epicicle even to the Zodiac. And this line by means of the regular moving of the excentrique upon the centre of the world, is equally carried through the Zodiac, showing the mean place of the Moon, and therewith the true place of the centre of the Epicicle: which line in the sixth figure hereafter following, is represented by the letters M B, which line passeth through the centre of every one of the four Epicicles set down in the said sixth figure. And this line in the Theoric of the Sun is threefold, whereof one proceedeth from the centre of the excentrique to the body of the Sun, the second. line being equally distant from the first, proceedeth from the centre of the world to the Zodiac. The third line proceeding also from the centre of the world, passeth through the body of the Sun to the Zodiac. All which three lines are before plainly set down in the second figure belonging to the Theoric of the Sun. And these three lines in this Theoric of the Moon, by reason that the centre of equality, and the centre of the world is here all one, they do make but one self line. What is the line of the true moving of the Moon? IT is a right line, which being drawn from the centre of the world, passeth through the mid body of the Moon, even to the Zodiac, which the letters M F C in the sixth figure following do show. What is the mean and true moving of the Moon? THe mean moving of the Moon is an arch of the Zodiac, which extendeth from the beginning of Aries, according to the succession of the signs, unto the line of the mean moving of the Moon. And the true moving of the Moon is an arch of the Zodiac, extending in like manner from Aries to the line of the true moving of the Moon. ¶ The fifth figure belonging to the Theoric of the Moon. THis figure is used by Mestelyn to show the armonie of the Sun and Moon, which is already more plainly demonstrated by Reinholdus his figure before set down, and it is the third figure belonging to the Theoric of the Moon. And the outermost circle of this fift figure signifieth the Zodiac, divided into 360 degrees, and the next greater circle is the excentrique of the Moon, which carrieth the Epicicle, whose centre is marked with the letter F. And A is the centre of the Zodiac: and B is the centre of the excentrique, which by turning about the centre A, describeth the little circle in the midst of the Figure, and the line A F is the line of the mean moving of the Moon, being in G, and the line A B D is the line of the Moons Auge, or of her excentrique, being in E, and the line A C is the line of the mean moving of the Sun, who unless the Moon and he be in Conjunction or Opposition, is always in the midst betwixt the Auge of the Moon, and the centre of her Epicicle, as is more plainly declared before in the third figure. And therefore I have set down this fift figure here, only to show the longitude & double longitude of the Moon, and the equation of the centre, as followeth. What is the longitude of the Moon from the Sun? IT is an arch of the Zodiac, proceeding according to the succession of the signs from the line of the Suns mean moving, to the line of the Moons mean moving, which the arch C G in the former fifth figure doth show. What is the double longitude or centre of the Moon? IT is an arch of the Zodiac, proceeding according to the succession of the signs, from the Auge of the excentrique unto the line of the Moons mean moving, represented in the former fift figure by the letters E C G, and is called the double longitude, because it is double so much as is the distance of the Moon from the Sun, represented in the said figure by the letters C G, as you may easily try with your Compass. Alphonsus and his followers do call it the centre of the Moon, because it dependeth upon the Auge of the excentrique, and is answerable to that arch, which in the Theoric of the Sun is called the yearly Inequality or Argument of the Sun, which is twofold, that is, mean and true, represented in the third figure of the suns Theoric by the letters C I and C K. And this double longitude is called of Coperni●us, Motus secundi Epicicli, the moving of the second Epicicle; which second, and also the first Epicicle, shall be declared hereafter in the eleventh chapter of my extract out of Maginus. What is the Equation of the Centre, or of the Excentrique? IT is an arch of the Epicicle, contained betwixt the mean and true Auge of the said Epicicle, represented in the said fift figure of the Moon, by the letters M N: and whensoever the centre of the Epicicle is either in the Auge or opposite Auge of the Excentrique, than this arch is no arch at all. But if the centre of the Epicicle be out of those two points, and is found to be in that half of the Excentrique which descendeth from the Auge towards the opposite point thereof, than it addeth to the Inequality of the Epicicle hereafter defined, some portion: but in the other half it taketh so much away from the Inequality of the Epicicle, for there the mean Auge of the Epicicle goeth backward from the true Auge thereof, contrary to the succession of the signs, towards that part into which the Epicicle tendeth; but in the first half it is clean contrary. And note, that according to the tables of Alphonsus and of Ptolomey, the greatest equation of the centre or excentrique containeth 13 degrees, i/9 but according to the Prutenicall Tables, it containeth no more but ●2 degrees, i/27 the difference whereof springeth of the diversity of their suppositions. What is the Anomalia or Inequality of the Epicicle, both mean and true? THe mean Inequality of the Epicicle, is an Arch of the Epicicle, contained betwixt the mean Auge of the Epicicle and the mid body of the Moon, counted towards that part whereunto the Epicicle is moved: But the true Inequality is an arch contained betwixt the true Auge of the Epicicle, and the mid body of the Moon. This Inequality is called of Ptolomey, Anomalia, of Alphonsus, Argumentum; and of Copernicus, motus primi Epicicli. What is the equation of the Epicicle, called of Alphonsus, Equatio Argumenti? IT is an arch of the Zodiac, contained betwixt the line of the mean moving and the line of the true moving of the Epicicle. And this arch is none at all, when the Moon is in the true Auge, or in the true opposite Auge of the Epicicle. And whilst the Moon passeth through the first half of the Epicicle, this equation maketh the true moving of the Moon lesser than her mean moving, and in the other half of the Epicicle it maketh her true moving greater than her mean moving. And this equation of the Epicicle may be sometime greater, and sometime lesser, according as the centre of the Epicicle is more or less distant from the Auge of the eccentric, but it is said to be greatest when the centre of the Epicicle is in the opposite Auge of the excentrique, and to be least when the centre of the Epicicle is in the Auge of the said excentrique. But to understand this and many other things belonging to this equation, it shall be necessary to set down this sixth figure here following, and appertaining to the Theoric of the Moon. ¶ The sixth figure belonging to the Theoric of the Moon. THis figure as you see consisteth of certain circles both greater and lesser, and of certain lines and points, marked with certain letters to show what they signify. You have then to understand, that the greatest and outermost circle of this figure signifieth the Zodiac, whose centre is marked with the letter M: and the circle that is blacker than his fellows, signifieth the circle excentrique, which carrieth the Epicicle of the Moon, whose centre is marked with the letter N. There be also within the Zodiac seven other circles, all drawn upon the centre M, making six equal spaces, every space containing 10 minutes, so as there be in all 60 minutes, which are called the proportional minutes; the use whereof, and whereto they serve, we shall show here by and by. Moreover, there be four little circles, signifying the Epicicle of the Moon, every one having his centre placed upon the excentrique, marked with the four letters H I K L. And the letters B C set down in four sundry places upon the Zodiac, right against every one of the Epicicles, do signify the arch of the Zodiac, which is called the equation of the Epicicle, which arch is contained betwixt the line M B, passing through the very centre of the Epicicle to the Zodiac, and the line M C passing through the midst of the Moon, marked with the letter F, betwixt which letter F and the letter D (set down in every Epicicle) is contained an arch of the Epicicle, whereof the arch of the Zodiac B C is said to be the equation. And the four letters H I K L before mentioned, do not only signify the centre of the Epicicle, but also certain other points in the excentrique to show the increase and decrease of the equation of the Epicicle. For the point H standing above, signifieth the Auge of the excentrique, in which point whensoever the centre of the Epicicle is found to be, than the equation is least, containing but 4 degrees, i/56 ii/20 But when the centre of the Epicicle is in the point I, than the equation is somewhat greater: and when it is in the point L, the equation is greater than that of I, because the more distant from the Auge of the Excentrique, the greater is the equation. But when the centre of the Epicicle is in the opposite Auge of the Excentrique, marked with the letter K, than the equation is greatest of all, containing 7 degrees, i/40 and the difference betwixt the greatest and least equation, is called of Alphonsus, Diversitas diametri, and of Ptolomey, Excessus, because the diameter of the Auge of the Excentrique, marked in this figure with the letters M H, doth far exceed in length the diameter of the opposite Auge of the Excentrique, marked with the letters MK, as you may easily try with your Compass, by applying the shortest diameter K M unto the longest diameter M H: the excess or overplus whereof is divided as you see into six equal spaces or sections, every one containing ten minutes, through which sections the seven circles before mentioned, do pass, making in all sixty minutes; which sixty minutes are not only set down in the right line of the Auges of the Excentrique, but also in each half of the circumference of the said Excentrique, proceeding on both sides downward from the Auge unto the opposite Auge of the Excentrique: and these sixty proportional minutes were invented to know thereby how much the equation of the Epicicle doth increase or decrease, according as the centre of the Epicicle is more or less distant from the Auge of the Excentrique. For if you suppose the centre of the Epicicle to be in the point I, then like as the diameter M I is lesser or shorter than the diameter M H, by twenty of the said minutes, so the equation of the Epicicle marked upon the Zodiac with B C, is greater than the equation of the Epicicle, being in H, by twenty such minutes: which excess is marked with the letters A C upon the Zodiac. Again, when the centre of the Epicicle is in the point L, then as the diameter M L is lesser than the diameter M H by i/40 so is the equation of the Epicicle, marked with B C, greater than the equation of the Epicicle, being in H, by i/40 which excess is also marked on the Zodiac with the letters A C. And to speak briefly, the further that the centre of the Epicicle is distant from the Auge H, the shorter is the diameter or right line drawn from the centre M to the centre of the Epicicle, and thereby the equation of the Epicicle is the greater. Now though these proportional minutes may be described another way, that is, by dividing the overplus or excess, whereby the arch of the greatest equation doth exceed the arch of the least equation into sixty minutes, and thereby to know the diversity of every equation, in what place soever of the Excentrique the centre of the Epicicle is found to be (being out of the Auge:) yet I omit to speak thereof, because the other way before set down, is the easier of the two, and is only the way whereby the tables of calculating the said equations are made. The fourth Intention, showing the twofold latitude of the Moon, and of the head and tail of the Dragon. THe latitude of the Moon is none other thing but her distance from the Ecliptic line, which distance is never above five degrees. And her latitude is twofold, that is, Northern and Southern. For the deferent of the Moon in the space of one month cutteth the Ecliptic in two places right opposite one to another, and thereby the one half of her deferent inclineth towards the North, and the other half thereof inclineth towards the South: and those two sections are called the two nodes, the one ascendent, which is the beginning of the Moons departing & ascending from the Ecliptic towards the North, and the other node is called the node descendent, from which node the Moon descendeth towards the South. And as the Ecliptic or way of the Sun is divided into four parts by the four principal points, that is, the two equinoctial points, and the two solsticiall points: even so the deferent of the Moon is divided into four quarters by the two foresaid nodes, and by the two limits of her greatest latitude. And as the node ascendent showeth the East, and the node descendent the West, so of the two limits the one showeth when the Moon is farthest North, and the other showeth when she is furthest South, as you may plainly see by the figure next following. ¶ The seventh figure belonging to the Theoric of the Moon. THe outermost circle of this figure drawn upon the centre A, signifieth the Zodiac, having the characters of the twelve signs described therein, and is marked with the letters C M N E D, within which circle are drawn two other circles, crossing one another in two points opposite, whereof that which is drawn upon the centre B, and is marked with the letters F I H G, is the excentrique or deferent, carrying the Epicicle of the Moon. And the other circle drawn upon the centre A, and marked with the letters K I L G, signifieth the ecliptic or way of the Sun, and these two circles are equal (because their semidiameters are equal) crossing one another in two points opposite: whereof that Intersection which is on the right hand, is called the node ascendent or head of the Dragon, figured thus ☊, and that on the left hand is called the node decendent or tail of the Dragon, figured thus ☋, and the limits are marked with the two letters F H, whereof the letter F signifieth the North limit, and H the South limit. And you have to note, that the head of the Dragon hath two motions or movings, the one mean and the other true. His mean moving is an arch of the Zodiac, extending from the beginning of Aries, marked in the former Figure with the letter C, contrary to the succession of the signs by the moving of the orb equant unto the letter D, showing the place of the head of the Dragon in the Zodiac, whereunto the line A G doth point, which arch is marked with the letters C D. Again, his true moving is an arch of the Zodiac, extending according to the succession of the signs, from the beginning of Aries unto the head of the Dragon. And this arch is marked with the letters C M N E D, which two arches being added together, do make up the whole Zodiac, and the self-same movings are also incident to the other three points, that is, to the tail of the Dragon, and to the two limits. ¶ Of the Inequality of the moons latitude both mean and true. What is the Inequality or Anomaly of her latitude? IT is an arch of the Zodiac, extending according to the succession of the signs, from the Dragon's head unto the place of the Moon: which if it be her mean place, than such arch is called the mean Inequality of her latitude: but if it be the true place of the Moon, than that arch is called the true Inequality of her latitude. How to know her mean and true place hath been showed before. But you have to note, that though the followers of Alphonsus do make this arch of latitude to begin at the Dragon's head: even as the Ecliptic is said to begin at the vernal Equinoctial point: yet Ptolomey and Copernicus, and also the Prutenicall Tables, do make the said arch to begin at the North limit of the moons latitude, and so to extend, according to the succession of the signs: by help of which arch the latitude of the Moon is always to be found in the said Tables. ❧ The Theoric of the three Superior Planets, that is, Saturn, jupiter, and Mars. Why are these three called the Superior Planets? BEcause they are placed above the Sun: even as the other three Planets, that is, Venus, Mercury, and the Moon, are called the Inferior Planets, because they are placed under the Sun, who is chief governor of them all. The Theoric of which three superior Planets, we think it best here to describe next after the Moon, because that though they be subject to more diversities of movings than either the Sun or Moon, yet to fewer than Venus or Mercury. Why are these three Planets joined together all in one Theoric? BEcause in the quality of their movings, as well according to longitude as latitude, they be like, differing only in quantity, and their orbs have like uniformity, and therefore may be very well described in one self Theoric. The first Intention, showing how many orbs do belong to the Theoric of every one of these Planets. VIZ. Four orbs, and one circle, that is, the Excentrique carrying the Epicicle, than the two deferents of the Auge and opposite Auge of the Excentrique, and the Epicicle carrying the body of the Planet, whereto is added the circle Equant: all which are set down in the Figure next following. ¶ The first figure of the three upper Planets. THis figure as you see is also environed with a great circle, signifying here the orb which carrieth the two sections, called the head and tail of the Dragon, and is the outermost circle of all, marked with the letter M, whose centre is the letter A, which is the centre of the world. And next to that are the two black deferents of the Auges, whereof the upper deferent is marked with D, and the neither deferent with E, both which are in divers respects concentrique with the centre of the world, and also excentrique: and within those two deferents is placed the Excentrique which carrieth the Epicicle, and the centre of the excentrique is marked with the letter B, and the little circle above is the Epicicle, whose centre is F, which centre by turning round about upon the plane of the Excentrique, describeth in the very midst thereof a circle marked with the letter C, which circle is crossed in two points opposite by another circle, called the circle equant, marked with the letter G, whose centre is marked with the letter H. Why are these four orbs placed in this Theoric of the three upper Planets? THe Excentrique is needful as well to show their unequal distances from the earth, as also for that the equations of their Epicicles are sometime greater, and sometime lesser, as hath been demonstrated before in the sixth figure of the Moon. And the two deferents of the Auges are here placed for the self-same causes that are before declared. Again, the Epicicle is necessarily supposed, because it is well known by often observation, that every one of these three Planets in like and self-same places of his Excentrique is found to have diverse and sundry motions, whereof they are said to be sometime swift and sometime slow, now stationary and now retrograde; moreover, they are sometime nigher to the earth, and sometime further off, as manifestly appeareth by the mutability of their apparent greatness: all which apparences are salved, by supposing an Epicicle. Wherefore is the circle equant added to this Theoric? BEcause the conversions of the Excentriques and of the Epicicles of these three Planets are not observed to be equated to their own centres, but to some other point, which point is called the centre equant, marked in the former figure with the letter H: and because it is not needful to appoint to that centre any peculiar orb, sith there is no use thereof, the Astronomers think it sufficient only to describe about that centre a circle upon the Plane of the Excentrique, equal to the circle Excentrique in every respect; for having both equal semidiameters, as I said before, they must needs be equal. Hath the Orb which carrieth the two nodes, no use in this Theoric? YEs, they may be used as well in the Theoric of these Planets, as in the rest. And yet because the varieties of the latitudes are observed to proceed equally according to the succession of the signs, together with the Auges, the office of carrying the Nodes, is most commonly by the Astronomers appointed to the two deferents of the Auges, so as this orb in this Theoric having none other use, is not thought so needful. The second Intention, showing towards what part such Orbs are moved, and in what time they make their revolutions, and also upon what centres or poles they make their regular movings: and first of all, how and in what manner the Excentriques, carrying the Epicicles of these Planets, are moved. THe Excentrique of every one of these Planets, is moved according to the succession of the signs, upon his own proper poles, declining unequally on both sides from the poles of the Ecliptic, and yet it moveth equally about the centre of the circle equant: and the Excentrique of Saturn is commonly said to make his revolution in thirty years, and the Excentrique of jupiter in twelve years, and that of Mars almost in two years. How much is the precise daily motion and perfect revolution of every one of these Excentriques? TO understand this the better, you had need to remember Coper●icus his division of the beginning of moving before mentioned, which is twofold, the one compound, and the other simple. The compound moving is to be accounted from the vernal equinoctial point, which point of beginning is unstable: and the simple moving is to be counted from the first star of the Ram's horn, called of the Astronomers, The firm and stable point, or beginning of moving: wherefore if you count from the Equinoctial point, than the daily moving of the Ex●●ntrique of Saturn containeth i/2 ii/0 iii/35 iiii/33 v/2· that of jupiter, i/4 ii/59 iii/15 iiii/49 v/53· and that of Mars, i/31 ii/26 iii/39 iiii/14 v/6· And one whole revolution of Saturn, counting from the Equinoctial point, containeth 29 Egyptian years, 161 days, 22 hours, i/28 ii●° iii/22 And the re●olution of jupiter, counting also from the equinoctial point, containeth 11 Egyptian years, 315 days, 15 hours, i/●. ii/10. iii/30. And that of Mars containeth one Egyptian year, 321 days, 22 hours, i/19 ii/49 iii/48 But if you count their moving from the first star of the Ram's horn, than the Excentriques of these Planets will not make their revolutions so soon, but be somewhat longer in returning to that first point of moving, for the excentrique of Saturn will then make his revolution in 29 Egyptian years, 174 days, 4 hours, i/58 ii/25 iii/30 And that of jupiter in 11 Egyptian years, 317 days, 14 hours, i/49 ii/31 iii/56 And that of Mars in one Egyptian year, 321 days, 23 hours, i/31 ii/56 iii/49 In what place is the centre of the circle equant to be found? IN the line of the Auge of the excentrique towards the same Auge, whose distance from the centre of the world is double to the excentricity of the excentrique: which excentricity is the space contained betwixt the centre of the world, and the centre of the excentrique. What followeth upon this Inequality or Irregularity of the Excentriques? WE have showed you before in the Theoric of the Moon, that the centre of equality is towards the opposite Auge of her Excentrique, and is all one with the centre of the earth, and thereby the moving of her excentrique, whilst her Epicicle moveth towards the Auge, is the swifter. But because in this Theoric of the three Planets, the centre of the equant is towards the Auge of the Excentrique, the Excentrique therefore moveth the more slowly; for a lesser portion of the Excentrique belongeth to the upper half of the circle equant, and a greater portion thereof is due to the neither half of the circle equant, as plainly appeareth by the former figure: for if you draw a right line through the centre of the equant, so as it may cut the line of the Auge with right angles, it will divide the circle equant into two equal semicircles, but it will divide the Excentrique into two unequal portions, whereof the uppermost is the lesser, and the nethermost the greater. And sith the moving of the Excentrique is equal about the centre of the equant, and that these unequal portions of the Excentrique do turn about the said centre in equal time, it must needs move more slowly above, and more quickly beneath. How are the deferents of the Auges moved? THey are moved according to the succession of the signs, about the centre and poles of the Ecliptic, by virtue of the eighth sphere, & according to Alphonsus do make their whole revolution in 49000 years, by which moving they put forward by little and little the Auges of the Excentriques. How and in what manner are the Epicicles of these Planets moved? THey are moved in their upper part according to the succession of the signs, and in their neither part contrary to the succession of the signs, which is clean contrary to the moving of the moons Epicicle before declared. And every one of these Epicicles is equally moved from his mean Auge, upon his own proper axle-tree, which is also movable, standing upon the plane of the Excentrique obliquely or slopewise, and not perpendicularly. And the Epicicles of Saturn and jupiter do go about in the space of one year and a few days more, but the Epicicle of Mars goeth about in a little more than two years: and by this moving every Epicicle carrieth about with him the body of his proper Planet. What is the daily moving and also the periodical revolution of every one of these Epicicles? THe daily moving of the Epicicle of Saturn, is i/57 ii/7 ii/●4· iii/4 u22· and that of jupiter, is i/54 ii/9 iii/3 iiii/●7· v/31· and that of Mars, is i/27 ii/41 iii/40 iiii/23 v/19· So as the Epicicle of Saturn maketh one period in 378 days, which is one year, 13 days, and 6 hours, i/24 ii/57 iii/26 And the Epicicle of jupiter maketh one period in 398 days, which is one year, 33 days, and 21 hours, i/13 ii/15 iii/33 And the Epicicle of Mars maketh one period in 779 days, which is two years, 49 days, 22 hours, i/28 i●9· iii/49 How is the mean Auge of every one of these Epicicles described? BY a right line drawn from the centre of the circle equant through the centre of the Epicicle, even to the circumference thereof, making there a point marked in the figure next following with the letter M, which is furthest distant from the centre of the equant. And the centre of the equant governeth the moving as well of the Epicicle, as of the Excentrique, as you may plainly see by this figure following. ¶ The second figure belonging to the Theoric of the three superior Planets. THis figure consisteth of diverse circles and centres, lines, and points, whereof the outermost circle signifieth the Zodiac, whose centre is marked with the letter A, and of the two greater circles drawn within that, cutting one another in two points opposite, the one is the circle equant, whose centre is marked with the letter C, and the other is the Excentrique, whose centre is marked with the letter B, and the Auge of the Excentrique is marked with the letter D, and the opposite Auge thereof is marked with the letter E: and the four lesser circles placed upon the Excentrique, are Epicicles, whereof two have their centres, marked with the letter H, as well on the right hand as on the left hand of the figure, for the right line C H M doth point to the mean Auge of the Epicicle, marked with the letter M on both sides of the figure, and the right line A H V doth point to the true Auge of the Epicicle, marked likewise on both sides of the figure with the letter V, and the right line B H P showeth the Touch-point, marked also on both sides of the figure with the letter P, which is always in the midst betwixt the mean and true Auge of the Epicicle, being out of the line of the Auges. Now what the other letters set down in the outside of this figure do signify, shall be showed when we come to describe the points, lines, and arches, belonging to this Theoric. What conclusions do follow upon this Inequality of the Epicicle? 1. THese four: First, the moving of the Planet to any other point in the circumference of the Epicicle, than to the mean Auge of the Epicicle and to the opposite Auge, is unequal. 2. Secondly, when the centre of the Epicicle is either in the Auge or opposite Auge of the Excentrique, than the three points, that is, the mean Auge, the true Auge, and the Touch-points are all united, and do meet in one self line: but being out of the line of the Auge, they are so severed, as the Touch-point is in the midst betwixt the mean and true Auge of the Epicicle, because that the centre of the Excentrique is in the midst betwixt the centre of the Equant, and the centre of the Ecliptic. 3. Thirdly, in the descending half of the excentrique from the Auge towards the opposite Auge thereof, that is from D to E, the mean Auge of the Epicicle, marked with M, goeth before the Touch-point, marked with P, according to the succession of the signs; and the true Auge of the Epicicle followeth the said Touch-point, according to the succession of the signs. But in the other ascending half of the Excentrique, the true Auge of the Epicicle being out of the line of the Auges of the Excentrique, always inclineth from the Touch-point towards the Auge of the Excentrique, and the mean Auge of the Epicicle inclineth towards the opposite Auge of the Excentrique. 4. Fourthly, in the upper part of the Excentrique the moving of the Planet is swifter than in the lower part of the Excentrique, because that the mean Auge of the Epicicle goeth in the upper part of the Excentrique, according to the succession of the signes●. But in the other neither half of the Excentrique, the moving of the Planet is slower, going there contrary to the succession of the sign. What harmony is there betwixt the moving of the Sun, and the movings of the three superior Planets, and whereof dependeth such harmony▪ IT chiefly dependeth upon the periodical revolutions and movings of their Epicicles: for it is well known by good observation, that in every mean conjunction of the Sun with any of the said three Planets, the Planet itself is in the mean Auge of his Epicicle; and in every mean opposition of the Sun with any of the said three Planets, the Planet itself is in the mean opposite Auge of his Epicicle: and in any other place look how much the mean place of the Sun is distant from the mean place of the Planet, so much is the Planet itself distant from the mean Auge of the Epicicle, as you shall easily perceive by this figure following. What mean Conjunction or Opposition is, shall be declared hereafter in the second book, treating of the passions of the Planets. ¶ The third figure belonging to the Theoric of the three superior Planets. THis figure as you see consisteth of two several circles, whereof the lesser circle which standeth above, signifieth the Epicicle, carrying the Planet, whose centre is marked with the letter B. And the greater circle beneath, is the deferent of the Sun. In each of which circles are set down the characters of the five Aspects, whereof in both circles, that of the Conjunction is placed above, and that of the Opposition beneath: and on each hand on both sides are placed the characters of the other three aspects, that is, the Sextile, the Quadrat, and the Trine aspect. The letters set down on both sides of either circle, do serve to show the points of moving, as well of the Sun in his deferent, as of the Planet in his Epicicle: for when the Sun by his mean moving is in the point C of his deferent, and the Planet in the mean Auge of his Epicicle, marked with D, then are both their mean movings joined in one self line, and so be in a Conjunction. And as the Sun departing from thence to the point E, set down on the left hand of his deferent, hath gone a sixth part of his deferent, and thereby is in the first Sextile aspect: so the Planet departing from the mean Auge of his Epicicle, and coming to the point F, hath gone also a sixth part of his Epicicle, and is thereby in the first Sextile aspect: and when the Sun cometh to the point G, and the Planet to the point H, than they are both in a Quadrat aspect: and when the Sun cometh to the point I, and the Planet to the point K, then are they both in a Trine aspect: and when the Sun is in the point L, and the Planet in the point M, then they are just opposite one to another, being both in one self line: and in departing from thence, they observe like order in going through the other half of their circles, until they come again to be in a Conjunction, as the letters N P R on the right hand, being the half of the suns deferent, and the letters O Q S on the right hand, being the half of the Epicicle, do show. Of this harmony do follow three conclusions. 1. FIrst one period of the Epicicle is justly accomplished in so much time as passeth betwixt two Conjunctions of the Sun and of the Planet. 2. Secondly, look how many degrees the Sun by his mean moving is distant from the mean moving of the Planet, so much doth the Planet depart from the mean Auge of his Epicicle. And therefore the mean moving of the centre of the Epicicle, and the mean moving of the Planet in his Epicicle, being joined together, are equal to the mean moving of the Sun. 3. Thirdly, of this way may be gathered, that the Epicicle and the Excentrique as touching their swiftness and slowness of gate in making their periodical revolutions, are clean contrary one to another, for in those places whereas the moving of the Excentrique is slowest, there the moving of the Epicicle is swiftest, and yet their movings being all joined together, are equal to the moving of the Sun. What measure doth Ptolomey appoint to every one of their Orbs? THeir measures do depend of the semidiameter of the Excentrique, which is supposed to contain 60 parts or degrees, and of such like parts the excentricity of the excentrique of Saturn containeth 3 degrees, i/25 and that of jupiter 2 degrees, i/45 and that of Mars 6 degrees, i/0 Again, the excentricity of the equant of Saturn containeth 6 degrees, i/50 and that of jupiter containeth 5 degrees, i/30 and that of Mars 12 degrees, i/0 And the semidiameter of the Epicicle of Saturn containeth 6 degrees, i/30 and that of jupiter 11 degrees, i/30 and that of Mars 39 degrees, i/30 And the least altitude from the earth of Saturn, is 50 degrees, i/5 and that of jupiter is 45 degrees, i/45 and that of Mars is 14 degrees, i/30 And the greatest altitude from the earth of Saturn is 69 degrees, i/55 and that of jupiter is 74 degrees, I●15. and that of Mars is 105 degrees, i30. The third Intention, showing what points, lines, and arches are necessary to be known in the Theoriques' of the three upper Planets, which are these here following. 1. FIrst, the Auge and opposite Auge as well of the Excentrique, as of the circle equant. 2. The lines of the mean and true moving of the Epicicle, and of the Planet. 3. The mean and true moving of the Epicicle, and of the Planet. 4. The Inequality or centre of the Excentrique, both mean and true. 5. The mean and true Auge of the Epicicle. 6. The equation of the Excentrique, or of the centre, as well in the Excentrique as in the Epicicle. 7. The inequality of commutation or argument, both mean and true. 8. The equation of the argument. 9 The mean longitude. 10. The excess of the longer longitude. 11. The excess of the nigher longitude. 12. The proportional minutes both nigher and more remote. 13. The diameter of the Auges. 14. The diameter of the mean longitude in the Epicicle. 15. The upper and neither half of the Epicicle. 16. The oriental and occidental half of the Epicicle, the descriptions of all which things do here follow. But first as touching the Auges and opposite Auges, as well of the Excentrique as of the Equant, they are already before described. The line of the mean moving of the Planet or of his Epicicle, is a right line drawn from the centre of the world to the Zodiac, and is a parallel or equally distant to another line, drawn from the centre of the Equant, and passing through the centre of the Epicicle. Of which two lines, the first is marked in the second Figure on the right hand thereof, with the letters A I, and the other line is marked on the same hand with the letters C H. But the line of the true moving of the Epicicle, is a right line drawn from the centre of the world through the centre of the Epicicle even to the Zodiac, represented on both hands of the said figure with the letters A K. Now the line of the true moving of the Planet, is a right line drawn from the centre of the world through the body of the Planet unto the Zodiac, signified by the letters A L set down on both sides of the said second figure. But if the Planet be either in the true Auge or opposite Auge of the Epicicle, than the two lines AK and ALL are united. But if the centre of the Epicicle be either in the Auge or opposite Auge of the Excentrique, that is either in D or E, than the three lines AI, AK, and CHM, are all one. The mean moving of the Planet or of his Epicicle, is an arch of the Zodiac, extending from the vernal equinoctial point, according to the succession of the signs unto the line of the mean moving of the Planet or Epicicle, marked in the said figure with the letters N F I, proceeding towards the left hand. The true moving of the Epicicle is an arch of the Zodiac, extending according to the succession of the signs from the said equinoctial point to the line of the true moving of the Epicicle, marked with the letters N F K. But the true moving of the Planet is an arch of the Zodiac, extending in like manner from the equinoctial point to the line of the true moving of the Planet, marked in the said figure with the letters N F L. And remember, that the letter N always signifieth the vernal equinoctial point, whereto is set the character of Aries. Of the Inequality of the Excentrique, both mean and true. THe mean Inequality of the Excentrique is an arch of the Zodiac, extending according to the succession of the signs, from the line of the Auge of the Excentrique unto the line of the mean moving of the Planet or Epicicle: which Inequality the followers of Alphonsus do call Centrum medium, marked on the left hand of the foresaid figure with the letters F I. But the true Inequality of the Excentrique is an arch of the Zodiac, extending according to the succession of the signs, from the line of the Auge of the Excentrique unto the line of the true moving of the Epicicle; which arch is marked on the left hand in the said figure with the letters F K. What is the equaction of the Excentrique? IT is an arch of the Excentrique, contained betwixt the line of the mean moving and the line of the true moving of the Epicicle, and is marked on both sides of the foresaid figure with the letters I K. What is the Equation of the centre in the Epicicle? IT is an arch of the Epicicle contained betwixt the mean and true Auge of the Epicicle, and is marked on both hands of the said figure with the letters V M. But this arch is no arch, when the centre of the Epicicle is in the Auge of the Excentrique, and it is greatest when the centre of the Epicicle is in any of the two mean longitudes. And you have to note, that the equation of the centre in the Excentrique, and the equation of the centre in the Epicicle are always like. Moreover, whilst the Epicicle descendeth in the one half of the Excentrique from the Auge of the Excentrique, marked with D, towards the opposite Auge thereof marked with E, this equation is taken away from the mean Inequality of the Excentrique, and is added to the mean argument (which is here by and by defined) so as it may make thereby and in that place, as well the equated Inequality of the Excentrique, as the equated argument. But whilst the Epicicle ascendeth in the other half of the Excentrique, it is clean contrary: for when the right line AHV in the foresaid second figure falleth into the two parallels A I and C H M, it maketh the two angles I A H and M H V to be equal. And to the two equal angles do belong two like arches, represented in the said figure by the letters I K, and V M, which arches or equations are not to be added or subtracted both together. But when the one is added, the other is always to be taken away, because the one cleaveth to the end, and the other to the beginning of their circles, tending towards one self part. What is the mean and true argument? THe mean argument is an arch of the Epicicle, contained betwixt the mean Auge thereof, and the body of the Planet, to be counted towards that part whereinto to the Epicicle is moved: which arch is represented in the said second figure by the letters M L. And the true argument is an arch of the Epicicle, contained betwixt the true Auge of the Epicicle and the body of the Planet, marked in the foresaid figure with the letters V L. What is the equation of the Epicicle, or of the argument? IT is an arch of the Zodiac, contained betwixt the line of the true moving of the Epicicle, and the line of the true moving of the Planet, marked in the foresaid second figure with the letters K L: and this arch is no arch when the Planet is either in the true Auge or in the true opposite Auge of the Epicicle. And it is greatest when the Planet is in the line, which being drawn from the centre of the world, toucheth in one point the outside of the Epicicle, which line is marked in the foresaid second figure on the left hand thereof, with the letters A L, and on the right hand, with the letters A I. And note, that when the Planet is in the first half of the Epicicle, descending from the true Auge to the opposite Auge, it addeth this equation to the true moving of the Epicicle, but in the other half of the Epicicle it taketh so much away. But now for the better understanding of the equations both least and greatest of all the three superior Planets, and of all the other terms belonging to the said three Planets, it shall be necessary to set down this other figure here following. ¶ The fourth figure belonging to the Theoriques' of the three upper Planets. THis figure differeth not much from the sixth figure belonging to the Theoric of the Moon before set down, for the outermost circle of this figure signifieth as well here as there the Zodiac, whose centre is marked with the letter A: and the inner blacker circle signifieth the Excentrique, carrying the Epicicle of any of the three upper Planets, whose centre is marked with the letter B: and above that centre is placed the centre of the circle Equant, marked with the letter C. but the circle itself cannot fitly be made here, because it must be equal in every respect to the Excentrique, as hath been said before. And each one of the five little circles, placed upon the Excentrique, doth signify the Epicicle whereto the body of any of the three Planets is fixed. And the 7 half circles making 6 spaces, every space containing ten minutes, as well above as beneath the centre A, do show the proportional minutes, which are partly described before in the sixth figure of the Moon, and shall be more fully again described here. Now, as touching the rest of the letters placed as well within the figure, as round about the same, we come now to show their significations: for the letters E F G H do signify the Excentrique, whose Auge is marked with the letter E, and his opposite Auge with the letter G. A description of the mean longitudes. Moreover, there is a point in the midst betwixt the centre A and the centre B, marked with the letter I, through which point is drawn a right line, marked with the letters F I H, which falling perpendicularly upon the line E A G, crosseth the same in the point I with right angles, and thereby showeth the two mean longitudes in the Excentrique, marked with the letters F H, in which two places the centre of the Epicicle is always equally distant as well from the centre B, as from the centre A. And therefore those two points do show the mean longitudes. And when the centre of the Epicicle cometh to any of those two points, than the greatest equation of the Excentrique of Saturn is 6 degrees, i/30 ii/30 and that of jupiter is 5 degrees, i/14 and that of Mars is 11 degrees, i/6 But when the centre of the Epicicle is in the Auge of the Excentrique, marked with E, than the arch Q R showeth the greatest equation for Saturn to be 5 degrees, i/55 ii/33 and for jupiter 10 degrees, i/30 ii/15 and for Mars 36 degrees, i/54 ii/20 And when the centre of the Epicicle is in the opposite Auge of the Excentrique, marked with G, than the arch QT showeth the greatest equation for Saturn to be 6 degrees, i/38 ii/40 and for jupiter 11 degrees, i/31 ii/30 and for Mars 46 degrees, i/38 ii/15 What be the excesses of the longer and nigher longitudes? BEfore I define what they be, it shall not be amiss to advertise you, that both Ptolomey, Purbachius, and the followers of Alphonsus, in counting or measuring the equations of the Epicicle of the Moon, or of the argument (as they term it) they have regard only to the excess of the longer and shorter diameter of the Auges of the Excentrique, which excess they call the diversity of the diameter; which is plainly described before in the sixth figure belonging to the Theoric of the Moon, and therefore resort thereunto, that you may the better bear it in mind. But in the other Planets they make two excesses, whereof they call the one the excess of the longer longitude, and the other the excess of the nigher longitude. The excess of the longer longitude, is an arch of the Zodiac, showing the equation of the Epicicle, when the centre thereof is in any of the two mean longitudes, marked in the Excentrique on the right hand with the letter H, and on the left hand with the letter F: for then the foresaid arch of the Zodiac is greater than that which showeth the equation of the Epicicle, his centre being in the Auge of the Excentrique, marked with E. But when the centre of the Epicicle is in the opposite Auge of the Excentrique, than the foresaid arch of the Zodiac which is right against the mean longitude, marked with H, is lesser than the arch of the Zodiac, which representeth the equation of the Epicicle, his centre being in the said opposite Auge of the Excentrique, and therefore is called the excess of the nigher longitude. And of these two excesses do rise two sorts of proportional minutes, that is, the longer and the nigher. All which things you shall better understand, by help of the last fourth Figure: in which figure the arch marked with the letters Q R S on the right hand of the said figure is the arch of the Zodiac, representing the equation of the Epicicle when his centre is in the point H, signifying the mean longitude of the Excentrique, which arch is greater than the arch marked with Q R, in the top of the Figure, showing the equation of the Epicicle, when his centre is in the Auge of the Excentrique, marked with E, by so much as that little portion of the Zodiac, marked on the right hand of the figure with the letters R S, doth show, as you may easily try with your Compasses. And the said arch Q R S is lesser than the arch Q T, standing in the lowest part of the figure, whereas the centre of the Epicicle is in the opposite Auge of the Excentrique, marked with the letter G, by so much as the letters ST on the right hand do show, so as in this figure the letters R S on the right hand do show the excess of the longer longitude, and the letters ST on the same hand do show the excess of the nigher longitude: of which two excesses do spring the two kinds of proportional minutes before mentioned, which do serve to show how much every equation of the Epicicle is greater or lesser than another, when the centre of the Epicicle is in any other place of the Excentrique, and is clean out of the Auge or opposite Auge, and also out of the mean longitude of the Excentrique. And as in the sixth figure of the Moon the equations of the Epicicle in every place of the Excentrique (his centre being neither in the Auge nor in the opposite Auge of the Excentrique) is known by the proportional minutes, for that as well the excess of the longest, as the excess of the shortest diameter of the Auges of the Excentrique is each of them there divided into sixty minutes: so here likewise the said proportional minutes are found out by dividing the difference or overplus that is betwixt the diameter of the mean longitude, and the longest diameter of the Auge of the Excentrique into 60 minutes; and also by dividing into 60 minutes the overplus or difference that is betwixt the diameter of the mean longitude and the shortest diameter of the Auges of the Excentrique, as you may plainly perceive by the last fourth figure, wherein as the line A E signifying the longer diameter of the Auges of the Excentrique, exceedeth in length the diameter of the mean longitude, marked on the right hand with A H, and on the left hand with A F, by a third part and somewhat more (which excess or overplus is divided into 60 minutes:) even so the difference or overplus, whereby the diameter A H or A F exceedeth the shorter diameter of the Auges of the Excentrique, marked with the letters A G, is also divided into 60 minutes; of which the first i/60 are called the longer proportional minutes, and the last i/60 are called the nigher proportional minutes, because they are nigher to the centre of the earth. And according as any other right line drawn from A the centre of the world to the centre of the Epicicle, being in any other place of the Excentrique, out of the Auge or opposite Auge of the Excentrique, or out of the mean longitudes, is longer or shorter; so doth the equation of the Epicicle increase or decrease: For as by supposing the centre of the Epicicle to be in the point K of the Excentrique, you shall find the right line A K to be longer than the line A H by 40 minutes; even so the equation of the Epicicle in K, marked with Q S, is lesser than the equation of the Epicicle in the point H, marked also with QUEEN'S S, by 40 of such minutes, as the little arch R S, signifying the excess of the longer longitude, doth contain 60 minutes. Likewise, as the line A L is shorter than the line A H by 40 minutes, even so the equation of the Epicicle, marked with QUEEN'S S (his centre being in L) is greater than the equation of the said Epicicle, marked also with QUEEN'S S, his centre being in the point H, by 40 of such minutes, as the arch S T, signifying the nigher longitude, doth contain 60 minutes. And remember here, that in seeking in this figure to know the length of the line A K by the minutes, you must put the firm foot of your Compass in the centre A, and the movable foot in the point L, and so to draw the movable foot from thence to the line A H Q, upon which line the numbers of the 60 proportional minutes are set down: and to know the length of the line A L, you must fit your Compasses to A L, and then draw the movable foot to the line A G Q, upon which line are also set down the 60 proportional minutes, in like manner as they are upon the line A H Q, saving that in the line A H Q the said 60 minutes are to be counted from H towards Q, and in the line A G Q they proceed upward from Q to G, according as the inferior half circles do show. And after this manner you must deal, to know the length of any other line drawn from the centre A to any other point of the Excentrique, whereinto the centre of the Epicicle chanceth to fall; considering always whether such line be either longer or shorter than the line A H, passing through the point of the mean longitude, to the intent you may know thereby how to apply the length of every line to the right number of the proportional minutes belonging to the same. But you have to note, that neither Copernicus nor the Prutenicall tables do make any more kinds of excesses or proportional minutes, but that only which is plainly declared before in the sixth figure of the Moon. What is the diameter of the Auges in the Epicicle? IT is a right line passing through the centre of the Epicicle, and also through the true Auge and the true opposite Auge of the said Epicicle: which line divideth the plane of the Epicicle into two equal hal●es, whereof the one is called the Oriental half, and the other the Occidental half, hereafter described in the sixth figure. What is the diameter of the mean longitudes in the Epicicle? IT is a right line drawn through the centre of the Epicicle, erected perpendicularly upon the diameter of the true Auges of the said Epicicle next before defined: and when the Planet falleth into this line, it showeth the mean distance that is betwixt the greatest longitude in the Auge of the Epicicle, and the least longitude in the opposite Auge of the said Epicicle, and thereof is called the diameter of the mean longitudes. And this line divideth also the plane of the Epicicle into two halves, that is, the upper half, and the neither half. The upper half is that which is above the diameter of the mean longitudes, and is farthest from the earth: and the lower or neither half is beneath the said diameter, and is nigher to the earth. What is the Oriental and Occidental half of the Epicicle? THe Oriental half is that, which being contained betwixt the Auge and opposite Auge, looketh towards the East: and the other half looking towards the West, is called the Occidental half. And you have to note, that as well in these three Planets, as in the other two Planets next following, that is, Venus and Mercury, the first half of the Epicicle is Oriental, and the later half Occidental: but in the Moon the later half of her Epicicle is Oriental, and the first half thereof is Occidental, For the Epicicle of every one of the foresaid five Planets going from the Auge, in his upper part, according to the succession of the signs, carrieth the Planet first into the Oriental half: but in the Moon it is clean contrary. The fourth Intention, showing the twofold latitude of the three upper Planets, and wherein their latitude differeth from the latitude of the Moon. THe latitude of the Moon is simple, having only respect to the distance of her Excentrique or Deferent, from the Ecliptic line; whose greatest distance from thence, either toward the North or South, is but five degrees, as hath been said before, by reason that the poles of her Excentrique are distant from the poles of the Ecliptic no more but five degrees. But the latitude of the three upper Planets is to be considered two manner of ways: First, according to the distance of any of their excentriques' from the Ecliptic: and secondly, according to the distance of any of their Epicicles from the Excentrique thereof, which two kinds of latitude Purbachius describeth the first in this manner: The first (saith he) chanceth by reason that the plane or superficies of the Excentrique of the Planet declineth from the plane of the Ecliptic in two parts opposite, the greatest distance of such declination remaining always invariable like as in the Moon, and yet the two Nodes or Intersections, that is to say, the node ascendent and descendent, otherwise called the head and tail of the Dragon, are not moved contrary to the succession of the signs (as in the Moon) but according to the moving of the eighth sphere, so as the Auges of the deferents of those Nodes do describe on the North side, parallel circumferences that be equally distant from the Ecliptic: and though such Auges be always septentrional, yet notwithstanding those Auges be not in all the three planets the very points or limits of the greatest latitude of their deferents from the Ecliptic; yea that falleth out only in Mars, the Auge of whose excentrique doth most decline from the Ecliptic to the North; but in Saturn the point or limit of his greatest latitude goeth before the Auge of his excentrique, contrary to the succession of the signs, and is distant from his Auge 50 degrees; and in jupiter such point goeth after the Auge of his excentrique according to the succession of the signs, and is distant from his Auge 20 degrees. All which things you shall more plainly perceive by this figure here following, set down by Reinholdus in his Comment upon Purbacchius. ¶ The fifth figure of the three superior Planets. IN this figure the letter D signifieth the centre of the world, whereupon is drawn a circle signifying the plane of the Ecliptic: and the said point D, representeth also both the poles of the Ecliptic. And upon the point C is drawn another circle, signifying the plane or superficies of the excentrique, marked in the upper part with the letters A B E, inclining as you see towards the plane of the Ecliptic. And because the two planes, that is, the plane of the Excentrique & the plane of the Ecliptic do cross or cut one another in the very centre of the world, marked with D; and because the Auges of the three Planets are all distant from the Ecliptic towards the North; therefore the centres of their Excentriques must needs be also Northerly, and out of the centre of the Ecliptic: so as the centre of the Excentrique for Saturn, is to be found in the line A D, and for Mars, in the line B D, and for jupiter, in the line E D. And the Auge of Saturn is marked with A, and that of Mars with B, and that of jupiter with E. Moreover, the right line, marked with the letters B F C G H, representeth the plane of the greatest circle, passing as well through the poles of the Ecliptic, as also through that right line, which passing through the centre of the world is erected with right angles upon the plane of the excentrique: For this plane of the greatest circle doth divide the arches, as well of the Eccentric, as also of the Ecliptic, two manner of ways: which arches are distinguished in this figure by the two usual characters, signifying the two nodes, otherwise called the head and tail of the Dragon: and either of the two distances, F B, or G H, showeth the greatest declination of the two planes, And finally, the point B is the limit of the North latitude, and G the limit of the South latitude of any of the three Planets. Thus you may perceive, that the Auge of the Excentrique of Mars is always in the North limit, and his opposite Auge in the South limit, but the Auge of jupiters' Excentrique, marked in the former Figure with E, goeth before the North limit B, that is to say, the centre of jupiters' Epicicle cometh to the Auge of his Excentrique, before that it arriveth to the North limit. And finally, the Auge of Saturn his Excentrique, marked in the said figure with A, followeth after the North limit, so as the centre of his Epicicle arriveth to the North limit, before it cometh to the Auge of his Excentrique. And the followers of Alphonsus do make the Node ascendent of Mars to be at this day in the sixteenth degree of Taurus, and his Node descendent to be in the sixteenth degree of Scorpio: and the Node ascendent of jupiter to be in the 14 degree of Cancer, and his Node descendent to be in the 14 degree of Capricorn, and his North limit to be in the 14 degree of Libra. And the Node ascendent of Saturn to be in the 24 degree of Cancer, and his Node descendent to be in the 24 degree of Capricorn, because his North limit is in the 24 degree of Libra, so as there is no great difference betwixt Saturn and jupiter, touching their limits. And partly hereby, and partly by that which followeth hereafter, it shall manifestly appear that Saturn whilst he passeth through the one half of the Zodiac, counting from the 24 degree of Cancer unto the 24 degree of Capricorn, he hath always North latitude; and whilst he passeth through the other half of the Zodiac, he hath always South latitude. Wherefore considering that he maketh his whole revolution in thirty years, he hath continually during the space of 15 years North latitude, and during the other 15 years South latitude: and the like is to be judged of jupiter and Mars, according to the time of their entire revolutions; for jupiter maketh his revolution in 12 years, and Mars in 2 years. But Mestlyn following Copernicus, setteth down the places of the North limit and Node ascendent of every one of the three upper Planets in this manner, that is to say, the North limit of ♄ to be in these days in the 9 degree, i10° of m, and that of ♃ to be in the 26 degree, i40° of ♎, and that of ♂ to be in the 28 degree, i24° of ♎ Again, the node ascendent of ♄ to be in the 9 degree, i10° of ♌, and that of ♃ to be in the 26 degree, i40° of 69, and that of ♂ to be in the 28 degree, i24° of ♉. And as for the South limit and the node descendent of every Planet, each one doth occupy in the Zodiac such degree and minutes as is opposite to the place of the North limit, and of the node ascendent of every one of the said Planets before set down. And Mestlyn saith, That as the greatest latitude of the Moon either North or South from the Ecliptic, is only five degrees, so he appointeth to the greatest latitude of the Excentrique of ♄ from the Ecliptic but 2 degrees, i30° and to that of ♃ 1 degree, i30° and to that of ♂ 1 degree, i0° Now to show the second manner of latitude belonging to the three upper Planets, caused by the inclining of the true Auge of the Epicicle from the Excentrique, I mind therein to follow Mes●lyn, who affirmeth that kind of latitude to be twofold, whereof the one is called Inclination, and the other Reflection: neither of them being fixed, but mutable, and yet proportionable to the period of their Excentriques, for the better understanding whereof he setteth down this figure following. ¶ The sixth figure belonging to the three upper Planets. IN which figure the centre A is the centre of the world, whereupon is drawn the outermost circle, signifying the plane of the Zodiac, marked with the letters B C D E, passing through the poles of the Ecliptic, marked with the letters C E. Then upon the centre F is drawn another circle, signifying the plane of the Excentrique, marked with the letters G H I K, passing through the poles of the Excentrique, marked with the letters M O, and also through the North limit, marked with L, and through the South limit, marked with N; and the two little circles placed upon the Excentrique, each of them signifieth the Epicicle. And you have to note, that the plane of the motion of the said Excentrique is signified here by the right line, marked with the letters L F N, which cutteth the Ecliptic in the centre A; so as when the centre of the Epicicle is in L, it hath then his greatest North latitude, likewise being in N, it hath his greatest South latitude: and by this Figure you may perceive, that the one pole of the Excentrique is more distant from the pole of the Ecliptic than the other, for O is more distant from K, than H from M. The signification of the rest of the letters wherewith the Epicicles are marked, shall be declared hereafter. In the mean time we will speak first of the latitude, called the Inclination of the Epicicle, in Greek En●lysis, which causeth the diameter of the Auges of the Epicicle to decline on both sides of the plane of the Excentrique, that is to say, as well inwardly as outwardly, in manner and form following: for when the centre of the Epicicle is in any of the two Nodes, the diameter of the Auges doth not decline at all either from the Excentrique orfrom the plane of the Ecliptic, because than it falleth just into their mutual fection. But when the centre of the Epicicle departeth from any of the Nodes, then in the upper half of the Excentrique, containing the Auge of the Epicicle, the foresaid diameter of the Auges declineth inwardly from the Excentrique towards the plane of the Ecliptic, and yet arriveth not to the same. But when the centre of the Epicicle is in the neither half of the Excentrique, containing the opposite Auge of the Epicicle, the diameter of the Auges declineth outwardly from the Eccentric towards the Ecliptic, and yet arriveth not to the same. And the greatest declination of this diameter is when the centre of the Epicicle is in any of the limits; and yet such declination is no where so great, as that being out of the Nodes, it can reach unto the Ecliptic: and this declination maketh his revolution upon the diameter of the mean longitudes. The most part of which things you may see plainly set forth in the sixth figure before described, in which both the Epicicles are marked with the letters P Q R, whereof P signifieth in either of the Epicicles the Auge, and R signifieth the opposite Auge of the Epicicle, and the arch P Q signifieth the greatest Inclination of the diameter of those Auges to the Excentrique. So as when the centre of the Epicicle is in the North limit marked with L, the foresaid Auge P declineth inwardly from the plane of the Excentrique towards the Ecliptic, and R the opposite Auge fleeth outwardly from the Ecliptic. But when the centre of the Epicicle is in the South limit, marked with N, than the Auge P being on the other side of the Excentrique, declineth again towards the Ecliptic, and R the opposite Auge occupieth the opposite place to P. And you have to understand, that the greatest declination here signified by the arch P Q for ♄ containeth 4 degrees, i30° and for ♃ 2 degrees, i30° and for ♂ 2 degrees, i15° And to the intent that you may the better conceive all the variety of the foresaid Inclination, Mestlyn setteth down this other Figure here next following, which also serveth to demonstrat the second kind of latitude, called Reflection, in Greek Loxasis, hereafter by him plainly described. ¶ The seventh figure belonging to the Theoric of the three upper Planets. IN this figure upon the centre F, signifying the centre of the world, is drawn a great circle, which signifieth the whole sphere of the Planet, whose poles are marked with D E, whereof D is the North pole, and E the South pole. And within this circle are drawn two other obliqne circles of shape, oval; whereof the outermost marked with the letters A B C, signifieth the Ecliptic: and the inward circle signifieth the Excentrique, whereon are placed four Epicicles, the highest whereof hath his centre marked with G, signifying here the North limit; and the centre of the lowest Epicicle is marked with N, signifying the South limit; and the centre of the Epicicle on your right hand is marked with M, signifying the Node ascendent; and the centre of the Epicicle on your left hand is marked with O, signifying the Node descendent. Moreover, every Epicicle is crossed with two diameters, whereof that which is marked with H K, doth signify in every Epicicle the line of the Auges of the Epicicle, that is to say, H the Auge, and K the opposite Auge; and the other diameter marked with I L, signifieth the line of the mean longitudes. Wherefore whensoever the centre of the Epicicle is in the Node ascendent, marked with M, than there is no Inclination of the diameter of the Auges, because it falleth into the common Intersection, as well of the Excentrique as of the Ecliptic: but the more that the diameter of the Auges departeth from thence towards the North limit, the more it falleth upon the line of the mean longitudes, marked with I L, insomuch, as when it arriveth to the North limit, marked with G, the inclination than is greatest, and the line of the Auge falleth directly and perpendicularly upon the line of the mean longitudes, and from thence the inclination decreaseth, until the diameter of the Auges arriveth to the Node descendent, marked with O, in which point it hath again no declination. But departing from thence towards N, the inclination of this diameter goeth unto the other side of the Excentrique. For as the Auge of the Epicicle passing first from M through G into O, declineth from the plane of the Excentrique towards E the South pole: even so departing from O, and passing through N to M, it declineth towards D the North pole: and so the Auge H is found again to incline to the Ecliptic: and K the opposite Auge to flee from the same until it hath his greatest declination, which is in the point N, and from thence it returneth to M, & there again hath no declination at all. Of the second latitude, caused by the Epicicle, called the Reflection. BY this Reflection the diameter of the mean longitudes of the Epicicle, marked in the former seventh figure with the letters I L, reflecteth or turneth backward, as well within as without the plane of the Excentrique, saving that when the centre of the Epicicle is in any of the limits, for then this diameter falleth just and wholly upon the plane of the Excentrique, but when the centre of the Epicicle departeth from any of the limits, than the Occidental half of this diameter turneth inwardly within the plane, as well of the Excentrique as of the Ecliptic; and the Oriental half of the said diameter turneth outwardly, that is, on the outside of both the said planes. What the Occidental and Oriental half is, hath been described before in the third Intention. And note, that the greatest reflection of this diameter chanceth when the centre of the Epicicle is in any of the Nodes, which greatest reflection for Saturn, is 2 degrees, i30° and for jupiter one degree, i30° and for Mars one degree, i0° And this greatest reflection is like unto the greatest obliquity or latitude of the Excentrique from the Ecliptic, as is before set down. Moreover, you have to note, that as in the former kind of latitude, called Inclination, the diameter of the Auges of the Epicicle maketh his revolution upon the diameter of the mean longitudes; so in this second kind of latitude called Reflection, the diameter of the mean longitudes maketh his revolution upon the diameter of the Auges. And for the better understanding of that which hath been said here touching the reflection of the diameter of the mean longitudes, mark well the former seventh figure, in which you may see, that when the centre of the Epicicle is in the North limit, marked with G, the diameter of the mean longitudes, marked with I L, lieth full upon the plane of the Excentrique, without any reflection. But when the centre departeth from thence, than the Occidental half of the said diameter, contained betwixt the centre and the letter L, bendeth inwardly towards the South pole, and this Occidental half still remaineth within the Ecliptic and within the Excentrique, until the centre of the Epicicle falleth into the Node descendent, marked with O, in which place the said diameter hath his greatest reflection, and even there is united to the plane of the Ecliptic. And the centre of the Epicicle departing from thence the said Occidental half, remaining out of the Ecliptic and out of the Excentrique, approacheth again to the plane of the Excentrique, and is united to the same in the point N: but in the other Oriental half it happeneth clean contrary. What conclusions do follow upon these two kinds of latitudes, called the Inclination and Reflection. 1. THese seven here following: for first, whensoever the centre of the Epicicle is in any of the Nodes, than the whole plane of the Epicicle falleth into the plane of the Ecliptic, for then the diameter of the Auges of the Epicicle is also there, having no Inclination at all. And then there is also the diameter of the mean longitudes of the Epicicle, whose obliquite from the Excentrique, is always so much as is the obliquite of the Excentrique from the Ecliptic. But the Epicicle is never united to the plane of the Excentrique, because neither of the foresaid diameters do decline both at once from the plane of the Excentrique. 2. Secondly, the centre of the Epicicle being in any of the Nodes, the axle-tree of the Epicicle standeth perpendicularly upon the axle-tree of the Ecliptic, from which it is then equally distant. But it is not equally distant to the axle-tree of the Excentrique. 3. Thirdly, hereof may be gathered, that the planes of the Excentriques and of the Epicicles do cut one another always in a divers diameter, for in the two nodes such section is made upon the diameter of the Auges, but in the two limits such section is made upon the diameter of the mean longitudes: and in all other mean places betwixt the said nodes and limits, such section chanceth sometime in one place, & sometime in another. 4. Fourthly, the line of the mutual section, whereas the Epicicle and the Excentrique do cut one another, doth wander through the plane of the Epicicle in such sort, as the one half of the Epicicle looking up towards the North limit, declineth from the plane of the Excentrique towards the South. And the other half approaching nigher to the South limit, declineth from the Excentrique towards the North, as you may plainly perceive by the former seventh figure, in which, that half of the Epicicle which looketh towards the North limit, marked with G, is the upper half of the Epicicle, marked with the letters L H I: but when that half cometh unto the Node descendent, marked with O, than it is called the Occidental half, marked with the letters K L H: and when it is come to the South limit, marked with N, than it is called the inferior or neither half, marked with the letters I K L: But when that half arriveth to the Node ascendent, marked with M, than it is called the Oriental half, and is marked with the letters H I K. And the other half of the Epicicle declining from the plane of the Excentrique towards the North pole, looketh towards the South limit. 5. Fifthly, when the Planet is in the upper half of the Epicicle, in which the Auge is, than he always walketh betwixt the Ecliptic and the Excentrique: but when he is in the neither half, he goeth clean without them both. 6. Sixtly, the diameter of the Auge being in the upper half of the Epicicle, and out of the Nodes, declineth towards the Ecliptic, and being again in the neither half, departeth from the Ecliptic towards that part whereunto the Excentrique declineth. Hereof it must needs follow, that the Planet whilst he is in the Oriental half, increaseth his latitude, and in the Occidental half deminisheth the same, but yet so, as his latitude from the Node ascendent to the Node descendent, is always Northerly, and from thence to the node ascendent it is always Southerly. What be the greatest latitudes of the three Planets, as well in the North and South limit, as also in the North and South true Auges of the Epicicle? ACcording to the tables of Alpho●sus, when the Planet is in the North limit of the Excentrique, and also in the North true Auge of the Epicicle, than the greatest North latitude for Saturn is 2 degrees, i3. for jupiter 1 degree, i5. and for Mars only i5. And when the Planet is in the North limit of the Excentrique, & therewith in the North opposite Auge of the Epicicle, than the greatest North latitude for Saturn is 3 degrees, i3. for jupiter 2 degrees, i5. and for Mars 4 degrees, i21s. But when the Planet is in the South limit of the Excentrique, and therewith in the South true Auge of the Epicicle, than the greatest South latitude for Saturn is two degrees, i5. for jupiter 1 degree, i4. and for Mars only i2. And if the Planet be in the South limit of the Excentrique, and therewith in the South opposite Auge of the Epicicle, than the greatest South latitude for Saturn is 3 degrees, i1s. for jupiter 2 degrees, i8. and for Mars 7 degrees, i30. But betwixt Alphonsus his tables and the Prutenicall tables there is some difference, for the Prutenicall tables when the Planet is in the North Auge of the Epicicle, do allow for the greatest North latitude of Saturn 2 degrees, i3. for jupiter 1 degree, i6. and for Mars i5. Again, the Planet being in the North opposite Auge, they allow for the greatest North latitude of Saturn 3 degrees, i2. for jupiter 2 degrees, i4. and for Mars 4 degrees, i/30. and when the Planet is in the South true Auge of the Epicicle, they allow for the greatest South latitude of Saturn 2 degrees, i2. for jupiter 1 degree, i5. and for Mars i4. Again, when the Planet is in the South opposite Auge of the Epicicle, they allow for the greatest South latitude of Saturn 3 degrees, i5. for jupiter 2 degrees, i7. and for Mars 6 degrees, i50. The seventh Conclusion. THe diameter of the mean longitudes, and the diameter of the mutual sections of the Epicicle and of the Excentrique, are always in a manner equally distant to the diameter of the section of the Excentrique and of the Ecliptic, and thereby are equally distant also, in a manner to the Ecliptic itself. I say here in a manner, because that neither of the foresaid diameters being out of the limits or nodes, are justly equally distant from the Ecliptic, yet the difference is so small, as it is scant sensible, and therefore may be taken for one simple latitude, whereby the plane of the Epicicle, which in the Nodes is united to the Ecliptic, maketh the diameter, which is parallel to the line drawn through both the limits to decline upon that diameter, which is a parallel to a right line drawn through both the Nodes, which the former seventh figure plainly showeth: for when the Epicicle is either in M or in O, than the diameter of Inclination, marked with I L, is parallel to the line G F N, drawn through the two limits, and also through the centre F. But when the Epicicle is in G or N, than the diameter HK, looking upward, is all one with the line G F N. Again, the Epicicle being in M and O, such declination is made upon the overthwart diameter H K, which then is all one with the line drawn through the Nodes, marked with the letters O F M: but the Epicicle being in G or N, the same Inclination is made upon the diameter I L, being parallel to the line O F M, so as in the mean places that are betwixt the limits and the Nodes, the inclining diameter looketh upward, and that diameter whereupon the Inclination is made, is always transverse or overthwart. From hence the Astronomers do calculate the latitudes of these three Planets, having regard only to the position or placing of the Epicicles in the two limits, and by the proportional minutes do find out the equation in every other place or position, according as the said Position is more or less distant from the limits, or from the Ecliptic. ¶ The Theoric of Venus. THe first Intention belonging to the Theoric of Venus, showeth of how many orbs her Theoric consisteth, which are in number five, like unto the Theoric of any of the three upper Planets, before described, viz. the Excentrique, the two deferents of the Auges of the said Excentrique, the Epicicle, and the circle Equant; all which are necessarily used in this Theoric for the self-same causes that are before declared in the first Intention belonging to the Theoric of the three upper Planets, the first figure whereof by certain letters plainly showeth all the orbs belonging to this Theoric of Venus. Wherefore I wish you to resort thereunto, thinking it superfluous here again to describe the same. The second Intention, showing the divers motions of the orbs whereof this Theoric consisteth, and upon what centres, axletrees, and poles, they make their revolutions, and in what time. First s●ew how and in what manner the Excentrique of Venus is moved? THe Excentrique of Venus is moved according to the succession of the signs, upon his own axle-tree and poles, together with the poles of the two deferents of the Auges, and that equally about the centre of the circle Equant, making his full revolution in the space of one year precisely together with the Excentrique of the Sun. Where is the centre of the circle Equant placed, about which the Excentrique of Ve●●s maketh his regular motion? THe centre of the circle Equant is placed in the line of the Auge beyond the centre of the Excentrique, being double so much distant from the centre of the world, as is the excentricity of the Excentrique: & hereof it followeth, that the orb excentrique doth carry the Epicicle more slowly about the point Auge, and more swiftly about the opposite Auge. How are the deferents of the Auges moved? THey are moved according to the succession of the signs upon their own poles, about the centre of the world, as well beyond as on this side of the vagrant poles of the Ecliptic, by virtue of the eighth sphere, making their revolution according to the account of Alphonsus, in 49000 years. And by this motion the Auge and opposite Auge of the Excentrique are by little and little put forward. And this unstableness of the poles of the two deferents causeth also the poles of the Excentrique to be unstable and to wander on either side. Ptolomey in his time found the Auge of Venus to be in the 25 degree of Taurus, and he thought that it crept forward one degree in a 100 years, even as the sphere of the fixed stars doth. But according to the later observations of Copernicus, the Auge of Venus in these days is found to be in the 16 degree and i20. of ♊. Now as touching the moving of the Auge of Venus, Copernicus agreeth with the ancient Astronomers, affirming, that it turneth about together with the fixed stars, always keeping a firm and fixed place under the Orb of the fixed stars. But as touching the time of the whole revolution of the said Auge, Ptolomey affirmeth it to be 36000 years, and the followers of Alphonsus do make the same to be 49000 years. Copernicus affirmeth that time of revolution to be no more but 25810 Egyptian years. Neither is the error of the Alphonsines here to be kept silent, who do not let to affirm, That the Auge of Venus and that of the Sun, are continually joined together, and that either of them in Ptolemies time, was in the 13 degree, i30. of ♊, which is clean contrary to his own observation. By which their false calculation, the Auge of Venus and of the Sun should be in these days in the 2 degree of Cancer, whereas indeed it is in the 16 degree, i●0. of ♊. How and in what manner is the Epi●icle of Venus moved? IT is moved in the upper part thereof according to the succession of the signs, and in the neither part contrary to the succession of the signs, upon his own movable axle-tree, standing slopewise upon the plane of his Excentrique, and is equally moved from his mean Auge, making his whole revolution almost in 19 months. And his daily moving is i/36 ii/59° iii/28° iiii/0· v/7· so as he maketh one period in 583 days, that is to say, in one year, 7 months, 8 days, 22 hours, i/10 ii/38° iii/31° How is the mean Auge of the Epicicle described? EVen as it is in the Epicicles of the three upper Planets, by help of a right line, being drawn from the centre of the Equant through the centre of the Epicicle to the circumference thereof. And you have to note, that all the conclusions belonging to the moving of this Epicicle, are like and all one with those that are gathered out of the moving of the Epicicles of the three upper Planets, before set down. What harmony is betwixt the movings of Venus, and of the Sun? THe periodical moving of her Excentrique is like unto that of the Excentrique of the Sun; with whose Excentrique, her Excentrique is exactly carried about. And the Alphonsines do not let to affirm, That both their Auges are continually joined together, contrary to the observation of Ptolomey, and of all others, as hath been said before. What conclusions do follow of this harmony? THese here following: for first the Sun and Venus in their mean moving are always joined together: and hereof it followeth, that they both must needs have one self line of mean moving, whereby their mean moving is bounded. And this line is a parallel as well to the right line which is drawn from the centre of the Sun his Excentrique to the centre of his body, as also to that right line which is drawn from the centre of Venus her Equant to the centre of her Epicicle; whereby it appeareth, that Venus can stray no further from the Sun, than the greatness of her Epicicle will suffer her. And hereto may be added, that the excentricity of the Excentrique of the Sun and that of the equant of Venus are like, for in Ptolemies time they were both like: And though that Copernicus found either of them in our time to be decreased, yet the equations of their Excentriques' cannot much differ, but be equal. Show the dimension of the Orbs belonging to the sphere of Venus. AS the semidiameter of the Excentrique of Venus containeth 60 parts or degrees, even so of the like degrees Ptolomey saith, that the excentricity of the said Excentrique containeth 1 degree, and i/15. and that the excentricity of her Equant containeth 2 degrees, and i/30. like to that of the Sun: and that the semidiameter of her Epicicle containeth 43 degrees, and i/10. and hereof it appeareth, that the least altitude of Venus from the earth is 15 degrees, i/35. and her greatest altitude is 104 degrees, i/25. But Copernicus saith, That in these days the excentricity of her Equant is no more but 2 degrees, i6. so as by that means the excentricity of the Excentrique should be no more but i/51. like to that of the Sun, being also diminished as he saith, in his particular propositions. The third Intention, describing all such points, lines, arches, semicircles, and such like things as are needful to be known for the calculating of the movings of Venus. IN this Theoric all such things are described in like manner as they be in the Theoric of the three upper Planets, and therefore resort to the third Intention of their Theoric before set down: but yet the line of the mean moving of Venus is all one with that of the Sun, and both their mean movings are also like and the self same. And the greatest equation of Venus her Excentrique, is according to the tables of Alphonsus 2 degrees i10° and according to the Prutenicall tables it is no more but 2 degrees, i17° And the greatest equation of her argument (the centre of her Epicicle being in the Auge of the said Excentrique) is according to the tables of Alphonsus 44 degrees, i44° but according to the Prutenicall tables it is 45 degrees, i10° ii30° But when the centre of her Epicicle is in the opposite Auge of her Excentrique, than the greatest equation of her argument according to Alphonsus his tables, is 47 degrees, i11° and according to the Prutenicall tables 46 degrees, i5●° ii/30 The fourth Intention, showing the moving of Venus according to latitude. Sigh the varieties of Venus her latitudes are like in all respects unto those of Mercury, I leave to speak thereof, until I come to treat of the motion of Mercury according to his latitudes, and so I end with Venus. ¶ The Theoric of Mercury. The first Intention belonging to the Theoric of Mercury, showing of what and how many orbs his Theoric consisteth. THis Theoric consisteth of seven Orbs, that is, the Excentrique, the two deferents, carrying the Auge of the Equant, the excentor of the Excentrique, the Epicicle, the circle Equant, and the circle of the Nodes, as this figure showeth. ¶ The first figure belonging to the Theoric of Mercury. IN which figure the letter A signifieth the centre of the world, and B the centre of the Excentrique, and C signifieth the Orb Excentrique, which is a white orb: and the two black orbs, marked with the letters D E, are the two deferents of the Auge of the Excentrique, and the letter F signifieth the centre of the Epicicle, in whose circumference the star of Mercury is turned about: and the letter G signifieth the circle Equant, whose centre is marked with the letter H, in the line of the Auge, a little above the centre A. And B H is the diameter of the little circle, which little circle is almost in the midst of the foresaid first figure, and the centre of that little circle is marked with the letter I, in the circumference of which little circle is carried about the centre of the Excentrique, marked with B. And the letter I is also the centre of the Orb called Excentrus excentri, which indeed are two orbs going close together, marked with the letters L and K, and are shadowed with little lines; and these two orbs do contain within the compass thereof the whole orb Excentrique, which carrieth the Epicicle of Mercury. And the outermost circle of all, marked with M, signifieth here the deferent of the nodes. Wherefore is the excentor of the Excentrique added to the sphere of Mercury? BEcause he hath a peculiar variety in his moving, not common to the other Planets, for his equations in departing from the Sun, are found to be least but once, and to be greatest twice, as though he ascended but once to the Auge, and descended twice to the opposite Auge: which things are salved by adding this orb to his Theoric. And all the rest of the orbs are placed in this Theoric for the self-same causes that are before declared. How and in what manner is the Excentrique of Mercury moved? IT is moved in like manner as is the Excentrique of Venus, according to the succession of the signs, upon his own axle-tree and proper poles, vagrant together with the poles of the deferents of the Auges, and that equally about the centre of the circle Equant, making one period in the space of one year precisely together with the Excentrique of the Sun. Where is the centre of Mercury his circle Equant to be found, about the which his Excentrique goeth regularly? THe centre of Mercury his Equant is in the line of the mean Auge, in the very midst betwixt the centre of the world and the centre of that orb which is called the excentor of the Excentrique: for it occupieth the lowest part of the little circle, described by the centre of the Excentrique, and this centre of the Equant is marked in the former figure with the letter H. How many Auges do belong to the Excentrique of Mercury? TWo, that is, the true Auge and the mean Auge. The true Auge is in the Excentrique, described by a right line drawn from the centre of the world through the centre of the Excentrique: and this Auge by reason that the centre of the Excentrique goeth round about the little circle, is not stable, nor keepeth always one place. But the mean Auge belonging as well to the Excentrique as also to the circle Equant, is described by a right line, drawn from the centre of the world through the centre of the Excentrique, and also through the centre of the Equant, both which centres are in one self line. And this mean Auge is the rule of the true Auge, because it remaineth fixed under the deferents of the Auges. And therefore these two deferents of the Auges are also said to carry about this Auge of the Equant. What is to be gathered hereof? THat the Excentrique of Mercury, like as that of the Moon, is swifter in his upper part towards the Auge, than in his neither part: for there the centre of the Equant approacheth nigher unto the opposite Auge, than to the Auge. How are the deferents moved, that do carry the Auge of the Equant, otherwise called the mean Auge? THey are moved according to the succession of the signs, about the centre of the world, upon their proper poles, both on this side and beyond the vagrant poles of the Ecliptic, by virtue of the eight heaven, making their revolution together with that heaven according to the Alphonsynes doctrine, in 49000. years: and by this moving the Auge and opposite Auge of the Equant are put forward. And this instability of the poles of the deferents, do also make the poles of either Excentrique to wander on both sides of the Ecliptic. Ptolomey in his time found the Auge of Mercury's Equant to be in the 10 degree of Libra, thinking that according to the observations of the former times, the said Auge, together with the sphere of the fixed stars, went but one degree in a hundred years. But according to Copernicus his observations, the said Auge is found to be in the beginning of Sagittarius: Whereby he gathereth, That the said Auge under the sphere of the fixed stars, maketh one degree in 63 years (so as the motion of that Auge is equal:) and according to these observations, it maketh his whole revolution under the Orb of the fixed stars, in 22405 Egyptian years, but under the Zodiac it maketh his period in 11995 Egyptian years, which lacketh but five years of 12000 Egyptian years. And the tables of Alphonsus' clean contrary to the manifold observations of Ptolomey do make the Auge of Mercury to have been in his time in the 12 degree i40° of Libra, according to which account, it ought to be in these days in the first degree and i12° of Scorpio. How is the excentor of the Excentrique moved? IT is equally moved contrary to the succession of the signs, about his own centre, which is also the centre of the little circle, and upon his own axle-tree and proper poles vagrant, together with the poles of the two deferents that do carry the Auge of the Equant: and it maketh his period in the space of one year, in which time the Excentrique also goeth once about the line of the Auge. And you have to note, that the excentor of the Excentrique, as the Excentrique itself, do both return in like time to the line of the Auge, that is to say, the excentor contrary to the succession of the signs, and the Excentrique according to the succession of the signs, both I say in the space of 365 days, 6 hours, i33° ii8° and iii35° What conclusions do follow of the moving of this Orb? diverse, but specially these three here following. 1. First, that the centre of the Excentrique is carried about the circumference of the little circle. 2. Secondly, that the excentricity of the Excentrique is sometime changed, for many times it is threefold so much as is the excentricity of the Equant, and specially when the centre of the Excentrique is in the top of the little circle; but when the centre of the Excentrique is in the lowest part of the little circle, than the excentricity of the Eccentric is equal to the excentricity of the equant. 3. Thirdly, that the Auge and opposite Auge of the Excentrique is turned about the Auge & opposite Auge of the Equant, as well contrary as also according to the succession of the signs, and yet doth never ex●eed his bounds, that is to say, the twelfth part of the Zodiac. Now for the better understanding of this which hath been and shall be said hereafter, all those that do write of the Theoriques' do set down this figure here following. ¶ The second figure belonging to the Theoric of Mercury. THis figure as you see consisteth of divers circles, some greater, some lesser; and of divers right lines, some longer, some shorter: and of the circular lines there is one that hath a shape Ovale, like to an egg; and there be two others, the one like to a half Moon, and the other like to an Oyster shell or Cockle shell: all which things, whereto they serve and what they signify, shall be here declared by help of the letters therein contained: for the double, round, and greatest circle being divided into twelve equal parts, marked with Arithmetical figures, signifieth the circle Equant, whose Auge is marked above with the letter A, and his opposite Auge being beneath, is marked with the letter B, and the line A B is the line of the Auges, which passeth through these three centres, that is, the centre of the world marked with the letter C, the centre of the Equant marked with the letter D, and the centre of the little middle circle marked with the letter E, which little circle is made by the turning of the centre of the Excentrique about the centre E, and therefore when the centre of the Excentrique cometh to the very top of the little circle, marked with the letter F, then is his excentricity three times as much as is the excentricity of the equant, which lieth betwixt D and C, for Ptolomey found the right line D C to be equal unto the semidiameter of the said little circle. But when the centre of the Excentrique falleth down from F to D, his excentricity is least of all, and there the Excentrique is also united to the Equant itself, and the Auge also of the Excentrique falleth into the line A B: but if the centre of the Excentrique doth fall from that line into any other part of the circumference of the said little circle, than his Auge doth wander either into the West part going contrary to the succession of the signs, or else into the East part, going according to the succession of the signs; as suppose the centre of the Excentrique to be in the point marked with P in the little middle circle on the right hand, than his Auge will be in G, and his opposite Auge in L: and if his centre be in O, than his Auge shall be in I, and his opposite Auge in M: and if his centre be in R, than his Auge will be in S, and his opposite Auge in T: but if his centre be in V, than his Auge will be in X, and his opposite Auge in Y: so likewise if his centre be in Z, his Auge will be in a, and his opposite Auge in d: and if his centre be in C, than his Auge will be in B, and his opposite Auge in E. And the outermost bounds of the wander of the Auges are the two letters G and I: and the bounds of the wander of the opposite Auges are the two letters L and M, which bounds do limit these four angles, that is, G C A, I C A, L C B, and M C B. To every one of which angel's in the circular concentrique doth answer one whole sign of the Zodiac, which Mestelyn doth prove by certain propositions of E●clides first book, which for brevity I here omit. You have also to note, that the foresaid Auge describeth the upper circle, made in a manner like a half Moon, marked with the letters N S G X A B I a: and the opposite Auge describeth the neither circle, made like an Oyster shell, marked with the letters Q T L Y B e M d, and upon the long Ovale circle are placed two little circles, of each hand one, signifying the Epicicle of Mercury, whose centres are marked with the letters K and H: for the centre of his Epicicle describeth the said Ovale figure, but not altogether like unto the Ovale figure of the Moon, as shall be showed hereafter. In the mean time you have to note, that when the centre of the Excentrique is in the top of the little circle, marked with F, than the Epicicle is furthest distant from the earth, because he is then in the Auge. But when the Epicicle is come down in the Ovale figure unto the point H, and the centre of the Excentrique is also come down in the little circle unto the point P, having made a third part of that circle, even as the Epicicle hath made a third part of the Equant, than the Epicicle is nighest unto the earth. But when the centre of the Excentrique is come down to the point D, and the Epicicle is come to the opposite Auge, marked with B, than he is more distant from the earth, than when he was in the point H, the demonstration whereof I here omit: and the Epicicle being come to the opposite Auge, hath then passed through the whole excentor of the Excentrique, and hath made one period, and doth the like in the other half: whereby you may gather first, that the centre of the Epicicle in making one period doth pass twice through the excentor of the Excentrique: secondly, that the said centre of the Epicicle in making one revolution, is but once in the Auge of the Excentrique, at which time he is most distant from the earth. But being in the very opposite Auge, he is not so nigh unto the earth, as when he is in the other two points before mentioned, each of which points is distant 120 degrees from the Auge of the Equant, and in those points is nearest to the earth. Thirdly, that the centre of the Epicicle, by these manifold motions, describeth the said Ovale figure, which notwithstanding is not like in many respects unto the Ovale figure of the Moon; how and wherefore, we come now to show. A comparison showing in what things the Moon and Mercury by their motions do agree or differ, in describing their Ovale figures: and first, they agree in these things following. FOr look how much the Excentrique of either Planet doth proceed according to the succession of the signs, that is to say, the Excentrique of the Moon from the line of the mean moving of the Sun, and the Excentrique of Mercury from the line of the mean Auge; so much do the orbs of unequal thickness revert contrary to the succession of the signs, that is to say, the two deferents carrying the Auge of the Moon, and the excentor of the Excentrique of Mercury do make like circuits as well to the foresaid lines, as to their opposite parts. Secondly, the centre of either of their Excentriques by the going backward of the said orbs, describeth about the centres of the same orbs a little circle. Thirdly, whilst the Excentrique maketh one period to the foresaid lines, the centre of the Epicicle of either Planet goeth twice about the foresaid orbs. Wherefore it followeth of necessity, that the Epicicle in every revolution is twice nighest, and twice furthest off from the centre of the little circle: and by this means, the Epicicle of either Planet in making one period describeth with his centre the figure Ovale. Thus much touching their likeness or agreement in describing the figure Ovale of either Planet. Now we will show you wherein they disagree in making the figure Ovale. The centre of the little circle in the sphere of the Moon, is also the centre of the world; but in the sphere of Mercury all that little circle is excentrical, because that in Mercury it is described by an orb which is excentrical, and in the sphere of the Moon it is described by those orbs, which in some respect are concentrical. Wherefore the Auge of the Moon doth wander equally throughout the whole Zodiac: but the Auge of Mercury is turned and writhed on each side of his mean Auge: and by his turning and wandering, now on this side, and now on that side, both the Auge and also the opposite Auge do each of them make a figure that wrieth in and out, and that which the Auge maketh, is marked in the former figure with the letters N S G X A b I a, almost like to a half Moon; and that which the opposite Auge maketh, is marked with these letters, Q T L Y B e M d, much like to an Oyster shell, as hath been said before. Whereof it followeth, that the Auge of the Moon is only moved contrary to the succession of the signs. But the Auges of Mercury doth sometime proceed by a reciprocke moving according to the succession of the signs. Moreover, the excentricity of the Moon in a whole period is never changed, but abideth always one and the same: but the excentricity of Mercury is continually changed. Again, the Moon in every her revolution falleth twice into the Auge, and twice into the opposite Auge, by means whereof she is twice furthest from the earth, and twice nighest to the same; and the limits of those distances is a just quarter of a circle one from another, which is 90 degrees. But Mercury falleth neither into the Auge nor opposite Auge but once only, and he is furthest distant from the earth when he is in the Auge. But he is nighest to the earth twice (not when he is in the opposite Auge) but in two places, each of them being distant on either side from the Auge the third part of a circle, which is 120 degrees. Finally, the Epicicle of the Moon describeth a figure, more like to a figure Lenticular, than to a figure Ovale. And the Epicicle of Mercury describeth a figure more Ovale than otherwise, the cause whereof is, for that the centre of the Moons Equant (about which her Excentrique maketh his regular motion) is also the centre of the little circle. But the centre of Mercury's Equant is resident in the lowest part of the said little circle, notwithstanding each figure is commonly called an Ovale figure. How and in what manner is the Epicicle of Mercury moved? THe Epicicle of Mercury in the upper part is moved according to the succession of the signs, and in the neither part contrary to the succession of the signs, about his own movable axle-tree, standing slopewise upon the plane of the Excentrique. And it is equally moved from the mean Auge, making his revolution almost in 4 months, and his daily moving containeth 3 degrees, i6° ii●4 iii14° iiii5° u16° so as it maketh one period in 115 days, 21 hours, i●° ii20° iii54° How is the mean Auge of this Epicicle described? IT is described by a right line drawn from the centre of the Equant, and passing through the centre of the Epicicle, even to the circumference thereof. What conclusions are to be gathered hereof? FIrst, that the Epicicle of Mercury, contrary to that which happeneth in the three upper Planets, and also in Venus, is slower of gate in the upper part of the Excentrique, & quicker of gate in the lower part of the Excentrique, because the centre of the Equant in this Theoric of Mercury approacheth nigher to the opposite Auge, but in the other Planets last named, the centre of their Equant approacheth nigher to the Auge. Secondly, when the centre of the Epicicle is in the line of the Auges, than both the mean and true Auge of the Epicicle, and also the point of concavity are all three united together in one self line, yea, the mean Auge and also the point of concavity are again united, when the centre of the Epicicle is in any of the two points of next approach to the earth, marked in the former second figure with the letters H K: and from thence above those points of next approach towards the Auge of the Excentrique, the mean Auge of the Epicicle is always in the midst betwixt the true Auge and the point of concavity. But beneath the foresaid points of next approach towards the opposite Auge of the Excentrique, the point of concavity is in the midst of the mean and true Auge of the Epicicle: the demonstration whereof for brevity sake I do here omit. What harmony or agreement is there betwixt Mercury and the Sun? MErcurie as well as Venus, in the periodical moving of their Excentrique, doth follow the Sun: for the revolution of Mercury agreeth most exactly with the Excentrique of the Sun. And hereto you may also add, that the excentor of the Excentrique of Mercury, maketh his revolution together with the Excentrique of the Sun, not simply, but in having respect to the mean Auge of Mercury, or of the Equant: yea, and moreover according to the late observations and special conclusions touching the orbs of the Sun (whereof we have spoken before in the Theoric of the Sun) Mercury touching so much as appertaineth to his moving according to longitude, agreeth with the Theoric of the Sun, both in number and in like disposition or placing of the orbs, and also in the quality of the moving of the said orbs. For according to Copernicus, there is in both Theoriques' an excentor of the Excentrique, going contrary to the succession of the signs, whereby the mean Auge is on both sides most distant from the true Auge, and causeth the excentricity to be mutable. What conclusions do follow of this harmony? THese here following: for first you have to note, that the Sun and Mercury, and also Venus, are always joined together in their mean moving: and as they have all three one self mean moving, so they must needs have also one self line of their mean moving. And hereof it followeth, that neither Mercury nor Venus can departed from the Sun any further than the bigness of their Epicile will suffer them. Moreover, look how much the Sun proceedeth forward from the mean Auge of Mercury: so much the centre of Mercury's Excentrique goeth backward in the little circle. How are the Orbs belonging to the sphere of Mercury to be measured? OF such like parts as the semidiameter of the Excentrique, marked with the letters D A, or with P H, in the former figure, containeth 60 parts, the excentricity of the Equant, marked in the said figure with the letters C D, containeth according to Ptolomey three parts, and the greatest excentricity of the Excentrique, marked with the letters C F, containeth 9 such parts. And the line of the Auge, marked with C N, containeth 69 such parts or degrees. And the line of the opposite Auge marked with C Q, (such as it is then) containeth 51 degrees. But when the centre of the Epicicle is in the very opposite Auge itself, marked with D, than the line of the said opposite Auge, marked with C B, containeth 57 parts. But the line of the nighest approach, marked on the left side of the former figure with C H, and on the right side with C K, is said to contain 55 degrees, and i3° and so the semidiameter of the Epicicle containeth 22 degrees and i30° Hereof it followeth, that the greatest distance of Mercury being placed in the Auge of his Excentrique and of his Epicicle, containeth 91 degrees and i30° and if his excentricity did continue always fixed and unmovable, the altitude of Mercury being in the opposite Auges of those orbs, should be 28 degrees, and i30° And though that Mercury himself with his body do never descend so far, for such causes as are before declared, yet it is necessary that this capacity be attributed to his orb. And when Mercury is in any of the points of nighest approach, than his least altitude is 33 degrees and i4°. The third Intention, showing what points, lines, and arches are meet to be known in the Theoric of Mercury. IN all these things Mercury agreeth with Venus and with the three upper Planets, which being already set down in those Theoriques', need not here again to be rehearsed, & therefore resort to the third Intention, as well of the three upper Planets, as to that of Venus. In the tables as well of Ptolomey, as in those of Alphonsus and of their followers, the equations of the arguments are counted at that place of the Excentrique, in which the distance of the centre of the Epicicle from the earth is equal unto the semidiameter of the Excentrique. And to these equations may be added the excess of the longer longitude, and also the excess of the nigher longitude, not that when the Planet is in the very opposite Auge, but when he is in any of the two points of nighest approach. To these equations also may be referred the proportional minutes both longer and nigher. The equations of the Parallax or of the Epicicle which are set down in the Prutenicall tables, do appertain to the Auge of the Equant. But the excess do belong to the points of next approach, marked in the second figure with the letters H K. What this word Parallax doth signify, shall be declared hereafter. And you have to understand, that the greatest equation of the centre containeth 3 degrees, i/0 ii/30 and that the greatest equation of the argument, when the centre of the Epicicle is in the Auge of the Excentrique, containeth 19 degrees, i/3 ii/6 But when the Epicicle is in any of the 2 points of next approach, than it containeth 23 degrees, i/51 ii/40 The fourth Intention, showing the latitudes, as well of Venus as of Mercury, and wherein they do agree or disagree. IN quality these two Planets are most like, for look in what manner the Excentrique of Venus doth decline towards the Ecliptic, or her Epicicle to the Excentrique; in like manner doth the Excentrique and the Epicicle of Mercury make their declination, but yet with this difference, that look in what sort those two circles in the Theoric of Venus do decline towards the North, in like sort the said two circles in the Theoric of Mercury do decline towards the South. How manifold is the latitude of these two Planets? THreefold, whereof one dependeth upon the movable obliquity or slopeness of the Excentrique, and the other two latitudes do depend of the inclinations of the Epicicles, which inclinations are also twofold and movable, whereof the one in Greek is called Engclysis, and the other Loxosis, as shall be declared hereafter. What manner of latitude is that which the Excentrique of either Planet causeth? WE have said before, that the poles of the deferents of the Auges do wander both beyond and also on this side of the poles of the Ecliptic, and therefore the plane of the Excentrique hath obliquity or slopeness, and yet not fixed as in the other upper Planets but movable. And as well the mutual section, as the swaying of the planes of the Excentrique and of the Ecliptic is made upon the diameter of the world, standing with right angles upon the line of the Auge, and therefore the diameter which governeth this declination, is the line of the Auge and of his opposite Auge. And by this means it falleth out, that the Auge and opposite Auge, or rather the each half of the plane of the whole Theoric doth sway from the Ecliptic, now towards the North, and now towards the South, but the nodes of such swaying are always distant from the Auge one whole quarter of the Zodiac: and this moving of latitude is commonly called the declination of the Excentrique. What proportion doth the swaying of the declination of the Excentrique, as well of Mercury as of Venus observe in the making of their periods? THis here following: for when the centre of the Epicicle is either in the Node ascendent or descendent, all the whole plane of the Excentrique doth fall into the Ecliptic; for though the centre of Mercury his Epicicle doth never ascend to the North, nor the centre of the Epicicle of Venus to the South, yet we may call the one node ascendent, and the other descendent, as well for the likeness or proportion that is betwixt those two Planets & the other Planets, as also for that the one node is in the ascendent half of the Excentrique towards the Auge, & the other node is in the descendent half of the Excentrique towards the opposite Auge. But if the centre of the Epicicle be in the upper half above the diameter of the section or swaying towards the Auge, than the Auge, or rather the whole upper half of the Excentrique doth decline from the Ecliptic, that is to say, in Venus towards the North, and in Mercury towards the South. But if the centre of the Epicicle be in the neither half, than the Auge of Venus declineth towards the South, and the opposite Auge towards the North: but in Mercury it is clean contrary, and the greatest declination is when the centre of the Epicicle is either in the Auge or opposite Auge of the Excentrique. What conclusions may be gathered hereof? FIrst, that the Auges are not always found to be in the North nor in the South, as it chanceth in the three upper Planets, but sometime in the one place, and sometime in the other. Secondly, that the centre of Venus her Epicicle doth never arrive unto the South, nor the centre of Mercury's Epicicle to the North: for this swaying is of such manner, as that half of the Excentrique, into which the Epicicle at any time entereth, doth by and by begin to decline into the said North part for Venus, and into the South part for Mercury: and this Inclination of the Excentriques, causeth that the North latitudes of Venus be always greater than her South latitudes; but in Mercury it is clean contrary. And you have to note, that the greatest angle or section of the Excentrique and Ecliptic, is for Venus, i/10 and for Mercury, i/45 But for the better understanding, as well of this that hath been said before, as of that which is to be said hereafter touching the foresaid latitudes, it shall be needful to set down this figure here following. ¶ The third figure showing the latitudes of the said two Planets. THis figure, made somewhat like to a Butterfly, with her wings spread open, containeth three several planes of orbs, cutting one another in the diameter of the world, which passeth through the centre of the world, marked here with A: which three planes do represent no more but one only plane, that is, the Excentrique of Venus or of Mercury, to show the diverse positions or placings of the said Excentrique, caused by the latitude of their inclination. And ye have to understand, that the middlemost of these three planes or orbs, marked with the letters L K M T, and containing therein four Epicicles, doth signify, that the Excentrique being in either of the two points K or T, is united to the Ecliptic: but the other two planes, whereof the first having the line of the Auge drawn through the limits of the greatest declination, marked with the letters B C, and the second plane having a line marked with Q P, doth signify the declination of the Excentrique from the Epicicle. Moreover, in this figure the two planes B C, and Q P, hard by the mutual section which is nigh unto K and T, are cut off, not for that such orbs are to be cut off indeed; but that by this means the Epicicles being in K or T, might be the better seen in the middlemost plane, marked with the letters L K M T. You see also, that in this figure the circumference of every one of the four Epicicles is marked with these four letters, G H F I, but yet placed in diverse order, according to the divers moving of the Epicicle. And you have to note, that when the centre of any of those Epicicles is in the Node ascendent, marked with K, than the plane of the Excentrique, whose diameter by passing through the Auge L, and the opposite Auge M, is the line L A M, wholly united to the Ecliptic, having no declination at all, whereby the axle-tree of the said plane, marked with N O, hangeth perpendicularly upon the plane of the Ecliptic. But when the centre of the Epicicle ascendeth from the Node K towards the Auge of the Excentrique, marked with B, than the upper part of the Excentrique doth by and by decline from the Ecliptic towards the North for Venus, and towards the South for Mercury; as when the centre of the Epicicle is in the Auge B, for then the diameter B A C, or rather the whole upper half of the Excentrique is found to be on this side of the Ecliptic, and the inferior part of the Excentrique to be beyond the Ecliptic, and the axle-tree of the Excentrique is then the line D E. But when the centre of the Epicicle is come down to the Node descendent, marked with T, than the plane of the Excentrique is united again to the Ecliptic, and the right line L A M is again the diameter of the Auge. But when the Epicicle is once passed the Node descendent, marked with T, than the upper part of the Excentrique which was before on this side of the Ecliptic, beginneth now to decline beyond the Ecliptic, wherefore the lower part of the Excentrique beginneth now to have the same declination which the upper part had before, that is to say, towards the North for Venus, and towards the South for Mercury. And therefore the centre of the Epicicle being in the opposite Auge, marked with P, the position of the Excentrique is the line P A Q, and the axle-tree thereof, is the line R S. It appeareth therefore, when the centre of the Epicicle is in any of the Nodes, either K or T, that then the Excentrique is united to the Ecliptic. But if the centre of the Epicicle be out of those Nodes, then as well towards the Auge B, as towards the opposite Auge P, the Excentrique hath the like latitude as before, that is, North latitude for Venus, and South latitude for Mercury. And therefore the centre of the Epicicle doth not go beyond the Ecliptic, either towards C or Q. What manner of latitudes have the Epicicles, as well of Venus as of Mercury? THe planes of their Epicicles, whose axletrees we have said before to be obliqne or sloping to the Excentriques upon the two diameters, that is to say, upon the diameter of the Auges, and upon the diameter of the mean longitudes are inclined and swayed on both sides of their Excentriques, and yet proportionally answerable to the periods of their Excentriques. How is the first diameter, passing through the Auges, declined? THe diameter of the Auges declineth on both hands from the plane of the Excentrique, in such sort as followeth: for when the centre of the Epicicle is in any of the limits, that is to say, either in the Auge or opposite Auge of the Excentrique, marked in the former figure with B P, then the diameter of the Auges have no declination at all, because it falleth just into the plane of the Excentrique; but the declination thereof is greatest, when the centre of the Epicicle is in any of the two Nodes, yet with such difference, as the inclination of this diameter, or rather of the one half of the plane of the Epicicle being made in the descending half of the Excentrique, is for Venus Northward, and for Mercury Southward: but in the ascending half of the Excentrique, the half of this diameter for Venus is Southward, and for Mercury Northward. And this declination is made upon the diameter of the mean longitudes, which the former figure doth plainly show: for the Epicicle being in B or P, which are the two limits, the declination of the diameter of the Auges is nothing at all. But the centre of the Epicicle being in T, which is the Node descendent, the upper part of this diameter, marked with T G, declineth from the plane of the Excentrique Northward for Venus, and Southward for Mercury: but the lower half, marked with T F, inclineth contrariwise, that is to say, Southward for Venus, and Northward for Mercury. And because that the declination is greatest when the Epicicle is in any of the Nodes, than the aforesaid diameter beginneth again to approach unto the plane of the Excentrique, and in the limit P is united again to the plane of the Excentrique, and from thence the upper part of the said diameter declineth beyond the plane of the Excentrique to the other side, and the inferior part to this side. Wherefore the Auge of the Epicicle, marked with G, being in the point K, which before was for Venus Northward, is now Southward, and for Mercury clean contrary. The greatest angle of this Inclination of the plane of the Epicicle unto the Excentrique, is demonstrated by Ptolomey and Copernicus, to be for Venus two degrees, and i/30 and for Mercury 6 degrees, and i/15 To these from the Auge of the Epicicle to the centre of the world, do agree for Venus one degree, and i/3 and for Mercury one degree, and i/46 But from the opposite Auge of the Epicicle to the centre of the world, it is for Venus 6 degrees, and i/22 and for Mercury 4 degrees, and i/5 Hitherto of the first manner of the declination of the Epicicles from their Excentriques, called in Latin Inclinatio, or Deviatio, in Greek Engclisis. Now show in what manner the other diameter, passing through the mean longitudes of the Epicicle, maketh his declination? THis kind of declination of the Epicicle, is commonly called the reflection, in Greek Loxosis, because it maketh the diameter of the mean longitudes to reflect on both sides from the plane of the Excentrique in such manner as followeth: for while the centre of the Epicicle is in any of the Nodes, which is distant a just quarter of the Zodiac from the Auge or opposite Auge, than the reflection of this diameter is nothing at all, because than it falleth wholly into the plane of the Excentrique; but such reflection is greatest, when the centre of the Epicicle is in any of the limits, or in the Auge or opposite Auge. And yet with such difference, as the reflection of the half of this diameter, called the Oriental half of the Epicicle, may be in the upper half of the Excentrique, Northward for Venus, and Southward for Mercury. But in the lower half of the Excentrique, the said Oriental half of the Epicicle reflecteth for Venus towards the South, and for Mercury towards the North. And this reflection is made upon the diameter of the Auges, all which things the former figure doth plainly show. For when the centre of the Epicicle is in K or T, which be the two Nodes, than the diameter of the mean longitudes, marked with H I, hath no reflection at all, but lieth whole upon the plane of the Excentrique, as you may see in the Node ascendent, marked with K: but in the upper part of the Excentrique towards the Auge, when the centre of the Epicicle is in the Auge B, then the Oriental half of the diameter H I, marked in the highest Epicicle of this figure with the letters H B, or else the Oriental half of the said highest Epicicle, marked with the letters G H F, doth reflect from the plane of the Excentrique for Venus Northward, and for Mercury Southward. But the Occidental half of the said diameter, marked with B I, or that half of the Epicicle marked with F I G, doth reflect clean contrary, that is to say, for Venus towards the South, and for Mercury towards the North. And when the reflection is greatest, than this diameter approacheth the Ecliptic, and falleth into the same in the point T, that is to say, in the Node descendent. And departing from thence downward towards the limit P, the said half of the diameter reflecteth on the other side beyond the Ecliptic, and then the Occidental half succeed, which as when it was in the upper part of the Excentrique, was for Venus' South, and for Mercury North: so now by going from T to P, and so to K, it is made for Venus Northward, and for Mercury Southward. And the greatest angle of the reflection of this diameter unto the Excentrique, is demonstrated to be for Venus 3 degrees, i/30 & for Mercury 7 degrees: and to these do agree at the centre of the world the latitudes for Venus to be 2 degrees, i/30 and as much for Mercury. Notwithstanding, because Mercury hath a greater excentricity, this angle in the Auge of the Excentrique, hath to the centre of the world two degrees, ii/15 and in the opposite Auge of the said Excentrique, it hath 2 degrees, ii/45 What conclusions are to be gathered of the inclinations and reflections of the Epicicles? 1. THese here following: First, the plane of the Epicicle is never united with the plane of the Excentrique or of the Ecliptic, by reason of the continual inclinations of the one or of the other diameter. And therefore the axle-tree of the Epicicle is never perpendicular to any of those planes. 2. Secondly, the declinations of the diameter of the Auges, and of the mean longitudes of the Epicicle of these two Planets, that is to say, of Venus and Mercury, are contrary to the declinations of the three upper Planets, for there the declinations of the diameters of the Auges are greatest in the limits, & nothing in the nodes, but the declinations of the said diameters in these two Planets are greatest in the nodes, and nothing in the limits. Again, the reflections in the three upper Planets are greatest in the nodes, and nothing in the limits, whereas in these two Planets the reflections are greatest in the limits, and nothing in the nodes. 3. Thirdly, the planes of the Excentriques and Epicicles of these two Planets do cut one another in divers diameters: for in the nodes such section is made in the diameter of the mean longitudes, but in the limits the same section is made in the diameter of the Auges; and in the mean places such section chanceth sometime in one place, and sometime in another, betwixt the said diameters: but the said section in the three upper Planets, observeth contrary order, as hath been said before. 4. Fourthly, the line of the mutual section of the Epicicle and of the Excentrique doth wander through the plane of the Epicicle in such sort, as the one half of the said plane departeth from the plane of the Excentrique for Venus towards the North, and for Mercury towards the South: so the other half of the said plane declineth clean contrary, that is to say, for Venus towards the South, and for Mercury towards the North: but in the three upper Planets such line of mutual section observeth a contrary order. By these conclusions it is manifest, that the latitude of Mercury and Venus hath three variations, the first by reason of the movable obliquity of the Excentrique: the second by reason of the movable declinations of the Epicicle: and the third by reason of the movable reflections of the said Epicicle. All which things you may the more easily perceive by the former figure, for the Epicicle being in the Node ascendent, marked with K, the diameter of the mean longitudes, marked with H I, is in the very plane of the Excentrique: but the diameter of the Auges of the said Epicicle, marked with FG, hath then greatest declination, so as the whole neither half of the said Epicicle, marked with the letters H F I, looking towards the Node descendent, is for Venus Northward, and for Mercury Southward. And the upper half of the said Epicicle, marked with the letters I G H, being partly hidden from our sight, by reason that it is under the Excentrique, is for Venus' Southerly, and for Mercury Northerly: and the diameter of the section, marked with H I, is aparalell to the line of the Auge of the Excentrique, which line is marked with these letters, L A M, whereof L signifieth the Auge, and M the opposite Auge of the Excentrique, and A the centre of the world: so in the other Node, marked with T, the self-same diameter H I is in the mean longitudes, but there the upper half of the Epicicle, marked with the letters I G H, looking towards the same part as before, is then for Venus towards the North, and for Mercury towards the South. But the lower half of the Epicicle, marked with the letters H F I, (whereof some part is now again hidden and covered as it were with the plane of the Excentrique) is for Venus towards the South, and for Mercury towards the North. The like and the same doth chance when the centre of the Epicicle is either in the Auge B, or the opposite Auge P; for in those places the diameters of the Auges, marked with F G, having no declination, the Epicicles are divided, and the diameters H I have their greatest reflection: and yet after the same manner as before, that is, when the East half is in B, and the West half in P, which letters do signify as well the two limits, that is, B the North limit, and P the South limit, as the two Auges; for here again the one half of the Epicicle is wholly to be seen, in which whilst it goeth towards the Node descendent, Venus is Northward, and Mercury Southward. But the other half of the Epicicle, (which the plane of the Excentrique doth partly hide and cover) doth reflect or turn backward on the the other side from the Excentrique. And even so it fareth in like manner in all the mean places that are betwixt the limits and the nodes. And here endeth the first book of the Theoriques'. The second Book or Part, treating of the Passions or Accidents of the Planets. Having sufficiently spoken of the three several latitudes, belonging as well to Venus as to Mercury, I mind here to make an end of the first part of the Theoriques'; wherein have been plainly declared all the diverse motions of the Planets, as well according to their longitude as latitude: and so now to proceed to the second part, wherein we have to treat of the passions, qualities, or accidents of the Planets; of which, though Purbachius maketh five kinds, counting their motions according to latitude to be one of those five: yet me thinks that Mestelyn hath more reason to make but four general kinds, sith the latitude of every Planet, that hath latitude, is rather a principal part of his motion than a passion: for all their motions are either according to longitude, or to latitude, and therefore minding herein to follow Mestelyn, I will set down but four kinds of passions, as he doth, which do grow of four several comparisons. First, by comparing the moving of the Epicicle of any Planet together with the moving of his Excentrique. Secondly, by comparing the moving of the Planets one to another. Thirdly, by comparing their movings to the Sun. And four, by comparing their movings or rather places to the centre of the world and to the globe of the earth, every one whereof containeth certain special kinds of passions or accidents, hereafter declared. What special accidents do belong to the first general kind, consisting of the comparison of the moving of the Epicicle to the moving of his Excentrique? BY this passion the Planets are said to be sometime direct, sometime retrograde, and sometime stationary; which three accidents do belong only unto the five Planets, the Sun and Moon not being reckoned. Moreover, they are said to be sometime swift, sometime slow, and sometime in a mean. Sometime also they are said to be either increased or diminished in number, and sometime to be ascendent, and sometime descendent. When is any Planet said to be direct, retrograde, or stationarie? IT is said to be direct, when the line of the true moving of the Planet, drawn from the centre of the world through the mid body of the Planet, proceedeth forward according to the succession of the signs, following the line of the true moving of the centre of his Epicicle, which goeth always according to the succession of the signs. And it is said to be retrograde, when the line of the true moving of the Planet goeth more backward, contrary to the succession of the signs, than the line of the true moving of the centre of the Epicicle proceedeth forward according to the succession of the signs. And it is said to be stationary, when both these lines are drawn to the Zodiac with an equal moving into diverse parts of heaven, so as the line of the Planets true moving maketh as great an arch of the Zodiac in going backward contrary to the succession of the signs, as the line of the true moving of the centre of the Epicicle maketh, in proceeding forward according to the succession of the signs, for then the Planet for a while seemeth to stand still, and not to be moved from his place, and thereof is said to be stationary, like to any of the fixed stars. And you have to understand, that these diversities of motions under the Zodiac proceedeth of the moving of the Epicicle, which in his upper part carrieth the Planet according to the succession of the signs, and in his neither part carrieth the same contrary to the succession of the signs, called his retrogradation. In which inferior or neither part of the Epicicle are the two points of station. But for the better understanding of that which hath been said touching the direction, retrogradation, and station of any Planet, it shall be needful to set down this figure here following, together with the description thereof, the signification of whose parts the letters do show as you may see in the page next following. ¶ The first figure of the second Book. IN this figure the letter A standing at the neither end of the right lines, signifieth the centre of the world, from whence all the said right lines are drawn to the Zodiac: and B signifieth the centre of the Epicicle: & the middle right line A B passing through the true Auge of the Epicicle, marked with C, doth show the true place of the said Auge under the Zodiac, marked with the letter D: and the letter E showeth the true opposite Auge of the Epicicle: and the highest arch above, containing certain degrees of division, signifieth a portion of the Zodiac: and the two outermost lines, A F G, and A H I, be lines of contingence, touching the Epicicle in the two points, marked with H and F: and the two inner right lines, marked with the letters A N, and A L, drawn from the centre A through the two points of station, marked with K and M, do show in the Zodiac the retrogradation, marked with the letters L N: and the two points H F do divide the Epicicle into two parts or halves, whereof the one is called the upper half, marked with the letters H C F, and the other the neither half, marked with the letters F E H. And as the point F showeth the Oriental or East part, so H showeth the Occidental or West part: and every one of the five Planets in the upper half of the Epicicle, marked with H C F, is said to go from H to F, according to the succession of the signs, describing the arch of the Zodiac, marked with I D G, which is called his direction or progression: but in the lower half, marked with F E H, the Planet is said to go contrary to the succession of the signs, called his retrogradation: and when he is in any of the two points, marked with K M, than he is said to be stationary; whereof the point K is the point of the first station, whereas the Planet beginneth first to be retrograde, and M is the point of the second station, whereas the Planet endeth his retrogradation, and beginneth his progression: which two points are always beneath the two Touch-points F H, towards the opposite Auge of the Epicicle, marked with E, from which the two points of station are always equally distant, and also from the true Auge of the Epicicle. And the letters C F K do show the arch of the first station, which arch is otherwise called the first station in the second signification; and C F K M do show the arch of the second station, otherwise called the second station in the second signification: and the letters M H C F K, do show the arch of progression, and KM do show the arch of retrogradation. But you have to note, that though the two points of station are always equally distant as well from the opposite Auge, as from the Auge of the Epicicle, yet such distance is not always of like quality, neither is the arch of their progression, nor the arch of their retrogradation always of one bigness, but do alter and that for four causes: First, for that the Epicicle through the moving of his Excentrique is sometime nigher and sometime further off from the centre of the earth: for the nigher that the epicicle is to the earth, the more are the stational points distant from the true opposite Auge of the Epicicle in all the five Planets, saving in Mercury. The second cause may be the diverse magnitude of the Epicicle, being compared to his Eccentric, for the stationall points of a greater Epicicle do approach nigher unto the opposite Auge, than the stationall points of a lesser Epicicle do. The third cause is the periodical slowness or swiftness of the Epicicle, being compared to the periodical moving of his Excentrique, for the slower revolution of the Epicicle maketh the stationall points to be nigher to the opposite Auge of the Epicicle, and thereby as well the arch of progression as of retrogradation do increase and decrease. Fourthly, the diversities of their excentricities may cause the stationall points to alter in their distances from the opposite Auge of the Epicicle. Wherefore is the Moon and Sun exempted from these passions? THe Sun hath no Epicicle, and though the Moon hath an Epicicle, yet she is neither said to be stationary nor retrograde, by means of the swiftness of the centre of her Epicicle, which maketh every day a greater arch of the Zodiac, according ●n the succession of the signs, than she can go backward, because her Epicicle is both small and slow in her gate. And though Saturn hath a very small Epicicle, yet the swiftness thereof doth supply that want, and thereby he is both stationarie and retrograde, and so are the other four Planets, viz. jupiter, Mars, Venus, and Mercury. When are the Planets said to be swift, slow, or in a mean? THey are said to be swift, when their true moving is quicker, according to the succession of the signs, than their mean moving is: and they are said to be slow, when their true moving is slower (according to the succession of the signs) than their mean moving is: and they are said to be in a mean, when their true moving (according to the succession of the signs) is equal unto their mean moving. When are Planets said to be increased or diminished in number? THey be increased when the line of the true moving goeth (according to the succession of the signs) before the line of their mean moving. And they are said to be diminished in number, when the line of their true moving doth follow after the line of their mean moving. When is any Planet said to be ascendent or descendent? HE is said to be ascendent, whilst he ascendeth from the opposite Auge of his Epicicle to the Auge thereof: and he is said to be descendent, whilst he descendeth in the other half of the Epicicle from the Auge to the opposite Auge of his said Epicicle. The second general kind of passions, rising of the comparison made by comparing the moving of every Planet one to another, comprehending the five Aspects of the Planets, which be these here following. THat is to say, their Conjunction, their Sextile aspect, their Quadrile aspect, their Trine aspect, and their Opposition: whose characters are here set down, together with the definition of every such Aspect. 1. The Conjunction, marked thus ●. is when two Planets are both in one self sign, and in one self degree, which aspect in Greek is called Synodos. 2. The Sextile aspect, marked thus *, is when two Planets are distant one from another by a sixth part of the Zodiac, that is to say, by two whole signs, or 60 degrees, which aspect is called in Greek Exagon●s. 3. The Quadrile aspect, marked thus ●, is when two Planets are distant the one from the other three whole signs, or 90 degrees of the Zodiac, and is called in Greek Tetragonos. 4. The Trine aspect, marked thus ●, is when two Planets are distant the one from the other by four whole signs or 120 degrees of the Zodiac, and is called in Greek Trigonos. 5. The Opposition, marked thus ☍, is when two Planets are right opposite the one to the other, and are distant the one from the other by six whole signs or 180 degrees of the Zodiac, and is called in Greek Diametros, that is to say, a diametral aspect, as when one is right against another in a right line. But you have to understand, that Ptolomey comprehendeth as well the Opposition as Conjunction of any two Planets, but especially of the Sun and Moon, under this Greek name Syzigias. And you have to note, that three of these aspects, that is, the Sextile, Quadrile, and Trine aspect, are said to be double, because they look two manner of ways, that is, towards the left hand, called the sinister aspect, and towards the right hand called the dexter aspect. The direction of the sinister aspect is according to the succession of the twelve signs, which succession beginneth at Aries, and so proceedeth forward to Taurus, Gemini, and Cancer, and so forth to the last point of Pisces. But the direction of the dexter aspect is contrary to the succession of the signs, looking backward from Aries towards Pisces, Aquarius, Capricornus, and so forth to the last point of Taurus. As for example, if one Planet be in the beginning of Aries, and another in the beginning of Gemini, those two Planets do look one to another with a sinister Sextile aspect. But if the one Planet be in Aries, as before, and the other in Aquarius, than they look one to another with a dexter Sextile aspect, as you may see by this figure following, which doth plainly show as well those aspects as all the other aspects before mentioned; it showeth also with what aspect every one of the twelve signs do regard one another. ¶ The figure of Aspects. But you have to understand, that all the Planets do not regard or behold one another with all the foresaid five aspects, for though the three upper Planets and the Moon may behold one another, or any of the rest with every one of the said five Aspects, yet Venus and Mercury cannot so do, for Venus is never distant from the Sun above 48 degrees, nor Mercury above 29 degrees: and yet they may be distant one from another by a Sextile aspect. And of the foresaid aspects, some are said to be mean, and some to be true, and specially their Conjunctions and Oppositions, whereof the Astronomers do not make any great account, but only of the Conjunctions and Oppositions belonging to the Sun and Moon, which two Planets the Astronomers do call in Latin Luminaria, that is to say, The two chief lights: the knowledge of whose mean and true Conjunctions and Oppositions, is necessary, for the better understanding of their Eclipses. When are their Conjunctions and Oppositions said to be mean or true? THey are said to be mean, when the two lines of both their mean movings do meet in one self point of the Zodiac, and do make one self line. And they are said to be true, when the two lines of their true movings do meet and make both one self line in one self degree of the Zodiac, and their Oppositions are either mean or true, according as the said lines do meet in the opposite points of the Zodiac. And the true Conjunctions of the said two lights are said to be true, sometime according to longitude only, as when the foresaid true lines do meet in one self point only according to longitude: for the Moon doth oftentimes wander from the Ecliptic line, and therefore though the line of her true moving do meet with the line of the suns true moving in one self point under the Zodiac (the Moon having then latitude) yet that is according to longitude only: but if those two lines do meet when the Moon hath no latitude, but is right under the Ecliptic line, than such Conjunction is both according to latitude, and also according to longitude, which is called a Corporal or Eclipticall Conjunction. And the like is to be said of their true Oppositions, when the said lines do meet in like manner in the opposite points of the Zodiac. Moreover, you have to note, that the true Conjunctions may differ from the mean Conjunctions by reason of time, for sometime the one may go before or after the other, and sometime meet both at one instant. They may meet both at one instant two manner of ways: First, when the Sun or Moon are in the Auge or opposite Auge of their Excentriques, or when the one is in the Auge, and the other in the opposite Auge, for then the foresaid lines of their mean and true movings are all one. Secondly, they do meet at one instant, when the equations of their arguments are equal and of like quality, which is to be known by the Prutenicall tables. But the true Conjunctions and Oppositions do go before the mean Conjunctions or Oppositions, when at the time of the mean Conjunction and Opposition the place of the Sun is before the place of the Moon. And the true Conjunctions and Oppositions do follow the mean, when at the time of the mean Conjunction and Opposition the place of the Moon is before the place of the Sunn●. The like is to be said also touching their quarters, both mean and true. And you have to note, that one whole period betwixt every two Conjunctions or Oppositions of the Sun and Moon doth contain a Synodical month, which is 29 days and a half, The third general kind of Passions, made by comparing of the movings of all the six Planets, unto the Sun, containeth these three special kinds of Passions here following. 1. FOr first they are said to be either increased or decreased in light, or else to be combust, called in Greek Hyppaugi, that is to say, hidden or covered with the beams of the Sun, so as they cannot yield their light. 2. Secondly, they are said to be Oriental or Occidental. 3. Thirdly, to have diverse kinds of rising and setting, like as the fixed stars have, that is to say, they rise or set sometime Cosmice, sometime Achronice, and sometime Helyace; of which three Poetical kinds of rising and setting, though I have somewhat spoken before in my first book of the Sphere, chap. 35. yet I will declare the same here once again more at the full, according to Maginus, who doth set them down in such manner as hereafter followeth. Show how and when these Passions do chance? THe Planets are said to be increased in light, when after that any of them hath been in Conjunction with the Sun, either the Sun departeth from that Planet, or the Planet departeth from the Sun, until it be at his furthest distance from the Sun. And it is said to be diminished in light, when after such furthest distance either the Planet approacheth to the Sun, or the Sun to the Planet. And it is said to be combust, when the Planet is hidden under the beams of the Sun, so as it cannot yield his light, as is before said. Secondly, all stars are said to be Oriental or Matutine, when they rise before the Sun; and they are said to be Occidental, when they go down after the Sun; and yet with some difference as Maginus saith: for the three upper Planets (that is to say) Saturn, jupiter, and Mars, are said to be Oriental, Matutine, and to go before the Sun from the time of their being in Conjunction with the Sun, until they come to be in Opposition to the Sun, as well when they are seen, as not seen: and this happeneth whilst any of those three Planets descendeth from the Auge of his Epicicle through the mean longitudes unto the opposite Auge of the said Epicicle: but the two inferior Planets, that is, Venus and Mercury, are said to be Oriental, Matutine, and to go before the Sun, when either of them ascendeth from the opposite Auge of his Epicicle unto the Auge of the said Epicicle, which you may evidently see by the first figure of this second book. But as for the Moon, she is said to be Oriental, Matutine, and to go before the Sun, during the time of her wane or decrease. Again, the three upper Planets are said to be Occidental, Vespertine, and to follow the Sun from their being in Opposition with the Sun, until they come again to be in Conjunction with the Sun; which chanceth whilst any of them is carried from the opposite Auge of the Epicicle through the mean longitudes, unto the Auge of the same Epicicle. But Venus and Mercury are said to be Occidental, Vespertine, and to follow the Sun, whilst either of them descendeth from the Auge of their Epicicle unto the opposite Auge of the same. But as for the Moon, she is said to be Occidental, Vespertine, and to follow the Sun all the time that she is in her increase. Now you have to understand, that the rising and going down of the fixed stars, as well Matutine as Vespertine, is twofold, that is, true and apparent. The Matutine rising is said to be true, when the star riseth together with the Sun in one self point of the Ecliptic, and at one self instant, at which time the star remaineth hidden under the beams of the Sun: but such Matutine rising is said to be apparent, when the star having been hidden a little before with the beams of the Sun, doth get out from thence, so as in the morning it may be seen, which chanceth when the Sun goeth from the star. Again, the Vespertine rising is said to be true, when the star is right opposite in any part of the Ecliptic to the Sun, at the time of his going down, and is so much elevated above the Horizon, as after the evening twilight it may be seen: but such Vespertine rising is said to be apparent, when the star in the evening after Sun setting, doth shine, and beginneth to appear in the West. Now the Matutine going down of any star is said to be true, when the star goeth down at such time as the Sun riseth, and is in the opposite point of the Ecliptic, to the Sun. But the Matutine going down is said to be apparent, when the star at the rising of the Sun (which a little before night have been seen) is now hidden under the beams of the Sun. Moreover, the Vespertine going down of any star is said to be true, when it goeth down together with the Sun at one self instant. And such Vespertine going down is said to be apparent, when the star at the going down of the Sun is hidden, which a little before might have been seen, and so continueth hidden until the morning, until it may get from under the beams of the Sun. Out of this difference of rising and going down of the Planets may be gathered these 6 rules here following. 1. First, that the three upper Planets, the Moon, and also the fixed stars are subject to the true rising & setting as well Matutine as Vespertine; but neither the apparent rising Vespertine, nor the apparent setting Matutine do belong to any of them, but only to the Moon, which notwithstanding suffereth neither the apparent rising Matutine, nor the apparent rising Vespertine. 2. Secondly, though Venus and Mercury be subject to the apparent rising and setting, as well Matutine as Vespertine, yet they cannot have the true Matutine setting, or the true Vespertine rising. 3. Thirdly, of all the fixed stars and of the three upper Planets, their true rising and setting Matutine, are before their apparent rising and setting Matutine: but their true Vespertine rising and setting are after their apparent rising and setting. 4. Fourthly, in the two inferior Planets, that is, Venus and Mercury, their apparent Matutine and Vespertine rising are after their true Matutine and Vespertine setting; but their apparent Matutine and Vespertine setting are before their true Matutine and Vespertine rising. 5. Fiftly, the apparent Matutine rising of the Moon doth follow her true Matutine rising, and contrary her apparent Matutine setting, doth go before her true Matutine setting. 6. Sixtly, it is meet that there be some distance of space betwixt any star and the Sun, whereby they should either appear to be out of the beams of the Sun, or else to be hidden under the Sun. And this distance is not of like quantity in every star, but varieth according to the greatness or littleness of the star, for the greater and more lightsome that the star is, the lesser time it stays under the beams of the Sun. And the limits of the quantity of distance that do belong to every star, as well to the fixed stars as to the Planets, are to be found in a great circle, passing both through the body of the Sun, and also through the pole of the Horizon. For to every limit the Astronomers do appoint his proper arch of quantity, called of them the arch of vision. Define what that arch is. THe Arch of Vision, is that portion of the Vertical circle that is comprehended betwixt the Horizon and the Sun, at such time as the star first beginneth to appear, or else ceaseth to be seen: which arches of vision in fixed stars are greater or lesser, according to the magnitude of the said stars, for to those stars, that be of the first bigness, they make the arch of vision to contain 12 degrees, and to those of the second bigness 13 degrees, and to those of the third bigness 14 degrees, and to those of the fourth bigness 15 degrees, and to those of the fift bigness, 16 degrees, and to those of the sixth bigness 17 degrees, and to the least fixed stars of all, they appoint 18 degrees, which 18 degrees is the beginning as well of the day light in the morning, as of the twilight in the evening: for when the Sun is departed from the Horizon 18 degrees, either upward or downward, it beginneth to wax day light in the morning, or twilight in the evening. Now as touching the quantity of the said arch of vision belonging to every one of the five Planets, they appoint to Saturn 11 degrees, to jupiter 10 degrees, to Mars 11 degrees, ½. to Venus' 5 degrees, and to Mercury 10 degrees: so as by knowing the degree of the Ecliptic, wherewith any star riseth or goeth down, and also the arch of vision, together with the angle of section, whereas the Ecliptic and Horizon do cross one another in one self part, you shall know what time the star spendeth in his rising or setting. And for the better understanding of the said arch of vision, Maginus setteth down this figure here following, together with the description thereof, by help of certain letters therein contained▪ ¶ The figure showing the arch of vision. THis figure as you see consisteth of two whole circles being of like greatness, and also it containeth the portion of a great circle. The whole circle, marked with G E C, signifieth the Horizon, whose pole or Zenith is marked with the letter A: and the other whole circle, marked with the letters F E D, signifieth the Ecliptic, whose pole is marked with the letter B: and the letter D showeth the place of the Sun, being hidden beneath the Horizon. And imagine the place of the star his appearing or departing to be in C, in the very Horizon itself. Now the portion of the great circle, drawn through the Vertical point of the Horizon, and also through the body of the Sun, is marked with the letters A C D. And the arch C D is the arch of vision. But now you have to understand, that the Moon observeth not like law or order of hi● appearing, after that she hath been in Conjunction with the Sun. For though the ancient Astronomers, as Theon, Alexandrinus, Alfraganius, Albategnus, and others, do appoint to her arch of vision twelve degrees of the equinoctial, yet that is not always certain, but sometime more, and sometime less, sith the Moon doth show herself sometime sooner and sometime later after her Conjunction with the Sun, and that for three causes or respects, first by reason of the inclination of the Zodiac to the Horizon, for whilst she is in the ascending half of the Zodiac, which is from the beginning of Capricorn to the end of Gemini, which is the half of long descension, she appeareth sooner above the Horizon, than when she is in the other half of short descension, which is from Cancer to Capricorn, because the Moon goeth down later and not before that the Sun be deeply hidden under the Horizon, making thereby a greater twilight. The second cause is the latitude of the Moon from the Ecliptic, for the more North latitude she hath, the more slowly she goeth down, and thereby is the sooner seen, and specially to those that dwell betwixt the Tropic of Cancer, and the circle Arctic. The third cause is the swiftness of her true moving, for in her swift moving she is sooner seen than in her slow moving. And when all those three causes do concur, it is possible that she may be seen the self-same day that the change is, albeit that seldom chanceth, and that only in those places, whose latitude is very far Northern. But if two of the foresaid causes do concur, than she may be seen the next day after her Conjunction with the Sun: if there be no more but one cause, than she is commonly seen the third day after the change. But if she be in the descending half of the Zodiac, and have therewith South latitude, and is slow of gate, there may pass four days before she appeareth. Here also it is meet to speak of the diversity of her shape, according as she is distant from the Sun, as well in her increase as decrease: for during her increase, she followeth the Sun, and turneth her horns from the Sun towards the East, and her lightsome part to the Sun, and riseth above the Horizon immediately after the Sun is set. But during her decrease, which is from the full unto the change, she goeth before the Sun, and turneth her horns towards the West, and riseth in the morning before the Sun. And as for the divers names which she hath both in Greek and Latin, according to her divers aspects to the Sun, are plainly set down before in a table made by Reinholdus, which table immediately followeth the third figure belonging to the Theoric of the Moon; and therefore I would wish you to resort thereunto, because I think it superfluous to repeat it again here. Notwithstanding lo hear the figure which is commonly used to show the diverse shapes of her light, as well in her increase as decrease. The fourth general kind of passions of the Planets, that do● chance by comparing their movings unto the globe of the earth. But you have to understand, that the passions rising of this comparison, are not so properly incident to all the Planets, as to the Moon; because that the greatness of the earth is not to be esteemed in respect of the other Planets, or at the least not with any great sensibility or affection. Show what passions the Moon hath to the earth, or the earth to the Moon? THese three here following: for first the greatness of the earth doth not suffer the true place of the Moon to be all one with her visible place. Secondly, the earth sometime taketh away the light of the Sun from the Moon, and so causeth her to be eclipsed. Thirdly, the Moon with her apparent magnitude taketh away the light of the Sun, causing the same in some parts of the earth to be eclipsed. And hereof dependeth the whole doctrine of the Eclipses, whereof we shall treat hereafter. In the mean time show what is the true place, and also what is the visible place of the Moon, or of any other star? THe true place of the Moon or of any other star, is appoint in the outermost heaven, determined by a right line being drawn from the very centre of the earth through the body of the Moon or star, unto the said outermost heaven. And the visible place to our sight, is a point in the outermost heaven, determined by a right line passing through the body of the Moon or star from our eye unto the said heaven, whilst we stand upon the upper face of the earth to behold the star. And the distance or portion of circle contained betwixt those two points, is called in Greek Paralaxis, which in English may be called the diversity of Aspects. All which things you may see plainly expressed in this figure following. THis figure as you see is made like a Quadrant: the neither right line whereof, commonly called the Base, signifieth the Horizon, and the perpendicular right line falling upon the same, and making therewith a right angle, is the axle-tree of the Horizon: and the said right angle, marked with the letter A, signifieth the centre of the earth, whose half globe, made like a half circle, is drawn upon the said centre, and the short line, marked with the letters A B, signifieth the semidiameter of the earth, & the letter F signifieth the Zenith, from which F to G is drawn the arch of the Quadrant, signifying here the Vertical circle. And you have to understand, that the right line that is drawn from A through the body of the Moon, marked with the letter C unto the point D, set down in the arch of the Quadrant or Vertical circle, showeth the true place of the Moon: and the right line drawn from B, through the body of the Moon unto the point of the foresaid arch, marked with E, showeth the apparent place of the Moon visible to our sight from the upper face of the earth: and the little arch contained betwixt D and E, is the Parallax or diversity of Aspects. And you have to note, that the apparent or visible place of the Moon is always lower in the heaven, than her true place, unless the Moon do chance to be in the right line of the Zenith, for then there is no Parallax at all, because both the lines and places do concur and meet in one, as the two lines A B and B F do show, making both one self line: and the further that the Moon is distant from the earth, the lesser is the Parallax, and the nigher that she is to the earth, the greater Parallax she hath. But the true quantity of her Parallax in every place is to be learned by the Prutenicall tables. And you have to understand, that the Astronomers do make the Parallax of the Moon to be threefold, that is, first simple, then according to longitude, and thirdly according to latitude. For if you have only respect to the Vertical circle, than it is said to be simple, which is before defined: but if you have respect to the Zodiac, than it is said to be sometime according to longitude, and sometime according to latitude. What is the Parallax according to longitude? IT is an arch of the Ecliptic, intercepted or contained betwixt two great circles drawn through the poles of the said Ecliptic; so as the one circle doth pass through the true place of the Planet, and the other great circle passeth through the apparent or visible place of the said Planet. What is the Parallax according to latitude? IT is an arch of a great circle, falling perpendicularly upon the Ecliptic, and is drawn either through the true place, or else through the apparent and visible place of the Moon, which arch is intercepted betwixt two circles, parallels to the Ecliptic, whereof the one passeth through the true place, and the other through the apparent place of the Moon. For the better understanding of all which things, it shall be necessary to set down here once again the Quadrant before described, together with his proper letters of signification; and then to add to the said Quadrant the Ecliptic line, and also the two circles which are parallels to the same; and thirdly, the two circles that are drawn from the pole of the Zodiac, so as the one may pass through the true place, and the other through the apparent place of the Moon: all which things this figure plainly showeth. A figure showing all the three kinds of Paralaxes. The description of the figure. FIrst the Quadrant of this figure, together with his former letters, do show the simple Parallax, otherwise called of some the mixed Parallax, because it comprehendeth both the other two Parallaxes, unto which Quadrant is added first the Ecliptic line, divided into degrees, and is signified by the letters I H: the arch whereof, marked with K L, intercepted betwixt the true and apparent place of the Moon, showeth the Parallax according to longitude: then the two circles, Parallels to the Ecliptic, which are marked with the letters N M, and Q P, through which two Parallels, and also through the Ecliptic are drawn from the pole of the Zodiac, marked with S, two great circles, whereof the one passeth through the true place of the Moon, marked with S D R, and the other passeth through the apparent place of the Moon, marked with S O E: so as each of the arches, intercepted betwixt the foresaid Parallels, that is to say, either D R or O E, signifieth the Parallax according to latitude; and the diagonal arch, marked with the letters D E, do show the simple or mixed Parallax. How the two Parallaxes of longitude and latitude are to be compared together. TO do this, it is first necessary to know what the 90 degree of the Moon is, which is a point in the Ecliptic, dividing that semicircle of the Ecliptic, which is above the Horizon, into two equal Quadrants, and is in the very midst of the said semicircle betwixt East and West: and this point is readily found by help of a celestial globe, in manner and form following. For first having set the globe at our latitude, which is 52, suppose the Moon to be in the first point of Taurus: here if you bring that point to the movable Meridian, you shall find, that the 17 of Leo then riseth above the Horizon, and that the 17 of Aquarius goeth down beneath the Horizon, which is the one half of the Ecliptic; of which half, by counting 90 degrees from the East point, that is, from the 17 of Leo, and so forward, you shall find, that the 17 of Taurus is the middle point or 90 degree, and the same to be nigher to the South than to the East. Now how to compare together the two foresaid Parallaxes, these five rules following do show. 1. First, if the Moon be in the 90 degree of the Ecliptic above the Horizon, than there is no Parallax of longitude, but only of latitude. 2. Secondly, when the Ecliptic passeth through the Zenith, there is no Parallax of latitude, but only of longitude. 3. Thirdly, when the Ecliptic passeth not through the Zenith, the two foresaid Parallaxes shall be differing one from another, and shall not fall one into another. 4. Fourthly, to those that have more latitude than 30 degrees, the Moon always appeareth more to the South, because her Parallaxes do always fall more Southerly. 5. Fiftly, the Moon from her rising until she come to the 90 degree, appeareth more Eastward: but from the 90 degree to her setting, she appeareth more Westward, as the globe plainly showeth. How to know whether the Moon be in the 90 degree, or not. YOu shall know this by observing the horns of the Moon, for if both the tips of the horns of the Moon do rightly hang one over another by a perpendicular line, than the Moon is in the 90 degree of the Ecliptic above the Horizon: but if the upper horn do more incline to the East than the neither horn doth, than the Moon is short of the 90 degree. But if the upper horn be more to the West, than the Moon is passed the 90 degree. And here I end with the description of the Parallax, and all the kinds thereof: minding now to treat of the Eclipses of the Sun and Moon, which are meet to be accounted amongst the chiefest Passions of these two Planets. ❀ Of the Eclipses of the Sun and Moon, and first of the Moon. THough this word Eclipse may be generally taken for the hiding or darkening of any star from our sight, yet here it is chiefly to be referred to the Eclipse of the Sun or Moon, which is the depriving of their light from the sight of us that dwell here upon the earth: but first we will treat of the Eclipse of the Moon, and show how and when it chanceth. The Moon having no light of itself, but only from the Sun, is never eclipsed, but when the earth is betwixt her and the Sun, which cannot chance, but when the Moon is at the full, and diametrally opposite to the Sun: and also when such Opposition is either in the head or tail of the Dragon, or somewhat nigh thereunto, which are nothing else but two sections of two circles, that is, the Ecliptic and the deferent of the Moon, cutting one another in two opposite points, otherwise called the two Nodes, which are before described in the Theoric of the Moon, and are also plainly declared in the first part of my sphere, chap. 15. But for so much as there be many other needful things to be known touching those two Eclipses, I mind here to treat thereof more at large. And first of the Eclipse of the Moon, showing first the causes why her eclipse is not always after one manner. Secondly, what shape the shadow of the earth hath at the time of her Eclipse, and how many kinds of shadows there be. Thirdly, how many ways she may be said to be eclipsed, either totally or in part. Fourthly, which be the bounds, within which she being at the full, may be eclipsed. Fiftly, how many points or digits she may be eclipsed. Sixtly, what things are to be considered touching the durance or continuance of her Eclipse, & how they are defined. And lastly, at what part the Moon beginneth to be eclipsed, and from what part her light is to her again restored. The causes why the Eclipse of the Moon is not always after one manner, but variable as well in magnitude as in continuance, are these four here following. 1. The first cause is the unequal latitude of the Moon, for sometime her latitude is very little or nothing at all, and then is her eclipse greater in magnitude, and longer in continuance: and sometime her latitude is so great, that she cometh but a very little within the shadow of the earth, and thereby looseth but a small portion of her light: and sometimes she cometh not within the compass of the shadow of the earth at all, and so she is not eclipsed. For this is a general rule, that when the latitude of the Moon, at the time of the true Opposition of the Moon and Sun is lesser than the sum of the two semidiameters, that is, of the shadow and of the moons body, being added together, there will be an Eclipse of the Moon. And the greater and more that the excess of those two semidiameters of the Moon and of the shadow is than her latitude, the greater and longer will the Eclipse be. And if the sum of those two semidiameters be just equal unto the latitude of the Moon, than she shall only touch the shadow, and so pass without any Eclipse. 2. The second cause of the change or variable shape of the eclipse of the Moon, is the unequal thickness of the shadow of the earth: for the higher that the shadow of the earth ariseth, the more narrow it groweth, ending with a sharp point, because the body of the Sun is greater than the body of the earth, and therefore the shadow cannot be of any other shape than conical: for there be three kinds of shadows, that is, conical, cylindrical, and Calathoidall. The shadow conical is that which endeth with a sharp point. The cylindrical is of like bigness everywhere, like a round pillar. And the Calathoidall shadow, the further it extendeth, the greater it is, like a cup or bowl, that is narrow at the bottom and broad at the brim; of which shape that shadow taketh his name, for Calathos in Greek is as much to say as a cup: as these three figures do plainly show. conical. cylindrical. Calathoidall. ANd it is to be noted, that when the Moon is in the lower part of her Epicicle near unto the opposite Auge thereof, her Eclipse continueth longer than it doth when she is near unto the Auge of her said Epicicle. 3. The third cause is the variable thickness of the shadow which the earth yieldeth, according as the Sun is either in the Auge or opposite Auge of his Eccentric, as you may easily perceive by this figure following, consisting of three circles and certain right lines. 4. The fourth cause of the variety of her Eclipses is her unequal moving in her true motion, either swift or slow, for when she is in her swift motion, the continuance of her Eclipse must needs be shorter than when she is in her slow motion. And to know her hourly motion, either mean or true, is to be found by the Prutenicall tables. But now though her Eclipse be thus variable, as you see, yet such variety may be brought into two chief heads, that is, when she is said to be totally, or partly, eclipsed; whereof we come now to speak. The total Eclipse of the Moon is twofold, that is, either without any continuance of time, or else with some continuance of time. In the former, so soon as she hath lost her whole light, she presently beginneth to recover the same again: but in the latter, she being wholly eclipsed, the same continueth some quantity of time. The first way chanceth when the latitude of the Moon and the semidiameter of her body being both added together, the sum thereof is equal unto the semidiameter of the earth, as this figure plainly showeth. ¶ The first figure belonging to the Eclipse of the Moon. IN which figure, the great black circle signifieth the shadow of the earth, and the three lesser circles being all of like bigness, each of them representeth the body of the Moon: and what the right lines do signify, the letters do show: for the letters B D do represent the semidiameter of the shadow of the earth, when the Moon is eclipsed: and B K showeth the latitude of the Moon from the Ecliptic, which Ecliptic is marked with the letters A C. Now K D signifieth the semidiameter of the Moon's body, and the letter I showeth the centre of her body in the beginning of her Eclipse, and the letter H the centre of her body at the end of her Eclipse. And the right line I K H signifieth the way of the Moon during the time of her Eclipse. Here for so much as the two semidiameters D K, and K B, being both added together, are equal unto B D, which is the semidiameter of the shadow, you may perceive, that the Moon being in the point I, began to lose her light by little and little, until she came to the point K, and there was wholly darkened, from whence she presently began again without any stay to recover her light, until she came to the point H, whereas she is fully restored again to her light. The second kind of total Eclipses of the Moon, is when she is wholly eclipsed, and the same continueth some quantity of time, which always happeneth when the semidiameter of the shadow of the earth in the place of the Eclipse, is greater than the latitude of the Moon and of her bodily semidiameter being both added together: as this second figure next following plainly showeth. ¶ The second figure belonging to the Eclipse of the Moon. IN which figure, suppose the semidiameter of the shadow of the earth in the place of the Eclipse to be the line BK, and the line B D to be the latitude of the Moon at the time of the middle of the Eclipse from the Ecliptic, marked with the letters A C, and the line R D to be the semidiameter of the Moon, & H I to be the way of the Moon in the time of her darkness, and I to be the place of the beginning of her Eclipse, and H the ending of the Eclipse, and M her place when she is wholly darkened, and L her place when she beginneth to recover her light again. Now you see, that when she cometh to the point M, she is wholly eclipsed, like as she is also when she cometh to the point L, and because she spendeth some quantity of time in going from M to L, and is wholly darkened, therefore is this called a total Eclipse with continuance. Thus much touching the total Ecllipse of the Moon, now we will speak of the Partial Eclipse of the Moon. The Partial Eclipse is when some part of the Moon is darkened, and not the whole: and of this Partial Eclipse there are three sorts. The first is, when half of the moons diameter is darkened, and the other half keepeth still her light, which happeneth when the latitude of the Moon is equal unto the semidiameter of the shadow of the earth in the place of the Eclipse, as you may perceive by this third figure next following. ¶ The third figure belonging to the Eclipse of the Moon. IN which figure, B D signifying the latitude of the Moon from the Ecliptic A C, is just equal unto the semidiameter of the shadow of the earth, marked also with B D. The second sort of partial Eclipse of the Moon, is when a lesser part than the semidiameter of the Moon is darkened, which happeneth when her latitude is more than the semidiameter of the shadow of the earth, as you may see by this fourth figure. ¶ The fourth figure belonging to the Eclipse of the Moon. IN which figure B K signifieth the semidiameter of the shadow, and B D signifieth the latitude of the Moon: now for that B D is more than B K, you see that there is but a little of her light taken away by the shadow of the earth. The third sort of Partial Eclipses is, when more than the semidiameter of the Moon is darkened: which happeneth when the latitude of the Moon is less than the semidiameter of the shadow of the earth, as you may see by this fift figure. ¶ The fift figure belonging to the Eclipse of the Moon. IN which figure, B D signifying the latitude of the Moon, is less than B K, representing here the semidiameter of the shadow, and therefore more than the semidiameter of the Moon is eclipsed. How to know the bounds or limits, whereby is easily known what kind of Eclipse of the Moon will happen when she is at the full. THe limits are most certainly known by the latitude of the Moon at the time of her true opposition to the Sun: for if you find the latitude of the Moon by the Prutenicall tables, or otherwise, to be more than the sum of the semidiameters of the shadow and of the Moon being added together, then there will be no Eclipse at that full, but if the latitude of the Moon be less than the sum of the two said semidiameters added together, you may be sure, that the Moon will be eclipsed at her full: so that the terms or bounds of the Eclipses are known by comparing the latitude of the Moon with the sum of the foresaid two semidiameters being added together. The least sum of which two semidiameters, that is to say, of the Moon and of the shadow of the earth is i/53 ii/53 which is, when the Moon is in the Auge of her Epicicle, and the Sun in the opposite Auge of his Excentrique, and that in his least excentricity. But the greatest sum of the said apparent diameters that can be, is one degree, i/7 ii/5 which happeneth when the Moon is in the opposite Auge of her Epicicle, and the Sun in the Auge of his Excentrique, and that in his greatest excentricity. And hereof you may gather these three rules. First, if the latitude of the Moon at the time of her true opposition to the Sun be less than i/53 ii/53 she must needs be eclipsed. Secondly, if her latitude be more than i/67 ii/52 she cannot be eclipsed at the Full. Thirdly, if her latitude be more than i/53 ii/5 and less than i/67 ii/52 than she may happen to be eclipsed, but not necessarily. And these bounds or limits may also be determined by the distance of the Moon from any of the two Nodes, that is, from the head or tail of the Dragon, which distance is never less than 10 degrees, i/22 neither at any time greater than 13 degrees, i/5 which bounds or limits are set down by Ptolomey thus. If the distance of the Moon at the time of her true Opposition from either of the two Nodes, be less than 12 degrees, i/12 or if the said distance of the Moon from either of the said Nodes at the time of her mean Opposition, be less than 15 degrees, and i/12 (the said distance being reckoned either according to the succession of the signs, or contrary to the succession of the signs, upon the Ecliptic) then the Moon may be eclipsed. Of the twelve Digits, whereinto the body of the Moon is wont to be divided, to know thereby how much at any Full she is eclipsed. THough that the diameters of the Moon and of the shadow may be accounted by degrees and minutes, yet notwithstanding, the magnitude or greatness of her Eclipses is usually reckoned by digits, or inches, by dividing the diameter of her body into 12 equal parts, because her diameter appeareth to our sight as it were a foot in length: and therefore as the foot is divided into 12 inches, so is the diameter of the Moon supposed to be also divided into 12 parts, which parts are called digits or points, and by them is the greatness of her Eclipse determined, and therefore they be called Eclipticall digits or points. And although that the diameter of the Moon is divided but into 12 digits, yet nevertheless the Eclipse of the Moon may sometimes happen to be very near 23 digits, by reason of the thickness of the shadow of the earth, whose semidiameter sometime exceedeth the diameter of the Moon, and such excess is wont to be divided also into 12 such parts as is the diameter of the Moon, and so the Moon may be eclipsed more than 12 points, as you may more plainly perceive by this sixth figure next following. ¶ The sixth figure belonging to the Eclipse of the Moon. IN which figure, the letters DK representeth the semidiameter of the shadow, and R S the diameter of the Moon at the time of her greatest darkness. Now supposing the said R S to be divided into 12 equal parts, the said 12 parts are called the Eclipticall digits: & for that some part of the semidiameter of the shadow, namely, S K, extendeth further than R S, which is the diameter of the Moon, the overplus SK is supposed also to be divided in this Eclipse into certain equal parts, namely into three such parts, as the diameter of the Moon containeth 12, so as the eclipticall digits in this Eclipse are 15: for you may easily perceive, that if the semidiameter of the Moon were longer by three digits than it is, yet it might be wholly eclipsed: and as you see the number of eclipticall digits in this Eclipse to be 15: even so the number of the said digits may amount sometime to be 22 digits and 51 minutes. For you may remember that I said before, that the sum of the semidiameter of the Moon and of the shadow being added together, may sometimes happen to be i/69 ii/52 when the Sun is in his greatest excentricity, and in the Auge of his Excentrique, and the Moon in the opposite Auge of her Epicicle: at which time the semidiameter of the Moon, is i17 ii/49 and so consequently her whole diameter is i/35 ii/38 than say by the rule of proportion, if i/35 ii/38 are equal unto 12 digits, what shall i/67 ii/52 be equal unto? so shall you find the fourth proportional number to be 22 digits and 51 minutes: and this is the greatest number of Eclipticall digits, that any Eclipse of the Moon can have. And the more Eclipticall digits that any Eclipse hath, the longer is the time of durance or continuance thereof. Of the continance of the moons Eclipse, what it is, and how many things are wont by the Astronomers to be considered therein. THe continuance of the Eclipse is that space of time which she spendeth in going from the very beginning of the Eclipse to the midst of the same, whereas she is most darkened. And these five things are wont therein to be considered, that is, the minutes of Incidence, the minutes of the half continuance, the time of Incidence, the time of half continuance, and the half continuance itself. 1. And first you have to note, that the minutes of Incidence are accounted in partial Eclipses after one way, and in total Eclipses with continuance another way: for in partial Eclipses & also in total Eclipses without continuance, the minutes of Incidence are said to be the arch of the moons way which she maketh in her moving of longitude from the beginning of her Eclipse to the midst thereof, where she is fully darkened, as appeareth by the third, fourth, and fift figures of partial Eclipses before set down: in all which, the point L signifieth the place of the Moon at the beginning of her Eclipse, and the point D the place of the Moon at the middle of her Eclipse. Now the arch of her way from L to D, is called the minutes of Incidence, for so long her light decreaseth by little and little, until so much be taken away, as can be in any of those partial Eclipses. But if the Eclipse be total, without any continuance, as in the first figure, than the way of her motion in going from the point I unto the point K, where she is wholly darkened, is called the scruples of Incidence. But if the total Eclipse have any continuance, than the minutes or scruples of Incidence are that portion of the Ecliptic, through which the Moon goeth from the very beginning of her Eclipse, until the time that she be wholly eclipsed, as in the second & last figures the letter I signifieth the point, in which the Moon is at the beginning of her Eclipse, and M the point in which she is fully darkened: and the arch I M is called the minutes or scruples of Incidence, and these minutes in the end of the Eclipse are called minutes of repletion, as in the third, fourth, and fift figures, the arch of the Moon's way, namely D M, or K H in the first figure, or L H in the second and last figures, do show: which minutes of repletion are reckoned from the very time of the beginning of her clearing unto the time that she hath fully recovered her whole light: and the minutes or scruples of repletion are equal to the minutes or scruples of Incidence. 2. The second thing which is considered in accounting of the continuance of Eclipses, is the scruples of half continuance, which is nothing else but the arch which the Moon maketh in going from the Sun, from the time of her whole darkness unto the very middle of the Eclipse: from which middle Eclipse, the Moon going still forward until she begin again to recover her light, the said arch is called the scruples of Emersion, as in the second and last figures the arch M D doth show, whereof M representeth the place in which she looseth her whole light, until she come to the point D, which signifieth her place when she is in the middle of her Eclipse, or in her diametral Opposition to the Sun. And this is called the scruples of half continuance: but the arch of her motion from D to L, where she beginneth again to receive her light, is called the minutes of Emersion, and these minutes of Emersion are equal unto the scruples of half continuance, as the scruples of Repletion were equal unto the minutes of Incidence. 3. The third thing to be considered in accounting the Eclipse of the Moon, is the time of Incidence: which is nothing else but the very time which the Moon spendeth in going of the minutes of Incidence, or the time of Incidence is that portion of time which the Moon spendeth in moving from the beginning of the Eclipse unto the point where she is most darkened (if the Eclipse be partial) as in the third, fourth, and fift figures, the time which the Moon spendeth in her moving from the point L, where she beginneth to be eclipsed unto the point D, where her darkness is greatest, is called the time of Incidence. Likewise if the Eclipse be total, the time which she spendeth in moving from the beginning of the Eclipse, unto the point in which she is wholly obscured, as in the first figure the time which she spendeth unto her moving from the point I unto the point K, so the time which she spendeth in going from I to D, in the second and last figures is called the time of Incidence. 4. The fourth thing to be considered, is the time of half continuance, which is that quantity of time which the Moon spendeth in her moving from the point in which she looseth her whole light, unto the point of the middle Eclipse, as in the second and last figures the time which she spendeth in going from the point M to the point D, is called the time of half continuance. And the time which she spendeth in her moving from D to L, in the said second and last figures is called the time of her Emersion: which time is equal unto the time of half continuance, saving that the variable motion of the Moon being swifter in the one than in the other, may make a little difference, which in so short a time cannot be sensible. And in like manner, the time of Repletion is equal unto the time of Incidence, unless the variety of her motion do make a little unsensible difference. 5. The last thing that is to be considered in the continuance of the Eclipse, is the half time of durance, which is nothing else but the time which the Moon spendeth in going from the point in which she began to be eclipsed, unto the point of the middle Eclipse: and this time is equal to the time of Incidence in Partial Eclipses, as in the third, fourth, and fifth figures, the time which she spendeth in going from L to D, is the time of half durance: and likewise the time which she spendeth in her moving from I to K in the first figure, is the time of half durance: but if the Eclipse be total with continuance, then is the time of half durance equal unto the time of Incidence, and also to the time of half continuance, being both added together. Furthermore, you have to note, that the Eclipse of the Moon doth always begin on the East side of her body (I call that the East side which is towards the East) for sith that her motion is from West to East, and that very swift, in respect of the Sun or of the shadow of the earth, it must needs follow, that the East side of her body first toucheth the shadow in the beginning of her Eclipse, and so continueth her moving through the said shadow, leaving the same behind her on the West side of her body. And although that this be true in all Eclipses of the Moon, yet in partial Eclipses, if the latitude 〈◊〉 if the Moon be North, then is the South part of her body darkened, but if her latitude be South, then is the North part of her body darkened. And note, that whensoever any Eclipse doth happen the said Eclipse may be seen of all them, above whose Horizon she is in the time of her Eclipse, and that at one self instant or moment of time, be it the beginning, middle, or ending of any such Eclipse: but it is not so in the Eclipse of the Sun, neither can any other of the Planers be eclipsed or darkened by the shadow of the earth, because the same shadow reacheth not so high as any of the three higher Planets are: and as for Venus and Mercury, their place is always so nigh unto the place of the Sun, as they cannot be eclipsed at any time. Thus much touching the Eclipse of the Moon, and now I will speak of the Eclipse of the Sun. Of the Eclipse of the Sun, how and when it chanceth. THe Eclipse of the Sun is nothing but the darkening or depriving of his light from our sight, caused by the interposition of the body of the Moon betwixt the body of the Sun and the body of the earth: and this Eclipse never happeneth but when the Moon and the Sun are in a visible Conjunction. For you have to note, that there be three kinds of Conjunctions, that is, mean, true and visible, or apparent to our sight. What the mean and true Conjunction is, hath been before defined: and it is called a visible Conjunction, when a right line being drawn from our eye or sight, passeth through the centre of the Moon unto the centre of the Sun, whereby the said two Planets appear to our sight to be in one self degree 〈…〉, that is to say, in one self point of the Ecliptic. For although that the centre of the Moon be betwixt the centre of the Sun and the centre of the earth at every true Conjunction, and also near to any of the Nodes, yet perhaps it shall appear no Eclipse to our sight, because the two Planets be not in a visible Conjunction, as have been demonstrated before, when we did speak of the Parallax, whereupon chiefly dependeth the knowledge of the Eclipses: neither can the body of the Moon, being far lesser than the earth, possibly shadow at any time all the earth: and the body of the Sun is far bigger than either of them both, by reason whereof, the Eclipse of the Sun may chance to one part of the earth, and not to another: neither can any Eclipse of the Sun or Moon chance, but when those two Planets are either in the head or tail of the Dragon, or else very nigh the same. All which things you shall better understand by this figure here following. ¶ The first figure belonging to the Eclipse of the Sun. THis figure as you see consisteth of certain circles, both greater and lesser, and of certain right lines: in which figure, the highest circle signifieth the body of the Sun, whose centre is marked with the letter P: and the middle lesser circle beneath that, made most part black, signifieth the body of the Moon eclipsed, whose centre is marked with the letter C, and the diameter thereof is marked with the letters L K: and the lowest lesser circle representeth the body of the earth, whose centre is marked with the letter A: and the two great circles, crossing one another in two points opposite, that is to say, in C, where also would be set the character of the Dragon's head; and in the other cross point opposite, is set the character of the Dragon's tail; of which two circles, the one is called the deferent of the Moon, and the other the Ecliptic. Now what the right lines do signify, the letters do show: for the two outermost right lines, F H, and G I, do signify the outermost beams of the Sun, which do fall upon the earth: but the two inner lines F L, and G K, do signify the beams of the Sun which do fall upon the Moon: which two lines being drawn out in length, do concur and meet in the point A, representing the centre of the earth, and thereby do make the cone to be F A G, the axletree of which cone, is the right line P A: and the little shadowed cone, marked with the letters L K A, signifieth the cone of the moons shadow at the time of a true Conjunction, when the Sun is eclipsed; the axle●ee of which little cone is signified by the line C A: and the two lines, K E, and L D, do signify the outermost sides of the moons shadow, falling upon the earth in the two points D and E. Now hereby you may perceive, that those people which have their dwelling betwixt D and E, are wholly deprived of the light of the Sun: but those that dwell betwixt E and I, or betwixt D and H, do still retain the light of the Sun. Moreover, the Sun is to some inhabitants of the earth totally eclipsed, and to some partly, and to some nothing at all, as this figure next following doth plainly show. ¶ The sec●nd figure belonging to the Eclipse of the Sun, with the description thereof. THis figure as you see consisteth of three circles and certain right lines: of which circles, the highest and greatest representeth the body of the Sun, whose centre is marked with P: and the middle little circle, made almost all black, signifieth the body of the Moon, whose centre is marked with the letter C, and her semidiameter with C B, and her whole diameter with L K, and the small upper portion of her body, made white, is that which is lightened by the Sun, all the rest of her body being darkened. The third and lowest circle being greater than that of the Moon, signifieth the body of the earth, whose centre is marked with A, and the semidiameter thereof with A E. Now as touching the signification of the right lines, the letters thereto belonging do show: for the outermost lines marked with QUEEN'S K, and O L, do signify the outermost beams of the Sun that do fall upon the body of the Moon, concurring or meeting in the point I, enclosing the conical shadow of the Moon, marked with the letters L K I, the axle-tree of which conical shadow is the middle line C I, for to those that dwell upon the earth under the point I, the Sun is totally eclipsed, and to those that dwell under the point N, he is partly eclipsed, and partly not, and to those that dwell betwixt N and H, he is not eclipsed at all. Again, the Moon is not always right under the Ecliptic line, as the Sun is, and therefore her shadow at the time of the Eclipse cannot point to the centre of the earth, as it doth when she is in either of the two Nodes: but sometime Northward and sometime Southward from the centre of the earth, according as her latitude is either Northerly or Southerly: so likewise her said shadow after every true Conjunction will point Eastward, and before a true Conjunction Westward. And further you have to note, that the true and visible Conjunctions do never happen together, except the true Conjunction of the Sun and Moon chance to be in the 90 degree, which what it is, is before declared, for in the 90 degree there is no Parallax at all. But in all other places, the true and visible places do differ, and the visible Conjunction is before the true Conjunction, if the said true Conjunction be in the East part of the Zodiac, that is, betwixt the Sun rising and the 90 degree. But if the true Conjunction be in the West part of the Zodiac, that is, betwixt the 90 degree and the Sun setting, than the true Conjunction is before the visible Conjunction. And generally, the further that the true Conjunction is from the 90 degree, the greater is the difference betwixt the true Conjunction and the visible Conjunction, which things are before fully declared, whereas I speak of the Parallax, and by help of the celestial globe are easily perceived. Of the variety of the Solar Eclipses, and why they be not always like, but do differ as well in magnitude as in time of continuance. OF this variety there be four causes. 1. First, the unequal apparent latitude of the Moon: for the greater that the latitude of the Moon is, the lesser and shorter is the Eclipse of the Sun: but the lesser that her latitude is, the greater and longer is the Eclipse of the Sun. For this is a general true rule, that if the apparent latitude of the Moon at the time of the visible Conjunction be greater than the sum of the two semidiameters of the Sun and of the Moon, being both added together, than the Sun shall not be eclipsed at the visible Conjunction: but if the apparent latitude of the Moon be less than the sum of the two said semidiameters, being added together, then shall the Sun be eclipsed at that visible Conjunction: and the greater that the difference betwixt the sum of the two semidiameters, and the moons latitude is, the greater is the Eclipse of the Sun. 2. The second cause of the varieties of the Eclipse of the Sun, is the unequal distance as well of the Sun as of the Moon, from the earth: for the changing of their distances from the earth, maketh the diameters of their bodies to appear greater or lesser. For the nearer that they approach to the earth, the greater do their diameters appear unto us: for when the Sun is in the Auge of his Excentrique, and therewith in his greatest excentricity, the semidiameter of his shadow is i15° ii40° But if he be in his greatest excentricity, and in the opposite Auge of his Excentrique, than his semidiameter is i17° ii2° which is greater than it was before by i1° ii/22 And if the Sun be in his least excentricity (as it is almost in these our days) and also in his Auge, than his semidiameter is i15° ii49° but being in the opposite Auge of his Excentrique, than his semidiameters is ii/16 i2° which is greater than it was before by i1° ii3° Likewise, when the Moon is in her Auge, whether it be at her Conjunction with the Sun, or at her Opposition to the Sun, her semidiameter is but i15° ii0° but being in her opposite Auge, her semidiameter will be i17° ii49° which is greater than it was before by i2° ii49° whereby it happeneth, that sometime the whole body of the Sun seemeth to be darkened, and at other times but some part of his body, and that either at some side thereof, or else in the very midst of his body, and then there appeareth round about him a narrow bright circle, which we commonly call a borough, all the other part in the midst of his body being darkened. 3. The third cause of the variety of the Solar Eclipses, is the twofold inequality of the moons motion, whereof the first dependeth upon the motion of her Epicicle, whereby she is sometimes swift, and sometimes slow of ga●e. And the second inequality of her motion happeneth by reason of her Parallax, which maketh her motion to appear variable every hour, and thereby her apparent motion is also sometime swift & sometimes slow. And it happeneth, that not only the time of the continuance of the Eclipse altereth, but also the time of Incidence is made to be unequal unto the time of repletion. 4. The fourth cause of the inequality of the suns Eclipses, is the small quantity of the body of the Moon, in respect of the Sun, or of the Earth, and the small distance of the Moon from the Earth: for by these two means neither can the Solar Eclipses appear of a like bigness in all places in which they may be seen, neither yet can the said Eclipses be seen at one time in all places of the earth, as was showed before. Lastly, by these two means it happeneth that the Eclipse of the Sun appeareth not at one self time in divers places, and it beginneth sooner to them which dwell Westward, than to those which dwell Eastward, in such sort, as the said Eclipse of the Sun will be ended in one place before it begin in another. And thus much touching the causes of the variety of the Eclipses of the Sun. Of the two special kinds of Solar Eclipses, that is, total and partial. THe total Eclipse is when the Sun is wholly darkened, or seemeth to us to have lost his whole light, and this Eclipse is always without continuance, which happeneth when the Moon hath no apparent latitude at the time of the visible Conjunction, as this figure plainly showeth. ¶ The third figure belonging to the Solar Eclipse. IN which figure, suppose the letter A to be the centre of the suns body, and the line A H to be the semidiameter of his body, and D B to be the Ecliptic line, and A B to be the semidiameter of the circle, in which the Moon is at the beginning and ending of the Eclipse, and the line F G to be the way of the moons motion, during the time of the Eclipse, crossing the line D B in the point A, which point A may also signify the head or tail of the Dragon, and the letter F signifieth the South latitude, and G the North latitude: and the point F doth also signify the centre of the Moon at the beginning, and G the centre of the Moon at the ending of the Eclipse, and the line R F or G S doth signify the semidiameter of the body of the Moon. Now you see, that the Moon by her motion cometh by little and little to shadow the light of the Sun until she have moved from the point F, where the Eclipse began, unto the point A, where his whole light is taken away; and then without any stay she moveth on forward from the point A unto G, where the Eclipse endeth. And although it falleth out sometimes, that the Moon doth shadow more than the body of the Sun (which is very seldom or never, although it may so happen) yet doth the total darkness continue so little a time, as it is insensible: and therefore the total Eclipse of the Sun is always without continuance. Of the Partial Eclipse of the Sun. THe Partial Eclipse of the Sun is when some part of the suns light is taken away, and not all his body darkened; and of this kind there are three sorts. 1. The first is, when the semidiameter of the Sun is darkened: which happeneth when the apparent latitude of the Moon is equal unto her apparent semidiameter. 2. The second sort is when more than the semidiameter of the Sun is darkened, which happeneth when the apparent latitude of the Moon is less than the apparent semidiameter of her body. 3. The third, is when less than the semidiameter of the body of the Sun is darkened, which happeneth when the apparent latitude of the Moon is greater than the apparent semidiameter of her body. Of all which three kinds, I have set an example in these three figures here following. ¶ Three figures showing the three kinds of the suns Partial Eclipses. OF which figures, the first showeth the first kind of Partial Eclipse, the second figure showeth the second kind, and the third figure showeth the last kind of Partial Eclipses. In every of which figures, the letter A signifieth the centre of the Sun, and the semidiameter of his body is the right line A B, and upon the centre A is drawn a great circle, marked with the letters C S D L, whereof the letter C signifieth the North, D the South, L the West, and S the East: unto which circle when the Moon cometh on the West part, the Eclipse of the Sun beginneth; and it endeth when the Moon cometh to the said circle on the East side. And the right line S L signifieth the Ecliptic line, and the right line H I signifieth the deferent of the Moon: and the point marked with the letter E, signifieth the place of the Moon at the beginning of the Eclipse, and G her place at the ending of the Eclipse, and F her place at the middle of the Eclipse, or at the time of her greatest darkness: and the right line F V in the second figure is the semidiameter of the Moon at the time of her greatest darkness. The characters of the Nodes on the East or West side of any of the foresaid figures do show what way the head or tail of the Dragon doth stand, and to which of the Nodes the Eclipse is nearest. Of the bounds or limits of the Solar Eclipses. ANd now that you know the several kinds of Eclipses, it will not be hard to judge which of them will happen at the time of any Eclipse of the Sun, especially if you know the bounds or limits within which the Eclipse of the Sun must needs be before he can be eclipsed: which bounds cannot be better determined, than by the apparent latitude of the Moon; for if the said latitude be more than the two semidiameters of the Sun and of the Moon being both added together, it is impossible that the Sun should be eclipsed at that Conjunction: but if the apparent latitude be less than the said two semidiameters, then may the Sun be eclipsed: and the least sum of the two semidiameters of the Sun and Moon that can be (which is when both the Sun and Moon are in the Auges of their orbs, and the Sun in his greatest excentricity) is i30. ii40. and the greatest sum of the said two semidiameters that can be, is but i34. ii1. from hence you may gather these three rules here following. 1. First, if the apparent latitude of the Moon at the time of the visible Conjunction be less than i30. ii40. it cannot be but that the Sun must be eclipsed. 2. Secondly, if the apparent latitude of the Moon at the time of the visible Conjunction be more than i30. ii40. and less than i34. ii31. it may be that the Sun shall be eclipsed in some part at the time of the visible Conjunction. 3. Thirdly, if the apparent latitude of the Moon be more than i34. ii51. the Sun cannot lose any of his light. But Ptolomey determineth the said bounds of the Solar Eclipses by the distance of the Moon from either of the two Nodes: for if the Moon be distant from either of the Nodes 20 degrees, i40. towards the North, or 11 degrees, i20. towards the South at the time of the mean Conjunction, than it may fall out that the Sun shall be eclipsed: but if she be further distant from the said Nodes at the time of the mean Conjunction, then cannot the Sun be eclipsed. And note, that Ptolomey maketh the North bounds bigger than the Southern bounds, because of the Parallax. And this distance from the Nodes may be reckoned either according to the succession or contrary to the succession of the signs. Of the Eclipticall digits belonging to the Solar Eclipses. AS the Eclipticall digits of the Moon were 12, so likewise are there 12 Eclipticall digits of the Eclipse of the Sun; but the Eclipse of the Sun can never exceed 12 digits and 15 minutes: for the greatest apparent semidiameter of the Moon is but i17. ii49. and the least apparent semidiameter of the Sun is i15. ii40. which two semidiameters if you add together, the sum will be i33. ii29. Then having doubled the least semidiameter of the Sun, which is i15. ii40. the sum will be i31. ii20. which is the least apparent semidiameter of the Sun: then say by the rule of proportion, if i31. ii20. be equal to 12 digits, to what or how much shall i33. ii29. be equal? so shall you find the fourth proportional number to be very near 12 digits and 50 minutes: and this is the greatest number of Eclipticall digits that any Eclipse of the Sun can have. And this may happen when the Sun is in the Auge of his Excentrique, and in his greatest excentricity: and the Moon in her opposite Auge, and therewith in such places as are situated within the compass of the moons shadow, the diameter of which shadow may at that time be very near 280 miles in length of our English miles, or 70 German miles, within which compass whosoever dwelleth, may lose the whole light of the Sun at that Eclipse. And you shall know the number of the Eclipticall digits by the 62 precept of the Prutenicall tables. And many times it may fall out, that although the Moon haae no apparent latitude, yet the Eclipse of the Sun will not be so great, for if the Moon be in her Auge, and the Sun in the opposite Auge of his Excentrique, and therewith in his least excentricity, the number of the Eclipticall digits can be no more but 11 degrees, and 15 minutes, so as the Sun will appear to have lost his light in the very midst; and round about that Eclipse will appear a little circle as it were three quarters of an inch in breadth. All which things touching the Eclipticall digits, will not be hard to conceive, if you remember what was spoken of this matter in the Eclipses of the Moon. What things are to be considered touching the continuance of the Solar Eclipse. IN accounting the continuance of the Eclipse of the Sun, the Astronomers do only observe two things. 1. The first is the scruples of Incidence, which are nothing else but the way or arch of the circle of the moons deferent, in which she goeth from the beginning of the Eclipse unto the middle of the same: which in the three last figures is signified by the line E F. 2. The second thing which they usually observe, is the time of Incidence, which is nothing else but the quantity of time which the Moon spendeth whilst she is in going of the said minutes of Incidence: both which two things you shall easily find, as also the minutes of repletion, by the 63 precept of the Prutenicall tables. And as the Eclipse of the Moon doth begin on the East side of her body and endeth on the West side thereof, even so the Eclipse of the Sun beginneth on the West side of his body, and endeth on the East; which happeneth by the motion of the Moon, which motion is from West to East: and if the Eclipse of the Sun be partial, and the apparent latitude of the Moon be North, then is the North side of the Sun eclipsed, and the South side retaineth still his light: but if her apparent latitude be South, then is the South side of the Sun darkened, and the North side keepeth still his light. And this is a general observation, that no Eclipse of the Sun is universal (except that which was against nature at the death of Christ) but always particular, that is, it may be seen in some few places, but not in all places of the world: neither doth it begin or end in all places at one self instant, neither doth it appear in all places of one self bigness, or of one shape, but in one place is total, and in another place at the same time Partial, and in other places again there appeareth no Eclipse at all. The causes of which diversity have been before declared. How to find out the quantities, increasing, decreasing, beginning, and ending of the Sun's Eclipses, without any offence of your eyesight. Having learned by the Ephemerideses, or by some other Almanac at what time the Eclipse shall be, resort to some tower or high fit, the higher the better, and see that the place whereas you would make your observation, be without light, and so dark, as you can possibly make it, leaving only a little hole or rift, through which the beams of the Sun may streeke through: and upon the pavement or on the wall that looketh right against that hole or rift, behold what light the Sun yieldeth, for that light will represent the true shape of the Sun at that present, and plainly show so much portion to be wanting from the lightsome circle, as the Moon coming betwixt the Sun & the earth, doth take away from our sight. Wherefore if you divide the diameter of the said lightsome circle into 12 parts or points, which the Astronomers do call digits, you shall find out all the things above mentioned, without looking up to the heaven. The Methodical doctrine of the Eclipses, set down by Reinoldus in his Commentary upon Purbachius. FIrst Ptolomey found out the true latitude of the Moon, and divided the same from her apparent latitude, as he teacheth in the 12 chapter of his fift book: for in the Eclipses of the Moon it is very necessary to have knowledge both of her true latitude, and also of her apparent latitude, for the Eclipse of the Sun without having knowledge of her apparent latitude, and of her Parallaxes, can never be well foreknown: and by this he did not only judge of other things, but also by a Geometrical way found, that the greatest distance of the Moon from the earth, she being either at the change or at the full, did contain 64 semidiameters of the earth, and one sixth part. Moreover, by other observations he did know the proportions of the semidiameters, as well of the Moons excentrique, and of her Epicicle, as also of her excentricity. Then by other observations he sought out the quantities of the apparent diameters of the Sun, of the Moon, and of the shadow, as well at the new Moon, as at the full, in manner and form following: for first by the help of an instrument, having a Diopter, he found the Sun and Moon to be in one self angle when she was most distant from the earth. Then he attributed to the Moon two Eclipses, in the one whereof, when her latitude was i48. ii30. the shadow darkened one quarter of her diameter: and in the other Eclipse, the shadow darkened the one half of her diameter, when as her latitude was i40. ii40. and in either of the Eclipses the Moon was very nigh to the height of her Epicicle. Hereof it manifestly appeared, that a quarter of the moons diameter, when she was most distant from the earth, contained in heaven according to our aspect, i/57. ii/0●. which being reckoned four times, do show that the diameter of the Moon was at that time i31. ii20. whereunto the observed diameter of the Sun was then equal: and the semidiameter of the shadow in the later Eclipse did appear to be i40. ii40. for the centre of the moons body did then touch the outermost brim of the shadow. Hereby it likewise appeareth, that the diameter of the shadow hath such proportion to the diameter of the moons body, as 13 hath to 5, and keepeth the self-same proportion in all other Eclipses of the Moon: and though it most manifestly appeareth by this, that the diameter of the shadow doth exceed in greatness the diameter of the Moon, yet it followeth not by & by thereof, that the Moon is lesser than the earth. Now therefore Ptolomey by comparing according to the doctrine of plain triangles, the semidiameters of the Moon and of the shadow together with the distance of the said Moon, being measured by the semidiameters of the earth, he found the semidiameter of the Moon only to contain i17. ii●3. and the semidiameter of the shadow to contain i45. and ii38. such like minutes, I say, as the semidiameter of the earth hath 60. And therefore it appeareth hereby, that either of the semidiameters, that is, of the Moon, or of the shadow, is less than the semidiameter of the earth: for the semidiameter of the earth is almost in like proportion to the semidiameter of the shadow, as 4 is to 3, and being compared to the semidiameter of the Moon, it is almost in such proportion, as 17 is to 5: whereof it followeth necessarily, that the shadow of the earth is conical, that is, round, growing to a sharp point, and therefore the Sun must needs be greater than the earth. Neither could any right judgement have been made touching the quantities of the said three bodies, that is, the Sun, the Moon, and the earth, unless that the Parallaxes of the Moon had first showed the distance of the Moon from the earth, the said distance being measured by the semidiameters of the earth. For if you suppose the distance betwixt the Moon and the earth to be 48 semidiameters of the earth, you shall find that the semidiameter of the shadow will be altogether equal to the semidiameter of the earth, and so the shadow shall be cylindrical, that is to say, in all parts round like a pillar. And if you suppose the said distance of the Moon from the earth to be greater, as to be 170 semidiameters of the earth, than the semidiameter of the shadow (the Moon being in Transit●) will contain two semidiameters of the earth, and so the shadow shall be Calathoidall, that is to say, like a cup or top, extending together with his length in breadth and wideness more and more infinitely. All which three shapes of shadows are before plainly set forth in their figures. By this Ptolomey doth prove, that the distance of the Sun from the centre of the earth, containeth 1270 semidiameters of the earth, and that the semidiameter of the Sun's body containeth five such semidiameters and a half, as the earth hath, and that the diameter of the Sun to the diameter of the earth is in such proportion as is 11 to 2. Finally, he proveth the axle-tree of the shadow to contain 268 such semidiameters as the earth hath. Wherefore according to the opinion of Ptol●mey, the excentricity of the Sun should contain 48 semidiameters of the earth, and almost one fourth part. Now by knowing the diameters of the three bodies, it is easy to find out their proportions: for by the last proposition of Euclid his twelfth book, look what proportion is betwixt the diameters of any two spheres, the same proportion being tripled, is the proportion betwixt the said two spheres. And therefore because the diameter of the Sun is to the diameter of the earth in like proportion, as 11 is to 2, the same proportion being tripled, shall be 1331 to 8, so as the body of the Sun doth contain the body of the earth 166 times and almost one half. In like manner you shall find the body of the Moon to be almost the 40 part of the body of the earth: for the diameter of the earth to the diameter of the Moon is in such proportion as is 17 to 5, so as the body of the earth containeth the body of the Moon almost 40 times, as was said before. And the body of the Sun containeth the body of the Moon almost 6600 times. The proportions of which three bodies are these numbers here following, that is to say, for the Sun 6539203, and for the Earth 39304, and for the Moon 1000 A brief Extract of Maginus his Theoriques', showing all the definitions of such names and motions as are needful to be known for the calculating of the places of any of the seven Planets, or other motions of any Heaven whatsoever, that are to be found out by the Prutenicall Tables. TO avoid the Paradoxical supposition of Copernicus, supposing the Earth to move, and the Sun to stand still in the midst of heaven, Maginus is fain to suppose that there be three movable heavens above the eight heaven, and so maketh in all eleven movable heavens, which is one more than all the other Astronomers have heretofore set down. And he calleth the highest or eleventh heaven, the first movable, describing the same as hereafter followeth: next to which is placed in his Theoriques' the tenth heaven, than the ninth and eight heaven, and under that, the seven Planets, that is, first Saturn, than jupiter, Mars, Sol, Venus, Mercury, and Luna, which is the lowest heaven of all. Of which his Theoriques' I thought good to make a brief Extract, because that more terms belonging to the Prutenicall Tables are therein both defined and demonstrated, than are set down either by Purbachius or by Mes●elyn in their Theoriques'. And according to the number of this eleven Heavens, I have divided this Extract into 11 chapters. CHAP. I. The description of the eleventh Heaven or first movable, together with such definitions as are contained therein. THe first movable is the greatest or highest heaven, which carrieth all the inferior heavens round about from East to West in 24 hours. The concave superficies whereof is imagined to be traced with certain circles, whereof some be greater and some lesser. 2. The greater circles chiefly serving for our purpose, are these, the equinoctial, the Ecliptic, and the two Colours, the one called the Colour of the Equinoxes, and the other the Colour of the Solstices. 3. The equinoctial is a great circle supposed to be in the convex superficies of the first movable, dividing the same superficies into two equal parts, the poles of which circle are the poles of the world, upon which poles the said first movable continually moveth, making his revolution in 24 hours. 4. The Ecliptic of the first movable is also a great circle, dividing the superficies thereof into two equal parts, & cutteth the equinoctial in two opposite points, which points are called the Equinoxes, one of them being called the Vernal Equinox, and the other the Autumnal Equinox: and the poles of this Ecliptic are always distant from the poles of the world 23 degrees, i/40 and do never alter. And this Ecliptic is called the mean Ecliptic. 5. The Colour of the Equinoxes, is a great circle passing through the two Equinoxes, and the two poles of the world. 6. The Colour of the Solstices, is also a great circle dividing the superficies of the first movable into two equal parts, and is drawn both through the poles of the world, and also through the poles of the mean Ecliptic. CHAP. II. Of the tenth Heaven. THe tenth Heaven is a great Orb next unto the first movable, having contrary motion to the first movable, that is, from West to East upon the poles of the Ecliptic of the first movable or mean Ecliptic, and maketh his revolution in 3434 Egyptian years, and 10 days. In which, imagine the letter A to be the pole of the mean Ecliptic of the first movable, and also the pole of the tenth heaven, about which pole the tenth sphere maketh his revolution in 3434 Egyptian years, and 10 days. And upon the point A imagine also a lesser circle to be drawn, whose semidiameter is A B, containing in length i●° and imagine the same lesser circle to be the circle B D F, in the circumference whereof, suppose the centre of another lesser circle equal to that, to be placed in the point D, and let the semidiameter of the said second lesser circle be D E, containing in length i/6 the centre of which second circle, viz. D, you must suppose never to change his place, but to move about the pole A, as the tenth heaven moveth about the same pole A. And so likewise suppose the second little circle A H E to be fastened to the first, so as the said second circle hath no other motion but that which the centre D hath, and imagine the right perpendicular line C G to be part of the Solisticiall colour of the first movable; which Colour the circumference of the second little circle A H E will cut in some one point or other, as in the point H, the place of which intersection wheresoever that happeneth upon the line C G, is the pole of the Ecliptic of the tenth heaven, whose pole doth continually alter his place, and therefore the place of the Ecliptic of the said tenth heaven, must needs alter, being sometimes far from the mean Ecliptic, and sometimes near unto it, and sometimes united therewith. But the greatest distance that can be betwixt the two Ecliptickes, is i/12 according to the greatest distance which is betwixt the poles of the Ecliptic, & the poles of the first movable: for the poles of the Ecliptic of the tenth heaven can never exceed i/12 and the Ecliptic of this tenth heaven is called the true Ecliptic, whose poles do differ from the poles of the mean Ecliptic i/12 as have been said before. 3. And such distance is called the equation of the obliquity of the Ecliptic, which the former figure doth plainly demonstrate: for the letter A is supposed to be the pole of the mean Ecliptic, and H the pole of the true Ecliptic: and this equation of the obliquity is to be found in the 16 Cannon of the Prutenicall tables, by help of which equation or Prosthapherisis, you may find at any time the obliquity of the true Ecliptic, as is taught in the 13 precept of the said tables. But now because the said Prosthapherisis cannot be found but by the Anomalia of the obliquity, you are to know first what that Anomalia is, which the foresaid figure doth also show. In which figure, you must suppose the right line A E to be the diameter of the second lesser circle, the one end whereof is always fixed in the point A: and the other end marked with E, by the motion of the tenth heaven, describeth the great circle C E G. 4. And this circle is called the circle of Anomalia of the obliquity of the true Ecliptic. 5. And the arch or portion of this circle, marked with the letters C E, is the Anomalia of the obliquity of the true Ecliptic: the motion of which Anomalia you shall find at any time by the Prutenicall tables in the 14 Cannon under the title Anomalia Aequinoctiorum in such order as the eight precept teacheth. CHAP. III. Of the ninth Heaven. THe ninth Heaven is a sphere situated next and immediately under the tenth heaven: the motion of which ninth sphere is from North to South upon his proper poles, which are fixed in the two equinoctial points, called the true equinoctial points of the tenth heaven, about which poles he maketh his revolution in 1717 Egyptian years and 5 days. In this sphere are imagined certain circles both greater and lesser to be drawn, as in the former two heavens: but the greater circles whereof we shall have most use, are these, that is, the Ecliptic and the equinoctial. 2. The Ecliptic of this ninth sphere is always in the plane of the Ecliptic of the tenth sphere, and therefore doth not differ from the true Ecliptic, because it never swerveth from the same: but the equinoctial line of this ninth sphere is movable, according as the two equinoctial points in which it crosseth the true Ecliptic, are movable, being carried both backward and forward, and sometimes are conjoined together with the equinoctial points of the tenth heaven, and sometimes again are removed from the said true equinoctial points of the tenth sphere, and the greatest distance that the said two points can have from the equinoctial points of the tenth sphere is 1 degree, i/12 ii/22 iii/30 IN which, the point A signifieth the Vernal equinoctial point, as well of the tenth heaven, as of the first movable, which point we will hereafter call the true vernal equinox, in which point one of the poles of the ninth sphere is supposed to be fixed, and the other pole is in the opposite point, which is the true Autumnal equinoctial point. Now upon the centre A imagine a little circle to be drawn, whose semidiameter is A B, containing in length upon the superficies of the said ninth sphere, i●5· ii/41 iii/15 and in the same convex superficies imagine a second little circle to be drawn, equal unto the former, the centre of which second circle is in the circumference of the first little circle, viz. in the point C, the semidiameter whereof is C D, containing in length i/35 ii/41 ii/15 so shall the whole diameter A D contain in length 1 degree, i/11 ii/22 iii/30 and suppose the right line K G to be the true Ecliptic, and the right overthwart line I F to be the Equinoctial line of the tenth heaven and also of the first movable. Now the circumference of the second little circle will cross the true Ecliptic K G in some one point or other, as in the point E, which point of Intersection, wheresoever it happeneth to be, is the place of the Vernal equinoctial point of the ninth sphere: which Vernal equinoctial point we will henceforth call the mean Equinox, as the point A is the true Equinox. So that hereby you may perceive, that the mean Equinox is nothing else but that point in which the equinoctial line of the ninth sphere crosseth the Ecliptic line of the said ninth sphere or true Ecliptic. 3. The Prosthapheresis of the Equinox is the distance which is betwixt the true and mean Equinox, as is the line A E: and this Prosthapheresis you shall find in the 16 Cannon, under the title Praecessionis Aequinoctiorum, the manner of finding whereof is taught in the 10 Precept. But because the said Prosthapheresis cannot be found but by help of the Anomalia of the Equinox. 4. I will therefore show what the said Anomalia of the Equinox is. For the understanding whereof, resort to the former figure, in which you see how the tip or extreme point of the diameter of the second circle, viz. the point D describeth by his motion, that is, by the motion of the ninth sphere, the circle D F G H I K L, which circle is called the circle of Anomalia, wherein the motion of the Anomalia is always reckoned: and the distance betwixt the point L and the point D, is the Anomalia of the Equinox itself, and is always double unto the Anomalia of the obliquity of the true Ecliptic, and therefore we use to do no more but to double the Anomalia of the said obliquity, otherwise called the simple Anomalia, which is to be found by the 14 Cannon, under the title, Anomalia Aequinoctiorum, in such order as the eight Precept teacheth. CHAP. FOUR Of the eight Heaven. 1. THe eight Heaven is situated under the ninth Heaven, and moveth from West to East contrary to the motion of the first movable, upon the poles of the true Ecliptic, making his revolution in 25816 Egyptian years, and dependeth wholly upon the mean Equinox. 2. In this sphere are imagined also an equinoctial and an Ecliptic line: and the Ecliptic line of this Heaven is always in the same plane with the Ecliptic of the 9 and 10 Heavens, and swerveth not from the true Ecliptic at all. But the equinoctial points of this sphere do move from the true Equinoxes, sometimes forward, and sometimes times backward, even as the mean Equinox of the ninth sphere moveth. 3. This sphere is apparent to the eye, by reason of the multitude of stars which are therein: the moving of all which stars, and all other the inferior lights, is accounted or reckoned from the first star of the Ram's horn, as from a visible beginning, although the same be unstable, by reason of the changeable moving of the Precession of the mean Vernal Equinox. As for example, suppose in this figure the line K G to be the true Ecliptic, and I F to be the equinoctial of the first movable, crossing one another in the point A, which representeth the true Equinox, unto which point when the Sun cometh, it is Equinox throughout all the world: and suppose M to be the first star of the Ram's horn, through which a right perpendicular line passeth, signifying a great circle drawn through the first star of the Ram's horn, & also through the poles of the true Ecliptic: and suppose L H to be another great circle drawn through the true equinoctial point A, and through the poles of the true Ecliptic, so shall M A be the true Precession of the Vernal Equinox. In like manner suppose the line D E to be another great circle, passing through the point E, signifying the mean Equinox, and also through the poles of the true Ecliptic, so as the arch of the true Ecliptic, which is comprehended betwixt M and E, is the mean Precession of the vernal Equinox. And this mean Precession is readily found by the 14 Cannon, as the 8 Precept teacheth, and the title thereof in the said 14 Cannon, is Praecessionis Aequinoctiorum. But the true Precession is to be found by help of the Prosthapheresis, which was defined in the third definition of the third chapter. And although that there be many other circle's both great and little, which the Astronomers use, as the circles of Positions, Azimuths, and many others, yet will I only speak of such circles, arches, and points in the Heaven as are belonging to our present purpose (because I have spoken of the others in my sphere) showing what is the longitude, latitude, and declination of any star or point in this Heaven. 5. The longitude of any star is an arch of the Ecliptic, comprehended betwixt the true Vernal Equinox, and the circle of latitude of the said star or point. 6. The circle of latitude is a great circle passing through the poles of the true Ecliptic and the centre of the star. Of which circle, that part which is betwixt the centre of the star and the true Ecliptic, is called the latitude of the star. 7. The circle of declination is a great circle, passing through the poles of the world, and through the centre of any star or other point in the firmament: and that part of this circle which is contained betwixt the said star and the true equinoctial line, is called the declination of the star. CHAP. V. Of the seventh Heaven, that is, the heaven of Saturn. 1. THe seventh Heaven is situated next under the eight Heaven or Sphere, and moveth from West to East, and is only proper to Saturn, which is the highest Planet: whose orbs and motions thereof, this figure here following doth plainly show. ¶ The first figure belonging to the Theoric of Saturn, together with the description thereof. In this figure, consisting of certain circles & right lines, you see that the three outermost great circles drawn upon the p●int A, signifying the centre of the world, do enclose two w●●●te several spaces, and in each space are set down the characters of the 12 signs: of which two spaces, the outermost representeth the Ecliptic both of the 10 and 9 Heaven, the beginning of which Ecliptic is marked on the right hand with the letter D, signifying the true Vernal Equinox: and the next space under that representeth the Ecliptic of the eight Heaven, whose beginning is marked with a little star, ●ignifying the first star of the Ram's horn. 2. And the two black orbs do represent the deferents of the Auge, which Auge is marked with the letter I, & the opposite Auge with the letter R, which deferents do move regularly, and do make their revolution in 35333 Egyptian years: and betwixt the two black orbs is another white orb, signifying the orb Excentrique, drawn upon his own centre, marked with the letter B, in the midst of which broad white circle is another circle described by the centre of the Epicicle, marked with the letter E, upon which point E is drawn a little circle, signifying the Epicicle itself, which carrieth the body of the Planet, in the circumference whereof is a little star, representing the body of Saturn. You see also that there is another circle which crosseth the foresaid middle circle of the Excentrique in two points opposite, drawn upon his own centre, marked with C, and is called the circle Equant. The motions of which circles, and also the significations of the right lines and arches in this figure contained, are by help of the letters hereafter declared: for the right line which is drawn from the point A unto the point I, and so forth to the Ecliptic, is called the line of Auge: and the point or degree of the Ecliptic, into which the line of the Auge falleth, is called the place of the Auge, which for example sake suppose to be in the first point of Gemini, marked with the letter F. And the arch comprehended betwixt the point F and the first star of the Ram's horn, signified by the little star set down on the right hand in the true Ecliptic is called the mean motion of the Auge. And the right line A B is called the excentricity of the Excentrique, containing in length 3 degrees, i/25 and the right line A C is the excentricity of the circle Equant, containing in length 6 degrees, i/50 3. The Auge is that point in the superficies of the Excentrique which is furthest distant from the centre of the world, marked with the letter 1. But the opposite Auge is that point in the superficies of the said Excentrique, which is nearest unto the centre of the world, marked with the letter R. 4. The place of each point is showed by a right line drawn through the centre of the world & also through the Auge of the Excentrique unto the Zodiac of the eight Heaven, marked with the characters of the twelve signs, and the line so drawn, is called the line of Auge. 5. The mean motion of the Auge is an arch of the Ecliptic, proceeding from the first star of the Ram's horn unto the place of the Auge, and is found in such order as is showed in the eight Precept, by help of the 13 and 14 Cannons in that Column, whose title is Apogaea Saturni. 6. But the true motion of the Auge is an arch of the Ecliptic, beginning at the true Vernal Equinox, and ending at the place of the Auge: the manner how to find the same, is showed in the 33 Precept. 7. The orb Excentrique, is an orb of one equal thickness, compassing the centre of the world, in which Excentrique the Epicicle is always carried, and maketh his revolution in 29 Egyptian years, 183 days, and almost 5 hours, the Diurnal motion thereof is i/2 ii/0 iii/21 iiii/16 almost. 8. The centre of the Excentrique, marked with B, is a point in the middle of the Excentrique, from which all right lines that are drawn unto the concavity of the Excentrique, are equal. 9 The distance betwixt which centre and the centre of the world is called the excentricity of the Excentrique: and the distance betwixt the two said centres, that is, of the world and of the Excentrique, is 3 degrees, i/25 10. The circle Equant is a circle described upon the point C in the plane of the Excentrique, in regard of the centre whereof, the motion as well of the Excentrique as of the Epicicle, is regular and equal. And this circle is sometimes called the circle of equality, sometimes the Equator, and other times the excentrical Equator, the distance of the centre whereof is from the centre of the Excentrique 3 degree, i/25 and from the centre of the world 6 degrees, i/50 and this distance from the centre of the world is called the Excentricity of the circle Equant. 11. The Epicicle is a little orb, whose centre is marked with the letter E, which the Excentrique carrieth about, which Epicicle notwithstanding hath his proper motion, for the higher part thereof hath his moving according to the succession of the signs, and the lower part contrary to the succession of the signs. The daily motion of the Epicycle about his own centre, is i/57 ii/7 iii/44 and maketh one ent●e revolution in 378 days, 21 hours, i/36 12. But because that the accounting of the motions by the circle Equant is troublesome, therefore the Astronomers do use to reckon the fame upon the Ecliptic, by imposing a line to be drawn from the centre of the world unto the Ecliptic, in such sort, as the same may be parallel unto the line before drawn: as in the foresaid figure, the line A G being parallel unto the line C E, is called the line o● the mean moving of the Epicicle or of the Planet. 13. The mean Anomalia of the Excentrique is an arch of the Ecliptic, beginning at the line of the Auge, and so proceeding according to the succession of the signs, until at end at the line of the mean moving, as in the foresaid figure the line A F is the line of the Auge, and A G is the line of the mean moving. Now the arch of the Ecliptic, which is comprehended betwixt the two lines, A F, and A G, that is to say, the arch F G is called the mean Anomalia of the Excentrique, and of some it is called the mean or equal centre. 14. But if the said arch be reckoned from the first star of the Ram's horn, unto the line of the mean moving, marked with A G, than the said arch is called the equal motion of longitude, which you may find by the Tables at any time, supposed by the 13 and 14 Cannons in the Column, whose title is Longitudinis Saturni, in such order as is showed in the eight Precept. The equal or mean moving of the longitude of Saturn, is daily i/2 ii/0 iii/27 iiii/18 and the yearly motion thereof is 12 degrees, i/12 ii/46 iii/4 and the whole revolution is in 29 Egyptian years, 174 days, 4 hours, i/58 ii/24 for in that time it returneth to the first star of the Ram's horn. 15. The line of the true moving of the Epicicle is a right line drawn from the centre of the world, passing through the centre of the Epicicle unto the Ecliptic, as in the foresaid figure the right line A E L is called the line of the true motion of the Epicicle. 16. The true or coequated Anomalia of the Excentrique (which is called by the Alphonsines the true centre) is an arch of the Ecliptic, beginning at the place of the Auge of the Excentrique, and endeth at the true place of the centre of the Epicicle, as in the foresaid Figure the arch F L is the true Anomalia of the Excentrique. 17. The true motion of the longitude of the Epicicle is an arch of the Ecliptic, beginning at the first star of the Ram's horn, and endeth at the true place of the centre of the Epicicle, as in the foresaid figure, the arch from the Ram's horn, marked with a little star in the Ecliptic of the eight sphere, to L, is called the true moving of the longitude of the Epicicle. 18. The Prosthapheresis or Equation of the centre, is the difference betwixt the mean Anomalia and the coequated Anomalia of the Excentrique, or the difference betwixt the equal moving and the true moving of longitude. As the arch L G is called the equation of the centre, and this equation is never greater than 6 degrees, i/30 ii/30 and is always greatest when the equal moving of the centre of the Epicicle from the Auge of the Excentrique, is 11 Sex. 33 degrees, whether the same be reckoned according to the succession of the signs, or contrary to the succession of the signs: and from thence it decreaseth until the line of the said mean moving cometh into the line of the opposite Auge. The finding of which Equation is taught in the 34 Precept, by help of the 19 Cannon in the Column, whose title is Eccentrici, and is to be added or subtracted according as the words Subtrahe and Add at the head or foot of the said Column, do show. 19 The two points in which the Prosthapheresis of the Excentrique is greatest, are called the mean longitude of the Excentrique: and these two points are showed by a right line perpendicularly drawn upon the line of Auge, and passing through the middle space of the distance betwixt the centre of the world and the centre of the Excentrique, as in the former figure, in which the point A signifieth the centre of the world, and the point B the centre of the Excentrique. Now if the space B A be divided into two equal parts, as in the point Q, and through the same point Q a right line be drawn, crossing the line A F with right angles, and is produced as well towards the right hand as towards the left, unto the two points of the circumference of the Excentrique, marked with the two letters T and V, the said two points T and V are called the mean longitudes of the Excentrique: in which mean longitudes the centre of the Epicicle is, when the equal motion of Saturn's longitude is 93 degrees or 267 degrees. 20. The mean Auge of the Epicicle is a point in the circumference of the Epicicle, which is furthest distant from the centre of the circle Equant: and this point is found by drawing a right line from the centre of the circle Equant unto the circumference of the Epicicle, through the centre of the said Epicicle, as in the former figure the right line C E being produced unto the circumference of the Epicicle, showeth the mean Auge of the Epicicle to be in the point H. 21. The true Auge of the Epicicle is a point in the circumference of the Epicicle, which is furthest distant from the centre of the world, and is found by drawing a right line from the centre of the world unto the centre of the Epicicle, and produced unto the circumference thereof, as the right line A E being produced unto the circumference of the Epicicle, meeteth with the same circumference in the point K, which is therefore called the true Auge of the Epicicle. 22. The Touch point is a point in the circumference of the Epicicle, which is furthest distant from the centre of the Excentrique, and is determined by a right line drawn from the centre of the Excentrique unto the centre of the Epicicle, and so produced unto the circumference of the Epicicle: as if the line B E be produced unto the circumference of the Epicicle, viz. unto the point N, the said point N is called the Touch point of the Epicicle. 23. The Anomalia of commutation is an arch of the Epicicle, beginning at the mean Auge of the Epicicle, and ending at the place of the Planet in the Epicicle: and this arch is always reckoned, according as the Planet moveth. As the arch H * of the Epicicle is called the Anomalia of commutation, and is otherwise called of some the mean Anomalia of the orb or Epicicle, and of others the mean argument: the finding of the Anomalia of Commutation is taught in the 8 Precept, by help of the 13 and 14 Cannons in his proper Collum, whose title is Anomalia comutationis Satura●. 24. The coequated Anomalia of Commutation is an arch of the Epicicle, beginning at the true Auge of the Epicicle, and ending at the place of the Planet in his Epicicle. As the arch K N H is called the coequated Anomalia of Commutation: which some call the true Anomalia of the Orb, and others call it the true Argument. 25. The Prosthapheresis or equation of the centre in the Epicicle, is an arch of the Epicicle, which is comprehended betwixt the mean and true Auge of the Epicicle: as in the former figure the point K is the true Auge, and the point H is the mean Auge of the Epicicle, the distance betwixt which two Auges is the arch K N H, and that is the equation of the centre in the Epicicle: and this equation is always equal unto the equation of the centre, before defined in the 18 definition of this chapter: Only this rule is generally to be observed, that if the Prosthapheresis were added in the coequating of the Anomalia of the Excentrique, the same Prosthapheresis must be subtracted in the coequating of the Anomalia of Commutation: and so again if it be subtracted in the former, than it must be added in the latter. 26. The line of the true motion of the Planet is a right line drawn from the centre of the world unto the Ecliptic, through the centre of the Planet. As in the former figure the right line A * S is called the line of the true motion of the Planet. 27. The true motion itself of the Planet is an arch of the Ecliptic, comprehended betwixt the true Vernal Equinox and the line of the true motion. As in the foresaid figure the arch D S is called the true motion of the Planet. 28. The equation of the Argument, which Copernicus calleth the Parallax of the orb, and others call the same the Prosthapheresis of the Epicicle, is an arch of the Ecliptic, comprehended betwixt the line of the true motion of the Epicicle, and the line of the true motion of the Planet, as in the former figure the arch S L is the equation of the argument. This equation is found by help of the coequated Anomalia of Commutation, in such order as is showed in the 34 Precept, and in the 19 Cannon in the Column, whose title is Paralaxis Orbis. The greatest equation that Saturn can have, when the Epicicle is in the Auge of his Excentrique, and the Planet is distant from the Auge of the Epicicle 96 degrees, is 5 degrees, i/55 ii/33 But the greatest equation belonging to him when the Epicicle is in the opposite Auge of the Excentrique, and the Planet is distant from the Auge of the Epicicle almost 97 degrees, is 6 degrees, i/38 ii/38 29. The excess of the equation of the Argument, which the Alphonsines call the diversity of the diameter, is an arch of the Ecliptic, whereby the equation of the Epicicle being in the opposite Auge of the Excentrique, exceedeth the said equation, when the Epicicle is in the Auge of his Excentrique. As you shall more plainly perceive by this figure following. 30. The proportional minutes are the 60 parts of the excess, by help whereof the equations of the Epicicle, being not in the Auge, nor in the opposite Auge of the Excentrique are equated or corrected. As in the former figure the arch P L, which is the excess, is supposed to be divided into 60 equal parts, by help of which division the proportional minutes are found in what place of the Excentrique soever the epicicle is placed. As suppose the true place thereof to be in the point F, in which situation of the Epicicle, the arch O L is the equation of the Argument, which equation is greater than it was when the Epicicle was in the point E, and the difference betwixt these two equations is the arch I L. Now if you suppose the arch P L to be divided into 60 equal parts, look how many of those parts the arch I L doth contain, so many proportional minutes are belonging to the equation of the argument of the Epicicle, when the place of the said Epicicle is in the point F. The finding of these proportional minutes is taught in the 34 Precept, and are set down in the 19 Cannon in the Column, whose title is Scrupula Proportionalia. 31. The absolute equation is an arch of the Ecliptic, which is compounded of the equation of the Argument, and the excess answerable unto the proportional minutes. And this absolute equation is either added or subtracted unto the true moving of the Epicicle, and the sum of such addition or the remainder of the subtraction will show the true distance of the Planet from the first star of the Ram's horn: whereunto if you add the true Precession of the Equinox, the sum of that addition will show the true longitude of the Planet. CHAP. VI Of the sixth Heaven, or the Heaven of jupiter. THe sixth Heaven, which is of jupiter, consisteth of like orbs as doth the Heaven of Saturn, & therefore the demonstrations belonging to this Heaven, do not differ from those which were set down in the heaven of Saturn, but only in the time of their motions & in the quantity of some arches: for the deferents of the Auge and opposite Auge in the heaven of jupiter do make their revolution in 109756 Egyptian years. And the Excentrique of this Heaven maketh his revolution in 11 Egyptian years, 318 days, and one hour almost. And the excentricity of the Excentrique of jupiter is 2 degrees, i/45 and the excentricity of the circle Equant is 5 degrees, i/30 The Epicicle of this Heaven maketh his revolution in 398 days, 21 hours, i/13 ii/15 iii●●° and the daily motion thereof is i/54 ii/9 iii/4 The greatest equation of the centre which belongeth unto jupiter, is 5 degrees, i/13 ii/59 and that is when the centre of the Epicicle is distant from the true Auge of the Excentrique 93 degrees, whether it be according or contrary to the succession of the signs. And the greatest equation of the Argument, when the centre of the Epicicle is in the Auge of the Excentrique, is 10 degrees, i/30 ii/9 and then the distance of the Planet from the true Auge of his Epicicle, is 100 degrees, i30 almost. And the greatest equation of the said Argument, when the Epicicle is in the opposite Auge of the Excentrique, is 11 degrees, i/31 ii/2 & then the Planet is distant from the true Auge of the Epicicle 102 degrees almost. The equal or mean moving of jupiters' longitude from the first star of the Ram's horn, is daily i/4 ii/59 iii/8 and the yearly motion thereof is 30 degrees, i/19 ii/4 iii/6 & maketh one entire revolution in 11 Egyptian years, 214 days, 21 hours, i/16 ii/24 The rest of the lines and arches belonging to this Planet, are defined in the former fift Chapter: and the finding of all such things as are needful for that purpose are set down in the said fift Chapter, differing nothing from the manner which was therein showed, except it be in the number of the Cannon, which for Saturn was the 19, and for this Planet it is the 20 Cannon. CHAP. VII. Of the fift Heaven, or Heaven of Mars. THe fift Heaven belonging to Mars, hath like number of orbs, as hath the Heaven of Saturn, and the said orbs are placed even as they were in Saturn. And therefore I shall not need to make any particular relation of the orbs or lines of this sphere, but to refer you to the fift Chapter, showing only here the difference of the motions. The deferents of the Auge in the Heaven of Mars do make their revolution in 45088 Egyptian years, so as their daily motion is iii/4 iiii/43 and their yearly motion is ii/28 iii/44 iiii/37 The Excentrique of this Heaven maketh his revolution in one year, and 322 days almost, so as his daily motion is i/31 ii/26 iii/26 iiii/15 and the yearly motion thereof is 191 degrees, i/15 ii/49 iii/44 iiii/3 The Epicicle of this Heaven maketh his revolution in 2 years, 49 days, 19 hours, i/43 and the daily motion thereof is i/27 ii/41 iii/40 and his yearly motion is 168 degrees, i/2 ii/30 iii/42 The greatest equation of the centre belonging unto Mars, is 11 degrees, i/5 ii/59 and that is when the centre of his Epicicle is distant from the true Auge of the Excentrique 95 degrees and i/30 be it according or contrary to the succession of the signs. The greatest equation of the argument, when the centre of the Epicicle is in the Auge of the Excentrique, is 36 degrees, i/54 ii/18 and then the distance of the Planet from the true Auge of his epicicle is 127 degrees almost. And the greatest equation of the Argument, when the centre of the Epicicle is in the opposite Auge of his Excentrique, is 46 degrees, i/38 ii/4 and that is when the Planet is distant from the Auge of the Epicicle 137 deg. The mean moving of the longitude of Mars is every day i/31 ii/26 iii/31 and the yearly motion thereof is 191 i/16 ii/18 iii/29 and maketh one entire revolution in one year, 321 days, 23 hours, i/32 All other lines and arches belonging to Mars are defined in the fift Chapter: and the Cannon serving for the finding of them and their places, is the 21 Cannon in number. CHAP. VIII. Of the fourth Heaven, or Heaven of the Sun. THe next Heaven under that of Mars, is the Heaven of the Sun, and hath his proper and peculiar motion from West to East. This Heaven consisteth of five orbs: whereof two are called the deferents of the mean Auge of the Suns Excentrique, the other two orbs are called the deferents of the true Auge of his Excentrique, or the orbs of the Anomalia of the true Auge and of the excentricity of the Sun. The fift Orb is called the deferent of the body of the Sun. All which you may evidently see in the figure following. ¶ The first figure belonging to the Theoric of the Sun. IN which figure, the outermost broad circle, in which are set the characters of the 12 signs, signifieth the Ecliptic of the eight Heaven, the centre whereof is marked with the letter A, which signifieth the centre of the world. Next unto this Ecliptic is one of the deferents of the mean Auge signified by the outermost black orb, the centre of whose convex superficies is the point A, and the centre of his concave superficies is the point B, the other deferent of the said mean Auge is the lesser broad black circle, the centre of whose convex superficies is the point B, and the centre of his concave superficies is the point A. And betwixt the black orbs are two shadowed orbs, which are the deferents of the Suns Excentrique: and the convex superficies of the outermost of these two shadowed orbs, as also the concave superficies of the lower of them have for their centre the point B, and the concave superficies of the higher and convex superficies of the lower have the point C for their centre. Betwixt which two orbs is the Excentrique of the Sun, which Excentrique is signified by the broad white circle: in the middle of which white circle is drawn a circle, in which the centre of the Sun is continually moved: and the centre of the Excentrique is marked with the letter C, which point is called the movable centre of the Excentrique, by whose motion is described the little circle in the middle of the figure, the centre of which circle is the point B. 1. The deferents of the mean Auge of the Sun are two orbs of unequal thickness, being in some respect concentrical with the Ecliptic, and in another respect excentrical: for the convex superficies of the higher, and the concave superficies of the lower have for their centre the centre of the world, marked with A: but the concave superficies of the higher, and convex superficies of the lower have a centre differing from the centre of the world: and these two orbs have their proper and peculiar motion from West to East upon the axes and poles of the true Ecliptic, and their Diurnal motion is iii●° iiii/12 and their yearly motion is ii/25 iii/33 iiii/12 and do make one entire revolution in 50717 Egyptian years: and these two orbs do only serve to carry the mean Auge of the Excentrique. 2. The mean Auge of the Excentrique is that point in the deferent of the Excentrique, which is furthest distant from the centre of the world. As for example, the point G in the former figure signifieth the mean Auge of the Excentrique. 3. And this point is always determined in the Zodiac by a right line, drawn from the centre of the world through the centre of the little circle, marked with B, unto the Ecliptic line, and the line so drawn, is called the line of the mean Auge, as the line A B G, which is called the line of the mean Auge. 4. But the motion of the mean Auge is an arch of the Ecliptic, beginning at the first star of the Ram's horn, and ending at the line of the mean Auge, as in the said figure the arch * G is the motion of the mean Auge: but if the said arch begin at the equinoctial, whether the same be mean or true, then is the said motion called the motion of the mean Equinox, extending from the mean Equinox or from the true Equinox unto the foresaid line of the mean Auge, the finding of every of which motions is showed in the 16 Precept. 5. The deferents of the Excentrique, which sometimes are called the orbs of the Anomalia of the excentricity, are the two shadowed orbs which do carry the orb Excentrique. And these two orbs have their proper motion also from East to West, making their revolution once in 3434 Egyptian years, and 10 days, and their daily motion is ii/1 iii/2 iiii/2 and their yearly motion is i/6 ii/17 iii/24 iiii/9 And those deferents are moved upon the centre of the little circle (which centre is marked with the letter B, and is distant from the centre of the world 2 degrees, i/1 such degrees as the length of the semidiameter of the Excentrique containeth 60 degrees) and their proper axle-tree is parallel unto the axle-tree of the Ecliptic, and passeth through the centre of the said little circle, as the next figure following showeth. And the, motion of these orbs doth begin at the line of the mean Auge before defined in the third definition of this chapter. And it is called the Anomalia or Argument of the Auge, and of the excentricity of the Sun. By the motion of which Orbs the centre of the Excentrique is imagined to describe a little circle above the centre of the world, whereby the excentricity of the Sun changeth every day. 6. The excentricity of the Sun is the distance betwixt the centre of the world and the centre of the Suns Excentrique: and this is threefold, greatest, lest, or mean. 7. The greatest excentricity of the Sun is when the centre of the Excentrique is in the Auge of the little circle, viz. in the point C, and the quantity of this greatest excentricity, is 2 degrees, i/3 ii/7 such like degrees as the semidiameter of the Excentrique containeth 60 degrees, or the quantity of the said greatest excentricity is 41700, when the semidiameter of the Excentrique is 1000000. 8. The least excentricity is when the centre of the Excentrique is in the opposite Auge of the little circle, and then the distance betwixt the centre of the earth and the centre of the Excentrique, is 1 degree, i/55 ii/53 supposing the semidiameter of the Excentrique to be divided into 60 equal parts, but if the said semidiameter be divided into 1000000, than the said least excentricity will be 32190. 9 The mean excentricity is when the centre of the Excentrique is in the middle distance betwixt the Auge and opposite Auge of the little circle, and then the said excentricity is 0 degrees, i34. ii14. such parts as the semidiameter of the Excentrique containeth 60. But if the said semidiameter be supposed to be divided into 1000000 parts, than the said mean excentricity is 9510. And the semidiameter of that little circle containeth 0 degrees, i/17. ii/7 10. The Anomalia of the Auge and excentricity, which is also called the centre of the Sun, is an arch in the concave superficies of the outermost deferent of the mean Auge, which arch is comprehended betwixt the line of the mean Auge, and a right line drawn from the centre of the little circle through the movable centre of the Excentrique unto the concave superficies of the said outermost orb. Or thus, the centre of the Sun is an arch of the little circle, beginning at the Auge of said little circle, and ending at the movable centre of the Excentrique. As for example. ¶ The second figure belonging to the Theoric of the Sun. In this figure suppose the point A to be the centre of the world, and B the centre of the concave superficies of the outermost of the two deferents of the mean Auge, and C the centre of the Excentrique, whose place was sometimes in the point P, but now is gone from thence unto C, so is A G the line of the mean Auge, and A P is the greatest excentricity, and A O the least excentricity, and P O is the difference betwixt the greatest and least excentricity, the half whereof is B O, and A B is the quantity of the mean excentricity, and the place of the centre of the Excentrique is in the point C, and the arch G F is the Anomalia or Argument of the Auge and of the excentricity in the concave superficies of the highest deferent of the mean Auge, and the arch P C of the little circle is the Anomalia of the Auge and excentricity: and the right line B C F is the line which showeth the mean Auge of the orbs of the Anomalia of the Auge, in respect of their centre. 11. The mean Auge of the orbs of the Anomalia of the excentricity, is that point in the concave superficies of the highest deferent of the Excentrique, which is furthest distant from the centre of the little circle, and is pointed out by a right line drawn from the centre of the said little circle, through the movable centre of the Excentrique. As in this second figure, in which the point B is the centre of the little circle, and C is the centre of the Excentrique, through which point C if you draw a right line from A unto the concavity of the highest deferent of the Excentrique, as unto the point E, the said point E is the mean Auge of the orbs of the Anomalia of the excentricity. Now if you add the daily moving of this mean Auge, which is ii/1 iii/2 iiii/2 (as was said in the fift definition of this Chapter) unto the daily moving of the mean Auge of the excentricity, which is iii/4 iiii/12 (as was said in the first definition of this Chapter) the sum of that addition will be ii/1 iii/6 iiii/14 and this is the daily distance betwixt the two mean Auges, viz. that of the excentricity, and this of the orbs of the Anomalia of the excentricity. 12. The orb Excentrique is an orb in the Theoric of the Sun, in which the body of the Sun is continually carried about. This orb is placed betwixt the two orbs, which are the deferents of the Excentrique, and moveth from West to East upon his own movable centre (which centre is movable, by reason of the moving of the two orbs, which are the deferents of the Excentrique) and the axle-tree which is also movable according to the motion of the centre of the Excentrique in the circumference of the said little circle. And the daily motion of this orb from the mean Auge of the orbs of the Anomalia of the excentricity is i/59 ii/9 iii●3· iiii/24 and maketh his entire revolution in 365 days, 3 hours, i/36 ii/25 which motion is reckoned from the mean Auge of the orbs of the Anomalia of the excentricity. For the Sun returneth to the said point or mean Auge in 365 days, 3 hours, i/36 ii/2 13. The line of the true place of the Sun is a right line drawn from the centre of the world through the centre of the Sun unto the Ecliptic: and the point in the Ecliptic in which the said line endeth, is the true place of the Sun. As in the former second figure, suppose the centre of the Sun to be in the point M of the Excentrique, and having drawn a line from A to M, and so forth unto the Ecliptic in the point R, the said line A R is called the line of the true place of the Sun, and the point R is said to be the true place of the Sun in the Ecliptic. 14. The yearly Anomalia of the Sun, which is also called the mean Argument of the Sun, is an arch of the Excentrique, which is comprehended betwixt the line of the mean Auge of the Excentrique, and the line of the true place of the Sun. As in the foresaid second figure the arch L M is called the yearly Anomalia of the Sun. Or thus, The yearly Anomalia of the Sun is the excess or difference, whereby the daily motion of the Sun from the mean Auge of the orbs of the Anomalia of the excentricity, exceedeth the daily distance betwixt the mean Auge of the Excentrique, and the mean Auge of the orbs of the Anomalia: and this Anomalia is found by subtracting the daily distance of the said two Auges, which is ii/1 iii/6 iiii/14 (as was showed in the 11 definition of this Chapter) out of i/59 ii/9 iii/13 iiii/24 which is the daily motion of the Excentrique from the mean Auge of the orbs of the Anomalia of the excentricity (as was showed before in the 12 definition:) the remainder of which subtraction will be i/59 ii/8 iii/7 iiii/10 And although that this Anomalia doth belong properly unto the Excentrique: yet notwithstanding the said Anomalia is also supposed to be in the Ecliptic, by imagining a line to be drawn from the centre of the world unto the Ecliptic, in such order as that the said line may be parallel unto another line which is drawn from the centre of the Excentrique unto the place or centre of the Sun: and the line so drawn, may be called the line of the Imaginary motion of the Sun. As in the foresaid second figure let a right line be drawn from C to M, then unto the same line draw another parallel right line from the centre A, and produce the same unto the Ecliptic in the point N; so shall the arch of the Ecliptic, which is comprehended betwixt the points E and N, be the yearly Anomalia or mean Argument of the Sun in the Zodiac. The finding of which Anomalia for any time appointed, is taught in the 8 Precept, by help of the 13 and 14 Cannons in that Collum, whose title is Anomalia annua Solis. 15. The true Auge of the Excentrique is that point in the Excentrique which is furthest distant from the centre of the world. And this true Auge is pointed or showed by a right line drawn from the centre of the world through the movable centre of the Excentrique unto the Ecliptic, and the point in the Ecliptic, in which the said right line doth end, is the place of the true Auge of the Excentrique in the Ecliptic: and the said right line is called the line of the true Auge of the Excentrique: as in the foresaid second figure the point A signifying the centre of the world, and the point C the centre of the Excentrique, in the superficies of which Excentrique the point D is furthest distant from the centre A, and therefore the point D is the true Auge of the Excentrique: and the right line A C D is called the line of the true Auge of the Excentrique: and the point K in the Ecliptic, in which the said line endeth, is the place of the true Auge in the Ecliptic, the finding whereof is taught in the 16 Precept. 16. The motion of the true Auge of the Excentrique is an arch of the Ecliptic, beginning at some principal point in the Ecliptic, and ending at the line of the true Auge of the Excentrique: which principal point if it be the first star of the Ram's horn, then is the said motion called the moving of the true Auge from the first star of Aries: and if the said motion or arch doth begin at the true Equinox, then is the said motion called the moving of the true Auge from the true Equinox. 17. The equation of the centre is an arch of the Ecliptic, which is comprehended betwixt the mean Auge of the outer black orbs, and the true Auge of the Excentrique, as in the foresaid second figure of this Chapter, the arch K G in the Ecliptic is called the equation of the centre: and this equation never exceedeth 7 degrees, i/23 ii/36 the manner of the finding of which equation is showed in the 15 Precept, by help of the 17 Cannon in that Column, whose title is Centri. 18. The true Argument of the Sun, which is also called the equated yearly Anomalia, is an arch of the Ecliptic, which is contained betwixt the line of the true Auge of the Excentrique, and the line of the Imaginary motion of the Sun. As in the foresaid second figure the line A K is the line of the true Auge of the Excentrique, and the place of the said true Auge in the Ecliptic is the point K. Likewise the line A N is the line of the Imaginary motion of the Sun. Now the arch of the Ecliptic, which is contained betwixt the 2 points K and N, is called the true Argument or equated Argument of the Sun. For the difference betwixt the mean and true Arguments of the Sun, is also the difference which is betwixt the mean and true Auge of the Excentrique, which difference is called the equation of the centre before defined in the 17 definition of this Chapter. The manner of equating the Argument, is taught in the 15 Precept. 19 The equal simple moving of the Sun is an arch of the Ecliptic, beginning at the first star of the Ram's horn, and ending at the line of the Imaginary motion (which line we call hereafter the line of the mean moving of the Sun) as in the foresaid second figure of this Chapter, the arch * N is the equal simple moving of the Sun: The quantity of which simple moving is i/59 ii/8 iii/1 iiii/22 every day, and according to this motion the Sun maketh one entire revolution in 365 days, 6 hours, i/9 ii/39 20. The equal compound moving of the Sun is an arch of the Ecliptic, beginning at the mean vernal Equinox, and ending at the line of the mean moving of the Sun. Whereby it appeareth, that if the mean Precession of the Equinox be added unto the equal simple motion of the Sun, the sum of that addition will be the compound motion of the Sun. And the daily compound motion is i●●° ii/8 iii/19 iiii/13 whereby the Sun according to the equal compound motion maketh his revolution in 365 days, 5 hours, i/49 ii/16 The manner of finding of these two equal motions of the Sun, that is to say, the simple and compound moving, is taught in the 8 Precept, by help of the 13 and 14 Cannons. 21. The true motion of the Sun is an arch of the Ecliptic, beginning at the first star of the Ram's horn, and ending at the true place of the Sun: and then is the said true motion called the true moving of the Sun under the 8 sphere. But sometimes the said arch of true motion is supposed to begin at the true Vernal Equinox, and then it is called the true motion of the Sun under the first movable. 22. The proportional minutes are the 60 parts whereby the equations of the Argument do increase or decrease, according as the excentricity of the Sun increaseth or decreaseth. The finding of which proportional minutes is taught in the fifteenth Precept, and are set down in the seventeenth Cannon in the Collum, whose title is Scrupula Proportionalia. 23. The equation of the Argument or yearly Prosthapheresis is an arch of the Ecliptic, which is comprehended betwixt the line of the mean moving and the line of the true moving of the Sun. And this equation of the Argument is nothing, when the Sun is either in the Auge or in the opposite Auge of the Excentrique, and is always greatest in the mean longitudes of the Sun: which mean longitudes are pointed out in the circumference of the Excentrique, by a right line drawn perpendicularly upon the line of the true Auge through the centre of the world. As in the foresaid second figure of this Chapter, the line A D is the line of the true Auge of the Excentrique, which another line crosseth with right angles in the point A, which perpendicular line is the line T V, and being produced unto the Excentrique, showeth the points T and V to be the points of mean longitudes. And the greatest equation of the Argument that can be, which is when the centre of the Excentrique is in the Auge of the little circle, is two degrees, i/23 ii/24 and that is when the Sun is distant from the true Auge or from the Auge of the Excentrique 93 degrees. But when the centre of the Excentrique is in the opposite Auge of the said little circle, then is the greatest equation of the Argument no more but 1 degree, i/50 ii/41 and that is when the distance of the Sun from the true Auge, is 92 degrees. And this equation is called in the tables, The equation of the orb: the finding whereof is taught in the 15 Precept, by help of the 17 Cannon, in the Collum whose title is Orbis. 24. The true argument of the Sun, is the distance of the Sun from the true Auge of his Excentrique. 25. The excess or diversity of the diameter, is an arch of the Ecliptic, whereby the equation of the argument (the centre of the Excentrique being in the Auge of the little circle) exceedeth the equation of the argument, when the centre of the Excentrique is in the opposite Auge of the little circle. The true argument of the Sun being of one self quantity in each position of the centre of the Excentrique in the circumference of the little circle. For the equations of the argument do decrease continually, so long as the centre of the Excentrique is descending from the Auge of the little circle, until it come to the opposite Auge of the said little circle, and from thence do begin again to increase, until the centre of the Excentrique returneth again unto the Auge of the little circle. The finding of which Excess is taught in the 15 Precept, and is set down in the 17 Cannon in that Column, whose title is Excessus. 26. The coequated and true equation, which is otherwise called the absolute equation of the orb, is an arch compounded of the true equation of the argument, and of the excess, proportionable unto the proportional minutes. CHAP. IX. Of the third Heaven, or Heaven of Venus. THe next Heaven under that of the Sun, is the Heaven of Venus, which hath his proper moving from West to East. This Heaven hath four orbs, as the Heaven of the three higher Planets have, that is to say, two, which are called the deferents of the two Auges, than the Orb Excentrique, or the deferent of the Epicicle, and the Epicicle itself, in the circumference whereof the Planet is always carried. And because I have defined the said orbs in the fift Chapter, I think them needless to be here again repeated: and therefore I refer you to that Chapter: For the Orbs of Venus do not differ from the Orbs of Saturn in shape and position, but only in the quantity of their motions. The deferents of the Auge and opposite Auge in the Heaven of Venus do continue without any motion, and the place of her Auge, which is in the Ecliptic of the eight Heaven, is always 48 degrees, i/21 reckoning from the first star of the Ram's horn: and the opposite Auge is always 3 Sex. 48 degrees, i/21 from the first star of the Ram's horn, accounting the said distance according to the succession of the signs. The Excentrique of Venus moveth according to the succession of the signs upon his proper centre, which is differing from the centre of the world, and the poles and axle-tree of this Orb are movable, sometimes approaching near unto the poles of the Ecliptic, and at other times are further off. Howbeit this Excentrique maketh one entire revolution, beginning at the first star of the Ram's horn in 365 days, 6 hours, i/9 ii/39 so as the moving of this orb is equal unto the simple equal moving of the Sun, before defined in the 19 definition of the 8 Chapter. And therefore the line of the mean moving of the centre of Venus her Epicicle, is always in the same place of the Zodiac, in which the line of the mean moving of the Sun is: so as in seeking for the mean moving of Venus her longitude, you are to find the simple equal moving of the Sun in such order as the eight Precept teacheth: from which if you subtract 48 degrees, i/21 the remainder will show the mean Anomalia of the Excentrique, or mean centre, before defined in the 13 definition of the 7 Chapter. Which if you subtract out of the true motion of the longitude of the Epicicle (which is defined in the 17 definition of the 7 Chapter) the remainder will be the true centre or the equated Anomalia of the Excentrique, which is defined in the 16 definition of the 7 Chapter. The Epicicle of Venus hath also his proper motion in the Excentrique, whereby it swerveth from the plane of the Excentrique. The semidiameter of the Epicicle is 43 degrees, i/10 such like degrees, as the semidiameter of the Excentrique containeth 60 degrees. And because that the line of the mean moving of her centre is all one with the line of the mean moving of the Sun, it may easily appear, that the star or Planet will be twice conjoined with the Sun in one revolution of her Epicicle, that is to say, once in the Auge, and once in the opposite Auge of the Epicicle. But if she be neither in the Auge nor in the opposite Auge of the Epicicle, then in her ascending from the opposite Auge of her Epicicle unto the Auge thereof she goeth before the Sun, and is our morning star, called of the Latins Lucifer. But in descending from the Auge of her Epicicle unto the opposite Auge thereof, she goeth after the Sun, and is our evening star, called of the Latins Hesperus. The daily moving of the Anomalia of Commutation (which was defined in the 23 definition of the 7 chapter) is i/16 ii/59 iii/28 and the yearly motion thereof is 3 Sex. 45 degrees, i/1 ii/45 iii/21 and maketh one entire revolution in one year 218 days, 21 hours, 15 minutes. The greatest equation of her Epicicle is 45 degrees, i/10 ii/20 if the centre of the Epicicle be in the Auge of her Excentrique, and that the Planet be distant from the Auge of the Epicicle any way 2 Sex. 15 degrees, i/5 but if the centre of the Epicicle be in the opposite Auge of the Excentrique, and that the Planet be distant 2 Sex. 17 degrees from the Auge of the Epicicle, then is the greatest equation of the argument of Venus 46 degrees, i/51 ii/29 What other points, lines, and arches are needful to be known for the calculating of her motion at any time, are set down before in the 7 Chapter, unto which I refer you, only the finding of the equations belonging unto this Planet, must be sought for in the 22 Cannon, in such order as is taught in the 34 Precept. And thus I end with Venus. CHAP. X. Of the second Heaven, or Heaven of Mercury. NExt under the Heaven of Venus is the Heaven of Mercury, which consisteth of six orbs, that is to say, 2 deferents of the Auge of the circle Equant, two deferents of the Auge of the Anomalia of the Excentrique, the fift orb is the Excentrique, and the sixth is the Epicicle. The five first orbs are in all respects like unto the five orbs of the Sun, whereof we spoke in the 8 Chapter. And the sixth orb, which is the Epicicle, is like unto the Epicicle in the other Planets whereof we spoke in the fift Chapter. Notwithstanding I think it not amiss for your better understanding to set down the said orbs in this figure here next following. ¶ The first figure belonging to the Theoric of Mercury. IN this figure the two outermost circles, in which are set the characters of the twelve signs, do signify the two Ecliptickes, one of the first movable, the other the Ecliptic of the eight Heaven. The two broad & black circles do signify the two deferents of the Auge of the circle Equant, and the two shadowed circles do signify the deferents of the Auge of the Excentrique, and betwixt them is a broad white circle, which representeth the Excentrique: in the midst whereof is the circumference of a circle, which the centre of the Epicicle is imagined to describe. And another circumference is also drawn in the said Excentrique, which cutteth the former circumference in the two points I and G, and this circumference signifieth the circle Equant. Again, in the Excentrique is another little circle, representing the Epicicle, the centre whereof is the point H, and in the circumference thereof is a little star, which signifieth the Planet of Mercury. The point in the middle of ●●is Figure, which is marked with the letter A, signifieth the centre of the world, and C is the centre of the Excentrique, and B is the centre of a little circle, in the circumference whereof the centre C always moveth about the centre B, and D is the centre of the circle Equant. The motion of the two deferents of the Auge of the Equant is like unto the motion of the deferents of the mean Auge of the Sun, for it is equal and regular upon the centre of the world according to the succession of the signs, that is to say, from West to East upon their own proper poles, which are equally distant from the poles of the Ecliptic: and the daily motion of these orbs is iii/9 iiii/31 and their yearly motion is ii/57 iii/50 iiii/38 and so do make one entire revolution in 22700 Egyptian years. The excentricity, that is to say, the distance of the centre of the circle Equant from the centre of the world, is 3 degrees, such degrees as the semidiameter of the said circle Equant containeth 60 degrees. The line A B N signifieth the line of the Auge of the circle Equant: and this line is drawn through the centre of the world, and also through the centre of the little circle, marked with B, even as the line of the mean Auge of the Sun is wont to be drawn, as was said in the third definition of the eight Chapter. And the place of the Auge of the said circle Equant is marked with the letter N, like as the point M is the place of the opposite Auge of the said circle Equant. And the arch of the eight Ecliptic, marked with the first star of the Ram's horn, and with the letters M N, is the motion of the Auge of the Equant under the eight sphere. But the arch D M N is the motion of the said Auge under the first movable or from the true Equinoctial point, marked in the said Ecliptic of the first movable with the letter D. The deferents of the Excentrique do move regularly about the centre of the little circle, contrary to the succession of the signs, as the orbs of the Anomalia of the Auge of the Sun do move namely upon their proper poles and axle-tree, and do make their revolution in 365 days, 6 hours, i/33 ii/8 and their daily motion is i/59 ii/8 iii●° iiii/52 And the centre of the little circle is distant from the centre of the world 6 degrees, and from the centre of the Equant 3 degrees, such degrees I mean as the semidiameter of the Equant containeth 60 degrees. By means of which motion, the excentricity of the Planet changeth every day, and is greatest when the centre of the Excentrique is in the Auge of the little circle, and the said excentricity is least when the centre of the said Excentrique is in the opposite Auge of the said little circle, and the said excentricity is mean when the centre of the centre of the Excentrique is in the middle point betwixt the Auge and opposite Auge of the said little circle. All which things were showed in the 7, 8, and 9 definitions of the 8 Chapter. The Excentrique hath his proper motion upon his own poles, which are also movable, and the motion thereof is according to the succession of the signs, which motion although it be irregular and unequal in respect of the centre of the world, yet is the same regular and equal in respect of the centre of the circle Equant: and the daily motion is i/59 ii/8 iii/1 iiii/52 and maketh one entire revolution in 365 days, 6 hours, i/33 ii/8 And this motion is found by subtracting the daily motion of the deferents of the Auge of the Equant (which is iii/9 iiii/31) out of the daily motion of the longitude of Mercury, which is i/59 ii/8 iii/11 iiii/22 for so the remainder will be i/59 ii/8 iii/1 iiii/52 which sum is the daily motion of the Excentrique, counting from the line of the Auge of the Equant. And you have to note, that the motion of the longitude of Mercury is equal unto the simple equal moving of the Sun, so as when you are to find out the equal longitude of Mercury, you have to seek in the Prutenical tables the equal simple moving of the Sun for the time given: and as for the moving of the Anomalia of the Excentrique, you are taught how to find the same at any time by the 8 Precept, by help of the 13 and 14 Cannons, in the Collum, whose title is Apogei Mercurij. As for the true Auge of the Excentrique, the same is found as was showed, in the 15 definition of the 8 Chap. The Epicicle of Mercury hath his proper motion upon his movable axle-tree, and the daily motion thereof is 3 degrees, i/6 ii/24 iii/14 iiii/5 v/36· and maketh one entire revolution in 115 days, 21 hours, i/3 ii/26 iii/54 and the semidiameter of the Epicicle is 22 degrees, i/30 such degrees as the semidiameter of the Excentrique containeth 60, like as was said before of Venus: For since the motion of his longitude is always equal unto the equal simple moving of the Sun, it cannot be but that this Planet must be always near unto the Sun; sometimes going before the same, and then it may be seen in the morning before the Sun riseth; and sometimes it followeth the Sun, and then it may be seen in the evening. Lastly, the greatest equation of the Argument of Mercury, when the centre of his Epicicle is in the Auge of his Excentrique (the Planet being then distant from the Auge of the Epicicle 109 degrees) is 19 degrees, i/3 ii/6 But if he be distant 114 degrees from the Auge of his Epicicle, and that the centre of the Epicicle be in the opposite Auge of the Excentrique, then is the greatest equation of his argument 23 degrees, i●1· ii/35 Now, as for the points, lines, and arches belonging to the calculating of the Motions of Mercury, because they do not differ from those which we have showed in the 5 Chapter, I therefore refer you to that Chapter: and as for the particular equations, you shall find them set down in the 23 Cannon of the Prutenicall Tables. CHAP. XI. Of the first Heaven, or Heaven of the Moon. THe last or lowest Heaven is the Heaven of the Moon, and it consisteth of four orbs, whereof the first is called the orb or circle of Nodes, or the deferent of the head and tail of the Dragon. The next orb is called the deferent of the Epicicles. The third orb is called the first Epicicle. And the fourth is the second Epicicle. All which orbs are set down in this figure following. ¶ The first figure belonging to the Theoric of the Moon. You shall find the two Epicicles of the Moon more plainly set down in the third figure here following. IN the former figure, the two outermost circles do signify the two ecliptics, as in the Heaven of Mercury. Next unto them is another white circle, in which are set the characters of the head and tail of the Dragon, signifying the deferent of the Nodes, and in the middle thereof is the circumference of a circle, in which the two Nodes do continually move. Next unto that is a great broad and black orb, signifying the deferent of the Epicicles: in which orb is a shadowed circle, which representeth the first Epicicle, whose centre is marked with the letter E: and upon the perpendicular line C B are placed two other little circles, one above, and another beneath the centre E, both whose centres are marked with the letter F, and these two little circles being white within, do signify the second Epicicles. And in the circumference of either of them is set the character of the Moon. The point A signifieth the centre of the world, the point B signifieth the Auge of the first Epicicle, and the point C is the opposite Auge of the said first Epicicle. 1. The deferent of the Nodes is an orb in the Theoric of the Moon, in which the Nodes do continually move, marked in the former figure with the head and tail of the Dragon, describing the middle circle of the said orb. This orb is concentrical, that is, hath one self centre with the Zodiac: and the motion of this orb is regular and equal in respect of the centre of the earth, upon the axle-tree and poles of the Zodiac, contrary to the succession of the signs, and the daily motion thereof is i/3 ii/10 iii/47 and in one year moveth 19 degrees, i/10 ii/3 iii/44 and so maketh one entire revolution in 18 Egyptian years, 223 days, 6 hours, i/12 and by the violence or strength of his motion, he carrieth the other orbs round about with him. 2. The deferent of the Epicicles is the foresaid black Orb in the Theoric of the Moon, in which the Epicicles of the Moon are carried continually about. And this black orb hath his own proper motion, which is according to the succession of the signs, and is regular in respect of the centre of the world, marked with the letter A, and moveth upon his own axle-tree, which cutteth the axle-tree of the Ecliptic in the point A, the centre of the world, and the poles thereof are always no more but five degrees from the Ecliptic: whereby it happeneth, that the plane of this Orb cutteth the plane of the Ecliptic in two points, which are called the Nodes, or the head and tail of the Dragon. For the understanding whereof I have set down this other figure next following. ¶ The second figure belonging to the Theoric of the Moon. IN which figure the circle F C E K signifieth the plane of the Ecliptic, and the centre thereof is marked with the point A: and the circle F B E I signifieth the plane of the deferent of the Epicicle, in the circumference whereof is the centre of the first Epicicle, marked with the letter L; and in the circumference thereof is the centre of the second Epicicle, marked with the letter M, and in the circumference thereof is the character of the Moon: and the centre of the deferent of the Epicicle, is the same which the Ecliptic hath, that is to say, the centre A; and this circle crosseth the Ecliptic in two opposite points, that is to say, in the point F and E, called the Nodes, the one of which is called the head of the Dragon, marked with this character 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, and the other is called the tail of the Dragon, marked with this character 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. Unto either of which two Nodes when the Moon cometh, than she is in the Ecliptic, and in her moving from either of the said two Nodes she goeth further and further from the Ecliptic, until she come to one of the 2 limits of her latitude either North or South. 3. Whereof her North limit is marked in this figure with the letter B, and her South limit with the letter l, either of which limits is never more distant from the Ecliptic than five degrees, but from the Nodes each limit is distant 90 degrees. 4. And hereby you may gather, that the two Nodes are nothing else but two points, in which the plane of the deferent of the Epicicles doth cross the plane of the Ecliptic. And the one of these Nodes is called the ascending Node or head of the Dragon, and the other is called the descending Node or the tail of the Dragon. 5. The head of the Dragon is that Node, unto which when the Moon cometh, she beginneth to go Northward from the Ecliptic: and that Node is marked with this character 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. 6. The tail of the Dragon is that Node, unto which when the Moon cometh, she beginneth to go Southward from the Ecliptic, which Node is marked with this character 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. 7. The line of the mean or true moving of the Nodes is a line drawn from the centre of the world unto any of the said Nodes: as in the former figure the line A F signifieth the line of the moving of the head of the Dragon, and the line A E signifieth the line of the moving of the tail of the Dragon. 8. The mean moving of the Nodes is an arch of the Ecliptic, beginning at the first star of the Ram's home or at the first true Vernal Equinox, and endeth at the line of the moving of the Node, so as the said arch be reckoned contrary to the succession of the signs. 9 The true moving of the Nodes is an arch of the Ecliptic, beginning at the first star of the Ram's horn, if the same be reckoned in the Ecliptic of the eight Heaven, or at the true Vernal Equinox, if the same be reckoned in the Ecliptic of the first movable, and ending at the line of the moving of the Node, so as the said arch be numbered according to the succession of the signs. 10. The line of the mean moving of the Moon is a line drawn from the centre of the world through the centre of the first Epicicle, and so forth unto the Ecliptic. As for example, in the first figure the right line A E B is the line of the mean moving of the Moon. 11. The place of the centre of the first Epicicle in the Ecliptic, is that point in which the line of the mean moving of the Moon falleth in the Ecliptic. As in the said first figure the point B in the Ecliptic is the place of the centre of the first Epicicle. 12. The mean simple moving of the moons longitude, is an arch of the Ecliptic, beginning at the first star of the Ram's horn, and ending at the place of the centre of the first Epicicle. As in the said first figure the arch * H K is called the mean, equal, or simple moving of the moons longitude: and the daily moving of this simple longitude is 13 degrees, i/10 ii/34 iii/53 and according unto this motion the Moon maketh her revolution in 27 days, 7 hours, i/43 ii/7 for in this time she returneth unto the first star of the Ram's horn, and this is called the periodical month. As in the first figure the arch * H K is the equal simple moving of the longitude of the Moon. 13. But if the said motion doth begin at the mean place of the Sun, that is, at the line of the mean moving of the Sun, then is it called the equal or mean longitude of the Moon from the Sun, and then the daily motion is 12 degrees i/11 ii/26 iii/41 and according unto this, the Moon maketh her revolution in 29 days, 12 hours, i/44 ii/3 and the time of this revolution is called the Synodical month. So as if you subtract the equal simple moving of the Sun out of the equal simple moving of the moons longitude, the remainder will show the mean longitude of the Moon from the Sun. As in the said first figure suppose the arch * H to be the equal simple moving of the Sun, and the arch * H K to be the equal simple moving of the moons longitude. Now if you subtract * H out of * H K, the remainder will be H K, and that is the mean longitude of the Moon from the Sun. And the finding of this at any time given, is taught in the 8 Precept, by help of the 13 and 14 Cannons, in the Collume whose title is Longitudo media à Sole. 14. And again, sometimes the mean moving of the centre of the first Epicicle or of the Moon, is accounted to begin at the North limit, and then is it called by Ptolomey and Copernicus the mean motion of the latitude of the Moon; because that after the same be corrected, it showeth the true latitude of the Moon: & the finding of this motion at any time is to be found in such order as is showed in the 8 Precept, by help of the 13 and 14 Cannons in the Column, whose title is Latitudinis Lunae. 15. But Alphonsus and his followers make the beginning of the said motion to be at the head of the Dragon, and is called by them the Argument of the latitude of the Moon, and the daily motion of the Moon's latitude is 13 degrees, i/1 ii/45 iii●9· and according unto this motion she maketh her revolution in 27 days, 5 hours, i/5 ii/36 And the Argument of the moons latitude is to be sound at any time given, by adding of 90 degrees unto the mean motion of her latitude: the manner of the finding whereof was showed in the 14 definition of this Chapter. 16. And you have to note, that according to the motion of the deferent of the Epicicle, the centre of the Epicicle is imagined to describe a circle in the middle of the said deferent: which circle is called the circle of the moving of the centre; and this circle is signified in the first figure by the white circle in the middle of the black deferent of the Epicicle, described by the centre of the first Epicicle. 17. The first Epicicle is an orb in the Theoric of the Moon, which continually carrieth about the second Epicicle of the Moon. This orb hath his own proper motion about his own poles and axle-tree, which axle-tree is perpendicular unto the plane of the deferent of the Epicicle, and is parallel unto the said axle-tree of the said deferent: whereby it cometh to pass, that the plane of this first Epicicle is always in the plane of his deferent. And the motion of this Epicicle is contrary to the succession of the signs, and the daily motion thereof is 13 degrees, i/3 ii/53 iii/56 and maketh one entire revolution in 27 days and 13 hours almost: and the semidiameter of this Epicicle is 6 degrees, i/35 whereof the semidiameter of the moving of his centre containeth 60. 18. The Auge of the first Epicicle is a point in the superficies thereof, which is furthest distant from the centre of the earth. And the opposite Auge is that point which is nearest unto the centre of the earth. And the Auge and opposite Auge is determined by a right line drawn from the centre of the earth unto the circumference of the said first Epicicle, through the centre of the same. As in the first figure the point B is the Auge of the first Epicicle, and the point C the opposite Auge thereof. 19 The mean Anomalia of the Epicicle, which is otherwise called the mean Argument, is an arch of the first Epicicle, containing the distance betwixt the centre of the second Epicicle, and the Auge of the first Epicicle. And this is determined by a right line drawn from the centre of the first Epicicle unto the centre of the second Epicicle, as this figure next following showeth. ¶ The third figure belonging to the Theoric of the Moon. IN which figure, the outermost circle representeth the Ecliptic, and the lesser circle within that is a circle which the centre of the first Epicicle is imagined to describe. The semidiameter whereof is the line A E, and the point E signifieth the centre of the first Epicicle, whose semidiameter is the line E B, and the point B is the Auge, and the point C the opposite Auge thereof: the point F signifieth the centre of the second Epicicle, and the arch B F is the mean Anomalia of the Moon: and this is called Anomalia motus in the Prutenicall tables, the finding whereof is taught in the 8 Precept by help of the 13 and 14 Cannons, in the Column, whose title is Anomalia Lunae. 20. The first Epicicle is imagined to be divided into two parts, whereof the one part is called the higher or upper part, and the other is called the lower part of the Epicicle. And these two parts are showed by two right lines, drawn from the centre of the world, marked with A, so as they touch the said first Epicicle on both sides. As in this present figure the two lines, A L and A M are drawn from the centre A, and do touch the first Epicicle in the points L and M: and that part of the Epicicle, which is above the points L and M, marked with the letters L B F M, is the higher part, but the other part, viz. L C M, is the lower part of the Epicicle. 21. And the two points L and M are the Touch-points of the first Epicicle. 22. The second Epicicle is an Orb in the Theoric of the Moon, in the circumference whereof the body of the Moon is always carried about. The plane of this Epicicle is always in the plane of the first, and the axle-tree thereof is perpendicular unto the plane of the first Epicicle, and therefore the axletrees of the two Epicicles and of the deferent of the first Epicicle, are parallels one to another. And the moving of this second Epicicle is contrary unto the moving of the first Epicicle: and the motion hereof beginneth at the Auge of the second Epicicle. 23. The Auge of the second Epicicle is that point in the circumference of the said second Epicicle, which is nearest unto the centre of the first Epicicle: and the opposite Auge thereof is furthest from the centre of the said Epicicle: for these Auges have respect to the centre of the first Epicicle, and not to the centre of the earth. 24. The Anomalia of the Excentrique, which some call the centre of the Moon, is an arch of the second Epicicle, beginning at the Auge of the said second Epicicle, and ending at the body of the Moon. As in the third figure of this Chapter the point R signifieth the Auge of the second Epicicle, and the place of the Moon is signified by her proper character in the circumference thereof, and the arch of the said little circle, contained betwixt R and the character of the Moon, is called the Anomalia of the Excentrique, or centre of the Moon. And this Anomalia is called in the Prutenicall Tables Longitudo Duplicata, or the double longitude of the Moon from the Sun: and the simple longitude was defined before in the 13 definition of this Chapter. And it is called the doubled longitude, because that the motion of the Moon in the second Epicicle is double unto the motion of the centre of the first Epicicle, from the line of the mean moving of the Sun. For according unto this motion the Moon maketh her revolution in 14 days, 18 hours, i/22 ii/1 and her daily motion is 24 degrees, i/22 ii/53 iii/23 and is found in the Prutenicall tables, by doubling the mean longitude of the Moon from the Sun. 25. The line of the true Anomalia of the Moon is a right line drawn from the centre of the first Epicicle unto the body of the Moon. As in the third figure of this Chapter the right line E G, and the character of the Moon is called the line of the true Anomalia, because it is drawn from the centre of the first Epicicle, which is marked with the letter E, unto the body of the Moon, marked with the character of the Moon. 26. The true Anomalia of the Moon, which the Alphonsines do call the true Argument, is an arch of the first Epicicle, contained betwixt the Auge of the said first Epicicle, and the line of the true Anomalia. As in the said third figure the arch B G is called the true or equated Anomalia, or the true Argument of the Moon. 27. The equation of the centre, which in the Prutenicall tables is called the equation of the second Epicicle, is an arch of the first Epicicle, whereby the true and mean Anomalias do differ the one from the other. As in the said third figure the arch B G is the true Argument of Moon, and the arch B F is the mean Anomalia or Argument of the Moon, or of the Epicicle, defined in the 19 definition of this Chapter: the difference betwixt these two arches, is the little arch G F, and this difference, is called the Prosthapheresis of the centre. The finding whereof by the Prutenicall tables, is taught in the 24 Precept, by help of the 18 Cannon, in that Collum whose title is Secundi Epicycli. And this equation is to be added or subtracted from the mean Anomalia, as is showed in the said 24 Precept, to the end that the true Argument or Anomalia may be had. And the greatest equation that can be, is 12 degrees, i/26 ii/57 which then happeneth, when the Moon is in either of the Touch-points of the second Epicicle: which Touch-points are determined by two right lines drawn from the centre of the first Epicicle: and touching the circumference of the second Epicicle, on each side thereof. 28. The line of the true motion of the Moon is a right line drawn from the centre of the world, through the body of the Moon unto the Ecliptic, & the point in the Ecliptic, where that line endeth, is the true place of the Moon: as in the third figure the line A G T signifieth the line of her true moving, and the point T is the true place of the Moon. 29. The true or apparent motion of the Moon is an arch of the Ecliptic, beginning at some known place of the Ecliptic, and ending a● the true place of the Moon: which arch doth begin either at the first star of the Ram's horn, or at the Vernal Equinox, either mean or true, or else at the line of the mean place of the Sun. As in the said third figure the arch * T is the apparent or true moving of the Moon from the first star of the Ram's horn. 30. The equation of the first Epicicle is an arch of the Ecliptic, contained betwixt the line of the mean moving of the Moon, and the line of her true moving. As for example, in the third figure of this Chapter the line A V is the line of the mean moving of the Moon, and the line A T is the line of her true moving, and the arch of the Ecliptic, contained betwixt these two lines, that is to say, the arch T V, is called the equation of the first Epicicle, or the equation of the Argument. And the finding of this equation at any time given, is taught in the 24 Precept, by help of the 18 Cannon, in the Collum, whose title is Primi Epicycli. But because this equation doth vary, and is sometimes greater and sometimes lesser, therefore the absolute and perfect equation is to be found by the proportional minutes, and the excess, which were defined before in the 29 definition of the fift Chapter, and therefore I need not here again to define the same, but only to tell you, that the proportional minutes are to be found in the 18 Cannon, in the Collum, whose title is Scrupula Proportionalia: and the excess is to be found in the said 18 Cannon, in the Column, whose title is Excessus. Here endeth my Extract of Maginus his Theoriques': And if this my labour shall content you, then look shortly for the use of the Prutenicall Tables. THE MAKING, DESCRIPTION, AND USE, OF TWO MOST INGENIOUS AND necessary Instruments for Seamen, to find out thereby the latitude of any place upon the Sea or Land, in the darkest night that is, without the help of Sun, Moon, or Star. First invented by my good friend, Master Doctor Gilbert, a most excellent Philosopher, and one of the ordinary Physicians to her Majesty: and now here plainly set down in our mother tongue by Master Blundevile. LONDON, Printed by Adam Islip. 1602. THE MAKING, DEscription, and use, of two most Ingenious and necessary Instruments for Seamen, to find out thereby the latitude of any place upon the Sea or Land, in the darkest night that is, without the help of Sun, Moon, or Star. OF which two Instruments, the one serveth to find out the declination of the Needle under any Horizon, which declination being once had, than the other Instrument showeth the latitude of that place, having such declination. But because the Instrument of Latitude consisteth of two parts, that is to say, of an immoovable part, which I call the Mater, having therein a Quadrant, containing the 90 degrees of Latitude, and also a spiral line: and the other part is movable, containing a Quadrant, divided into 90 degrees, which are the degrees of declination, and also an Index, with a Fiducial line, showing the Latitude: I mind first here to set down the making of the Instrument of Latitude, because it requireth a number of circles, to find out thereby the spiral line, contained in the Mater of the said instrument of Latitude, the order whereof is here plainly set down, as well by this figure demonstrative, hereto annexed, as by this my description of the same. The Figure. FIrst draw a circle upon a piece of smooth pasteboard, so great, as the whole diameter thereof may contain in length at the least seven or eight inches, and mark the centre of that circle with the letter C: and by drawing two cross diameters, marked with the letters I F and K E, passing through the said centre, and crossing one another in the same with right angles, you shall thereby divide the whole circle into four Quadrants or quarters. And remember, that of the two cross diameters, the perpendicular, marked with I F, must be produced in such sufficient length, as may serve to such purpose as is hereafter showed, as from I to H, so as this perpendicular line is marked with four letters, that is, F C I H, and the other cross or overthwart diameter is marked with three letters, viz. K C E. That done, divide the neither quarter of the said circle on the right hand, marked with the letters F E, into 90 degrees, proceeding from five to five, till you come to 90, marking the same Quadrant with the letters F C E, beginning to account from F to E, which is the arch of the said Quadrant, which I will call from henceforth the inner Quadrant, by help whereof you have to divide as well the middle Quadrant, marked with L N, as the outwardmost Quadrant, marked with M H, as the Figure showeth. And the two last Quadrants do contain each of them 19 circular lines of division, making 18 spaces, every space containing five degrees, and are to be drawn in such order as followeth. First, you have to draw a right line parallel to C E▪ beginning at F, and so proceeding forward towards your right hand in some sufficient length, for the longer, the better to serve your purpose. Then take with your Compass the distance betwixt C and F, and apply that distance to the said right parallel line, by putting the one foot of your Compass in F, and the other at the end of that distance, marking that point with the letter L: then by setting the firm foot of your Compass in C, and by extending the other foot to L, draw a portion of a circle somewhat more than a Quadrant, towards your left hand, and mark the end of that arch with the letter N, which arch is to be divided into 90 equal parts or degrees, by help of 19 circular lines of division, to be drawn as followeth. First set the firm foot of your Compass in F, and with the other foot, extended to the centre C, draw a circle from C to L, and that shall be the first circle of division, showing that the point L is the first point from whence you have to account the 90 degrees of the middle Quadrant, proceeding upward by five and five, until you come to 90. Then to draw the rest of the circles of division, belonging to the said middle Quadrant, you have no more to do but to remove the firm foot of your Compass to every fift degree of the first and inner Quadrant, and always to extend the other foot to the centre C, so shall you justly divide the arch of the middle Quadrant into 90 degrees. Now to draw the arch of the outwardmost Quadrant, marked with M H, you must do thus. First take with your Compass the distance betwixt the letter L and the centre C, and apply that distance to the quarter of the first whole circle on the left hand, marked with the letters F K, which you shall find to be all one, then by setting the one foot of your Compass in F, and by extending the other foot to the end of that distance upon the right parallel line before drawn, and marked with the letters F L, mark that point or end of distance with the letter M, as you see in the foresaid Figure. Then set the firm foot of your Compass in the centre C, and by extending the other foot to the point M, draw a portion of a circle somewhat more than a Quadrant, towards your left hand, and mark the end thereof with the letter H, which shall be the arch of the outwardmost Quadrant, and must be divided into 90 equal parts or degrees, by help of 19 circles of division to be drawn as followeth. First, by setting the firm foot of your Compass in F, and the other in K, draw a circle from K to M, from which point you must begin to account the 90 degrees of that arch, and so to proceed towards your left hand from 5 to 5 until you come to 90, which division is to be made by removing the firm foot of your Compass to every fift point of division, contained in the arch of the first inner Quadrant, marked with the letters F E, extending always the other movable foot to the letter K, and so to draw all the circles of division belonging to the outwardmost Quadrant? That done, you have to draw the spiral line, which cannot be rightly done, until you have divided every one of the circles of division, belonging to the outwardmost Quadrant, each one into 90 parts or degrees, beginning your account at every fift degree of the arch of the same outwardmost Quadrant, and so to proceed from 5 to 5, until you come to the letter K, whereas the 90 degree of every such circle endeth. How to draw the spiral line. You see that in the foresaid Figure the spiral line beginneth at the point L, and endeth at the centre of the first whole circle, marked with C, as the first circle of division, belonging to the middle Quadrant, drawn from C to L, doth plainly show. But because the said spiral line is to be drawn so as it may contain 18 several portions, you have to draw the first portion thereof thus. First divide the second circular line of division, belonging to the outwardmost Quadrant, into 90 equal parts or degrees, proceeding from the fift point of the said second line of division unto K, whereas is set down the 90 degree, serving to all the 19 circles of division belonging to the said outwardmost Quadrant: which is to be done, by dividing the said second line first into three equal parts, and every one of those parts again into three. Then last of all every one of them into two parts, every part whereof shall contain five degrees. And after this manner is to be divided every one of the 19 lines of division belonging to the said outwardmost Quadrant. That done, take with your Compass the first fift part of that second circle, being so divided, and there make a prick: at which prick, lay the one end of your Ruler, and lay the other end thereof at the first fift degree of the inner Quadrant, and so draw a dead right line, which will cut the second line of division belonging to the middle Quadrant, and there make a prick, from which prick to the letter L you have to draw the first portion of the spiral line. Now to draw the second portion of the said spiral line, you must resort to the third circular line of division, belonging to the outwardmost Quadrant: and having divided that line into 90 equal parts or degrees, as you did before the second line, and taken thereof with your Compass ten degrees, there make a prick, to which prick lay the one end of your Ruler, and the other end to the tenth degree of the inner Quadrant, and draw a dead right line, which will cut the third circular line, serving to the middle Quadrant, and there make the second prick, from which prick you have to draw the second portion of the spiral line, so as it may join with the first portion. Then to draw the third portion of the spiral line, you must proceed to the fourth circular line of division, belonging to the outwardmost Quadrant, and divide that into 90 degrees, as you did before, whereof you must take 15 degrees, and there make a prick, to which prick you must lay the one end of your ruler, and the other end to the 15 degree of the inner Quadrant, and having drawn a right dead line, you shall find that it will cut the fourth circular line belonging to the middle Quadrant, and there make a prick, from which prick you have to draw the third portion of the spiral line, so as it may join to the end of the second portion thereof. Now to find out the rest of the 18 portions of the spiral line, you must observe the self same order of working, which you did before in finding out the first three portions. Thus having plainly described unto you the making of the immovable part or Mater of the said Instrument, I will now show you how to make the movable part: which, as I said before, is none other thing but a Quadrant, having an Index, with a Fiducial line, answerable in all respects to the first inner Quadrant, differing only in letters. For whereas the inner Quadrant is marked with the letters F C E, this for difference sake, and for the right placing the same upon the Mater, is marked with the letters A B G. For when you come to use this Instrument, you must place the angle A of the movable Quadrant upon the centre C of the inner Quadrant, there to be fastened with a pin, so as the movable Quadrant may turn round about upon the Mater. The description of the said Instrument. THe outward broad hoop or circle of this Instrument would be of fine Latton or Brass, containing in breadth about an inch and a half, and in thickness almost a quarter of an inch, and the whole diameter thereof would be about five inches, and in the very midst of the inside of the broad circle is traced a middle circle, which is divided into four quarters, every quarter containing 90 degrees, whereof no more are graven with numeral figures, but the two neither quarters, the one on the right hand, and the other on the left hand, and the 90 degree is placed at the neither end, whereas both those quarters do meet. And at the upper end of the broad circle is to be placed a ringle to hold the Instrument thereby, when you would use the same. Now overthwart the said broad circle are fastened in the very midst of the two outsides thereof, two thin plates of Latton, signifying the Horizon, bearing in breadth about a quarter of an inch. The one plate on the one side of the broad circle, and the other plate on the other side of the said circle, standing right and just one against another: of which two plates, each one is bored in the very midst on the inside with a little hole, so as into those two holes may be put an axle-tree of iron, which axle-tree must be biggest in the very midst, to the intent that the Needle being wrought into the axle-tree, may hang just in the midst of the said axle-tree; which Needle would be smaller at the one end than at the other, for the smallest and sharpest end thereof being touched with a perfect stone, doth always show the Magnetical declination of the place, whereas you make your trial. And the Needle itself would be in length almost equal to the whole diameter of the broad circle, yet so, as it may easily play and turn up and down, without touching the same. These parts being fitly and artificially set together, you have to cover the two outsides of the Instrument, each of them with a round and clear glass, that through them you may always see upon what degree the sharp point of the Needle falleth, after it remaineth steady without moving: which glasses, serving to keep the Needle from wind and dust, would be so fastened to the outwardmost edge of the broad circle, as they may stand sure, and not fall away. The use of the said two Instruments. FIrst to find out by this Instrument the declination of the Needle under the Horizon upon the land, you must resort into a place void of wind: or if you would try it upon the Sea, I think it best to go to that place or coubbard of the ship, wherein the Mariner's Compass is wont to stand, and there steadily to hold the Instrument, hanging upon your right or left thumb, so as it may hang right North and South, according as the Mariner's Compass doth direct you, or else by help of some little Dial, whose Needle is touched with a perfect stone, and when you see that the Needle standeth still, mark well upon what degree in the middle line of the broad circle it falleth, for that shall be the degree of Declination for that place. And having found the degree of Declination, take into your hand the Instrument of Latitude, made of Brass or Pasteboard, in such form as you see set down on the right hand of the first figure demonstrative: which Instrument of Latitude consisteth (as I have said before) of two parts, the one unmovable, called the Mater, and the other movable. In the Mater is described a Quadrant, divided into 90 degrees, which are the degrees of Latitude, and also the spiral line. And the movable part containeth a just Quadrant, divided also into 90 degrees, which are the degrees of Declination, together with his Index, having a Fiducial line to show the latitude: and this movable part, when you come to use it, must be placed upon the Mater, so as the angle A of the movable part must be fastened with a pin upon the centre or angle of the Mater, marked with the letter C, in such sort as the movable Quadrant may turn round about upon the Mater. That done, seek out in the arch of the movable Quadrant, the degree of Declination, before found by the instrument of Declination; and lay that degree just upon the spiral line, described in the Mater, and holding it fast there with your thumb, look at that very instant upon what degree of latitude the Index with his Fiducial line falleth, for that shall be the latitude of that place. As for example, M. Doctor Gilbert having found by the Instrument of Declination, as he wrote to me, the declination at London to be 72 degrees: then by applying the same to the Instrument of Latitude, in such order as is before taught, he found the latitude of London to be 51 degrees, 32 minutes. And I proving the same at mine own house at Newton Flotman, not distant above four miles Southward from Norwich, I found the declination of the Needle to be 73 degrees and a little more, and thereby I found our latitude here to be 52 degrees or thereabout. Both these Instruments I received not long since from my dear friend M. Doctor Gilbert, for the which I most heartily thank him, the invention of which Instruments deserveth more worthy commendation and praise, than I am able any way to yield, hoping that all Seamen will be as thankful to him as I am in heart and good will, for whose profit there was never invented from the beginning of the world two such noble and necessary Instruments as these are, and therefore worthy to be esteemed of all men accordingly. By help of the said Instrument of Declination, you may also readily find out the variation of any Mariner's Compass in Northeasting or North-Westing, if you place the Instrument within such a standard as Robert Norman doth set down by figure in his book called, The new Attractive: which point, Master Borough would have to be called the Respective point, and not the Attractive. But M. Doctor Gilbert in his book De magnet, proveth by divers good demonstrations that it ought most properly to be called the point of Coition, or the point Coitive, and neither Respective nor Attractive. The manner how to use the said Instrument, in seeking to know the variation of the Mariners Compass in any latitude, is the self-same which Robert Norman and Master Borough do set down in the foresaid book, whereunto I do refer you, and so bid you well to far. FINIS. A short Appendix annexed to the former Treatise by Edward Wright, at the motion of the right Worshipful M. Doctor Gilbert. BEcause the making and using of the foresaid Instrument, for finding the latitude by the declination of the Magnetical Needle, will be too troublesome for the most part of Seamen, being notwithstanding a thing most worthy to be put in daily practice, especially by such as undertake long voyages: it was thought meet by my worshipful friend M. Doctor Gilbert, that (according to M. Blundeviles earnest request) this Table following should be hereunto adjoined; which M. Henry Brigs (professor of Geometry in Gresham College at London) calculated and made out of the doctrine and tables of Triangles, according to the Geometrical grounds and reason of this Instrument, appearing in the 7 and 8 Chapter of M. Doctor hearts fift book of the Loadstone. By help of which Table, the Magnetical declination being given, the height of the Pole may most easily be found, after this manner. With the Instrument of Declination before described, find out what the Magnetical declination is at the place where you are: Then look that Magnetical declination in the second Collume of this Table, and in the same line immediately towards the left hand, you shall find the height of the Pole at the same place, unless there bosom variation of the declination, which must be found out by particular observation in every place. The Table follows on the next Page. First Col●●●. Second Col●●●. First Col●●●. Second Col●●●. First Col●●●. Second Col●●●. Height of the Pole. Magnetical declination. Height of the Pole. Magnetical declination. Height of the Pole. Magnetical declination. Degrees. Deg. M●n. Degrees. Deg Min. Degrees. Degr. Mi●. 1 2 11 31 52 27 61 79 29 2 4 20 32 53 41 62 ●0 4 3 6 27 33 54 53 63 80 38 4 8 31 34 56 4 64 81 11 5 10 34 35 57 13 65 81 43 6 12 34 36 58 21 66 82 13 7 14 32 37 59 28 67 82 43 8 16 28 38 60 33 68 83 12 9 18 22 39 61 37 69 83 40 10 20 14 40 62 39 70 84 7 11 22 4 41 63 40 71 84 32 12 23 52 42 64 39 72 84 57 13 25 38 43 65 38 73 85 21 14 27 22 44 66 35 74 85 44 15 29 4 45 67 30 75 86 7 16 30 45 46 68 24 76 86 28 17 32 24 47 69 17 77 86 48 18 34 0 48 70 9 78 87 8 19 35 36 49 70 59 79 87 26 20 37 9 50 71 48 80 87 44 21 38 41 51 72 36 81 88 1 22 40 11 52 73 23 82 88 17 23 41 39 53 74 8 83 88 33 24 43 6 54 74 52 84 88 47 25 44 30 55 75 35 85 89 1 26 45 54 56 76 17 86 89 14 27 47 15 57 76 57 87 89 27 28 48 36 58 77 37 88 89 39 29 49 54 59 78 15 89 89 50 30 51 11 60 78 ●3 90 90 0