The theoriques of the seuen planets shewing all their diuerse motions, and all other accidents, called passions, thereunto belonging. Now more plainly set forth in our mother tongue by M. Blundeuile, than euer they haue been heretofore in any other tongue whatsoeuer, and that with such pleasant demonstratiue figures, as euery man that hath any skill in arithmeticke, may easily vnderstand the same. ... VVhereunto is added by the said Master Blundeuile, a breefe extract by him made, of Maginus his Theoriques, for the better vnderstanding of the Prutenicall tables, to calculate thereby the diuerse motions of the seuen planets. There is also hereto added, The making, description, and vse, of two most ingenious and necessarie instruments for sea-men ... First inuented by M. Doctor Gilbert ... and now here plainely set downe in our mother tongue by Master Blundeuile.

CHAP. VIII.

Of the fourth Heauen, or Heauen of the Sunne.

THe next Heauen vnder that of Mars, is the Heauen of the Sunne, and hath his proper and peculiar mo∣tion from West to East.

This Heauen consisteth of fiue orbes: wherof two are called the deferents of the meane Auge of the Suns Ex∣centrique, the other two orbes are called the deferents of the true Auge of his Excentrique, or the orbes of the A∣nomalia of the true Auge and of the excentricitie of the Sunne. The fift Orbe is called the deferent of the body of the Sunne. All which you may euidently see in the figure following.

¶The first figure belonging to the Theorique of the Sunne.

[illustration]

IN which figure, the outermost broad circle, in which are set the caracters of the 12 signes, signifieth the Eclipticke of the eight Heauen, the centre whereof is marked with the letter A, which signifieth the centre of the world. Next vnto this Eclipticke is one of the defe∣rents of the meane Auge signified by the outermost blacke orbe, the centre of whose convex superficies is the point A, and the centre of his concaue superficies is the point B, the other deferent of the said meane Auge is the lesser broad blacke circle, the centre of whose con∣vex superficies is the point B, and the centre of his con∣caue superficies is the point A. And betwixt the blacke orbes are two shaddowed orbes, which are the deferents of the Sunnes Excentrique: and the convex superficies of the outermost of these two shaddowed orbes, as also the concaue superficies of the lower of them haue for their centre the point B, and the concaue superficies of the higher and convex superficies of the lower haue the point C for their centre. Betwixt which two orbes is the Excentrique of the Sunne, which Excentrique is signifi∣ed by the broad white circle: in the middle of which white circle is drawne a circle, in which the centre of the Sunne is continually moued: and the centre of the Ex∣centrique is marked with the letter C, which point is cal∣led the moouable 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 meane Auge of the Sunne are two orbes of vnequall thicknesse, being in some re∣spect concentricall with the Eclipticke, and in another respect excentricall: for the convex superficies of the higher, and the concaue superficies of the lower haue

for their centre the centre of the world, marked with A: but the concaue superficies of the higher, and convex superficies of the lower haue a centre differing from the centre of the world: and these two orbes haue their pro∣per and peculiar motion from West to East vpon the axes and poles of the true Eclipticke, and their Diurnall motion is ⁱⁱⁱ _•° ⁱⁱⁱⁱ ₁₂· and their yearely motion is ⁱⁱ ₂₅· ⁱⁱⁱ ₃₃· ⁱⁱⁱⁱ ₁₂· and do make one entire reuolution in 50717 Aegyptian yeares: and these two orbes doe only serue to carry the meane Auge of the Excentrique.

2. The meane Auge of the Excentrique is that point in the deferent of the Excentrique, which is furthest di∣stant from the centre of the world. As for example, the point G in the former figure signifieth the meane Auge of the Excentrique.

3. And this point is alwaies determined in the Zodi∣ake by a right line, drawne from the centre of the world through the centre of the little circle, marked with B, vnto the Eclipticke line, and the line so drawne, is called the line of the meane Auge, as the line A B G, which is called the line of the meane Auge.

4. But the motion of the meane Auge is an arch of the Eclipticke, beginning at the first starre of the Rams horne, and ending at the line of the meane Auge, as in the said figure the arch * G is the motion of the meane Auge: but if the said arch begin at the Aequinoctiall, whether the same be meane or true, then is the said mo∣tion called the motion of the mean Equinox, extending from the mean Equinox or from the true Equinox vnto the foresaid line of the meane Auge, the finding of eue∣ry of which motions is shewed in the 16 Precept.

5. The deferents of the Excentrique, which some∣times

are called the orbes of the Anomalia of the ex∣centricitie, are the two shaddowed orbes which do carry the orbe Excentrique. And these two orbes haue their proper motion also from East to West, making their re∣uolution once in 3434 Aegyptian yeares, and 10 dayes, and their daily motion is ⁱⁱ ₁· ⁱⁱⁱ ₂· ⁱⁱⁱⁱ ₂· and their yearly moti∣on is ⁱ ₆· ⁱⁱ ₁₇· ⁱⁱⁱ ₂₄· ⁱⁱⁱⁱ ₉· And those deferents are moued vpon 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 se∣midiameter of the Excentrique containeth 60 degrees) and their proper axletree is paralell vnto the axletree of the Eclipticke, and passeth through the centre of the said little circle, as the next figure following sheweth. And the, motion of these orbes doth begin at the line of the mean Auge before defined in the third definition of this chap∣ter. And it is called the Anomalia or Argument of the Auge, and of the excentricitie of the Sunne. By the mo∣tion of which Orbes the centre of the Excentrique is imagined to describe a little circle aboue the centre of the world, whereby the excentricitie of the Sunne chan∣geth euery day.

6. The excentricitie of the Sunne is the distance be∣twixt the centre of the world and the centre of the Suns Excentrique: and this is threefold, greatest, least, or meane.

7. The greatest excentricitie of the Sunne is when the centre of the Excentrique is in the Auge of the little circle, viz. in the point C, and the quantitie of this grea∣test excentricitie, is 2 degrees, ⁱ _3•° ⁱⁱ ₇· such like degrees as the semidiameter of the Excentrique containeth 60 de∣grees, or the quantitie of the said greatest excentricitie

is 41700, when the semidiameter of the Excentrique is 1000000.

8. The least excentricitie is when the centre of the Ex∣centrique is in the opposit 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 deuided into 60 equall parts, but if the said semidiameter be deuided into 1000000, then the said least excentricitie will be 32190.

9. The meane excentricitie is when the centre of the Excentrique is in the middle distance betwixt the Auge and opposit Auge of the little circle, and then the said excentricitie is 0 degrees, ⁱ ₃₄. ⁱⁱ ₁ ⁴. such parts as the semi∣diameter of the Excentrique containeth 60. But if the said semidiameter bee supposed to bee deuided into 1000000 parts, then the said mean excentricitie is 9510. And the semidiameter of that little circle containeth 0 degrees, ⁱ ₁₇·. ⁱⁱ ₇·

10. The Anomalia of the Auge and excentricitie, which is also called the centre of the Sunne, is an arch in the concaue superficies of the outermost deferent of the meane Auge, which arch is comprehended betwixt the line of the meane Auge, and a right line drawn from the centre of the little circle through the mouable cen∣tre of the Excentrique vnto the concave supe••ficies of the said outermost orbe. 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 mouable centre of the Excentrique. As for example.

¶The second figure belonging to the Theorique of the Sunne.

[illustration]

In this figure suppose the point A to be the centre of the world, and B the centre of the concave super∣ficies of the outermost of the two deferents of the meane Auge, and C the centre of the Excentrique, whose place was sometimes in the point P, but now is gone from thence vnto C, so is A G the line of the meane Auge, and A P is the greatest excentricitie, and A O the least excentricitie, and P O is the difference betwixt the greatest and least excentricitie, the halfe

whereof is B O, and A B is the quantitie of the meane excentricitie, and the place of the centre of the Excen∣trique is in the point C, and the arch G F is the Ano∣malia or Argument of the Auge and of the excentrici∣tie in the concaue superficies of the highest deferent of the meane Auge, and the arch P C of the little circle is the Anomalia of the Auge and excentricitie: and the right line B C F is the line which sheweth the meane Auge of the orbes of the Anomalia of the Auge, in re∣spect of their centre.

11. The meane Auge of the orbes of the Anomalia of the excentricitie, is that point in the concave superfi∣cies 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 drawne from the centre of the said little circle, through the mouable 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 vnto the concauitie of the highest deferent of the Excentrique, as vnto the point E, the said point E is the mean Auge of the orbes of the Anomalia of the excentricitie. Now if you adde the daily mouing of this meane Auge, which is ⁱⁱ ₁· ⁱⁱⁱ ₂· ⁱⁱⁱⁱ ₂· (as was said in the fift definition of this Chapter) vnto the daily moouing of the meane Auge of the excentricitie, which is ⁱⁱⁱ ₄· ⁱⁱⁱⁱ ₁₂· (as was said in the first definition of this Chapter) the summe of that addition will be ⁱⁱ ₁· ⁱⁱⁱ ₆· ⁱⁱⁱⁱ ₁₄· and this is the daily distance betwixt the two meane Auges, viz. that of the excentricitie, and this of the orbes of the Anomalia of the excentricitie.

12. The orbe Excentrique is an orbe in the Theorique

of the Sunne, in which the body of the Sunne is conti∣nually caried about. This orbe is placed betwixt the two orbes, which are the deferents of the Excentrique, and mooueth from West to East vpon his owne moouable centre (which centre is mouable, by reason of the moo∣uing of the two orbes, which are the deferents of the Excentrique) and the axletree which is also mouable ac∣cording to the motion of the centre of the Excentrique in the circumference of the said litle circle. And the dai∣ly motion of this orbe from the meane Auge of the orbes of the Anomalia of the excentricitie is ⁱ ₅₉· ⁱⁱ ₉· ⁱⁱⁱ _•3· ⁱⁱⁱⁱ ₂₄· and maketh his entire reuolution in 365 dayes, 3 houres, ⁱ ₃₆· ⁱⁱ ₂₅· which motion is reckoned from the meane Auge of the orbes of the Anomalia of the ex∣centricitie. For the Sunne returneth to the said point or meane Auge in 365 dayes, 3 houres, ⁱ ₃₆· ⁱⁱ _2•°

13. The line of the true place of the Sunne is a right line drawne from the centre of the world through the centre of the Sunne vnto the Eclipticke: and the point in the Eclipticke in which the said line endeth, is the true place of the Sunne. As in the former second figure, sup∣pose the centre of the Sunne to be in the point M of the Excentrique, and hauing drawne a line from A to M, and so forth vnto the Eclipticke in the point R, the said line A R is called the line of the true place of the Sunne, and the point R is said to be the true place of the Sunne in the Eclipticke.

14. The yearely Anomalia of the Sunne, which is al∣so called the meane Argument of the Sunne, is an arch of the Excentrique, which is comprehended betwixt the line of the meane Auge of the Excentrique, and the line of the true place of the Sunne. As in the foresaid second

figure the arch L M is called the yearely Anomalia of the Sunne.

Or thus, The yearely Anomalia of the Sunne is the excesse or difference, whereby the daily motion of the Sun from the mean Auge of the orbes of the Anomalia of the excentricitie, exceedeth the daily distance betwixt the meane Auge of the Excentrique, and the meane Auge of the orbes of the Anomalia: and this Anoma∣lia is found by subtracting the daily distance of the said two Auges, which is ⁱⁱ _1•° ⁱⁱⁱ ₆· ⁱⁱⁱⁱ ₁₄· (as was shewed 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 meane Auge of the orbes of the Anomalia of the excentricitie (as was shewed before in the 12 definition:) the remainer of which subtraction will be ⁱ ₅₉· ⁱⁱ ₈· ⁱⁱⁱ ₇· ⁱⁱⁱⁱ ₁₀· And although that this Anomalia doth belong properly vnto the Ex∣centrique: yet notwithstanding the said Anomalia is al∣so supposed to be in the Eclipticke, by imagining a line to bee drawne from the centre of the world vnto the E∣clipticke, in such order as that the said line may be para∣lell vnto another line which is drawne from the centre of the Excentrique vnto the place or centre of the Sun: and the line so drawn, may be called the line of the Imagina∣rie motion of the Sun. As in the foresaid second figure let a right line be drawn from C to M, then vnto the same line draw another paralell right line from the centre A, and produce the same vnto the Eclipticke in the point N; so shall the arch of the Eclipticke, which is compre∣hended betwixt the points E and N, bee the yearely Anomalia or meane Argument of the Sunne in the Zo∣diake. The finding of which Anomalia for any time ap∣pointed, is taught in the 8 Precept, by helpe of the 13

and 14 Cannons in that Collum, whose title is Anoma∣lia 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 shewed by a right line drawne from the centre of the world through the moouable centre of the Excentrique vnto the Eclipticke, and the point in the Eclipticke, in which the said right line doth end, is the place of the true Auge of the Excentrique in the Eclipticke: and the said right line is called the line of the true Auge of the Ex∣centrique: 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 Eclipticke, in which the said line endeth, is the place of the true Auge in the Eclipticke, the finding whereof is taught in the 16 Precept.

16. The motion of the true Auge of the Excentrique is an arch of the Eclipticke, beginning at some princi∣pall point in the Eclipticke, and ending at the line of the true Auge of the Excentrique: which principall point if it be the first starre of the Rams horne, then is the said motion called the moouing of the true Auge from the first starre of Aries: and if the said motion or arch doth begin at the true Equinox, then is the said motion called the moouing of the true Auge from the true E∣quinox.

17. The equacion of the centre is an arch of the

Eclipticke, which is comprehended betwixt the meane Auge of the outer blacke orbes, and the true Auge of the Excentrique, as in the foresaid second figure of this Chapter, the arch K G in the Eclipticke is called the equacion of the centre: and this equacion neuer excee∣deth 7 degrees, ⁱ ₂₃· ⁱⁱ ₃₆· the manner of the finding of which equacion is shewed in the 15 Precept, by helpe of the 17 Cannon in that Colume, whose title is Centri.

18. The true Argument of the Sunne, which is also called the equated yearely Anomalia, is an arch of the Ecliptick, which is contained betwixt the line of the true Auge of the Excentrique, and the line of the Imaginarie motion of the Sunne. As in the foresaid second figure the line A K is the line of the true Auge of the Excen∣trique, and the place of the said true Auge in the Eclip∣ticke is the point K. Likewise the line A N is the line of the Imaginarie motion of the Sunne. Now the arch of the Eclipticke, which is contained betwixt the 2 points K and N, is called the true Argument or equated Argu∣ment of the Sunne. For the difference betwixt the mean and true Arguments of the Sunne, is also the difference which is betwixt the meane and true Auge of the Excen∣trique, which difference is called the equacion of the cen∣tre before defined in the 17 definition of this Chapter. The manner of equating the Argument, is taught in the 15 Precept.

19. The equall simple mouing of the Sunne is an arch of the Ecliptick, beginning at the first starre of the Rams horne, and ending at the line of the Imaginarie motion (which line we call hereafter the line of the meane moo∣uing of the Sunne) as in the foresaid second figure of this Chapter, the arch * N is the equall simple moouing of

the Sunne: The quantitie of which simple moouing is ⁱ ₅₉· ⁱⁱ ₈· ⁱⁱⁱ _1•° ⁱⁱⁱⁱ ₂₂· euery day, and according to this motion the Sunne maketh one entire reuolution in 365 dayes, 6 houres, ⁱ ₉· ⁱⁱ ₃₉·

20. The equall compound mouing of the Sunne is an arch of the Eclipticke, beginning at the meane ver∣nall Equinox, and ending at the line of the meane moo∣uing of the Sunne. Whereby it appeareth, that if the meane Precession of the Equinox be added vnto the e∣quall simple motion of the Sunne, the summe 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 Sunne according to the equall compound motion ma∣keth his reuolution in 365 dayes, 5 houres, ⁱ ₄₉· ⁱⁱ ₁₆· The manner of finding of these two equall motions of the Sun, that is to say, the simple and compound moouing, is taught in the 8 Precept, by helpe of the 13 and 14 Cannons.

21. The true motion of the Sunne is an arch of the Eclipticke, beginning at the first star of the Rams horne, and ending at the true place of the Sunne: and then is the said true motion called the true mouing of the Sun vnder the 8 sphere. But sometimes the said arch of true motion is supposed to begin at the true Vernall Equi∣nox, and then it is called the true motion of the Sunne vnder the first mouable.

22. The proportionall minutes are the 60 parts wher∣by the equacions of the Argument doe encrease or de∣crease, according as the excentricitie of the Sun encrea∣seth or decreaseth. The finding of which proportionall minutes is taught in the fifteenth Precept, and are set downe in the seuenteenth Cannon in the Collum, whose

title is Scrupula Proportionalia.

23. The equacion of the Argument or yearely Pro∣sthapheresis is an arch of the Eclipticke, which is com∣prehended betwixt the line of the meane moouing and the line of the true mouing of the Sun. And this equa∣cion of the Argument is nothing, when the Sunne is ei∣ther in the Auge or in the opposit Auge of the Excen∣trique, and is alwaies greatest in the meane longitudes of the Sunne: which meane longitudes are pointed out in the circumference of the Excentrique, by a right line drawne perpendicularly vpon the line of the true Auge through the centre of the world. As in the foresaid se∣cond 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 perpen∣dicular line is the line T V, and beeing produced vnto the Excentrique, sheweth the points T and V to be the points of meane longitudes. And the greatest equacion 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 Excen∣trique 93 degrees. But when the centre of the Excen∣trique is in the opposit Auge of the said little circle, then is the greatest equacion of the Argument no more but 1 degree, ⁱ ₅₀· ⁱⁱ ₄₁· and that is when the distance of the Sunne from the true Auge, is 92 degrees. And this equa∣cion is called in the tables, The equacion of the orbe: the finding whereof is taught in the 15 Precept, by helpe of the 17 Cannon, in the Collum whose title is Orbis.

24. The true argument of the Sunne, is the distance of the Sunne from the true Auge of his Excentrique.

25. The excesse or diuersitie of the diameter, is an arch of the Eclipticke, whereby the equacion of the ar∣gument (the centre of the Excentrique being in the Auge of the little circle) exceedeth the equacion of the argument, when the centre of the Excentrique is in the opposit Auge of the little circle. The true argument of the Sunne being of one selfe quantitie in each position of the centre of the Excentrique in the circumference of the little circle. For the equacions of the argument doe decrease continually, so long as the centre of the Excentrique is descending from the Auge of the little circle, vntill it come to the opposit Auge of the said litle circle, and from thence do begin againe to encrease, vn∣till the centre of the Excentrique returneth again vnto the Auge of the little circle. The finding of which Ex∣cesse is taught in the 15 Precept, and is set downe in the 17 Cannon in that Colume, whose title is Excessus.

26. The coequated and true equacion, which is other∣wise called the absolute equacion of the orbe, is an arch compounded of the true equacion of the argument, and of the excesse, proportionable vnto the proportio∣nall minutes.