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.

A breefe Extract of Maginus his Theoriques, shewing all the definitions of such names and motions as are needfull to be knowne for the calculating of the places of any of the seuen Planets, or other motions of any Heauen whatsoeuer, that are to be found out by the Prutenicall Tables.

TO auoid the Paradoxicall supposition of Copernicus, supposing the Earth to mooue, and the Sunne to stand still in the middest of heauen, Maginus is fain to suppose that there be three mo∣uable heauens aboue the eight heauen, and so maketh in all eleuen mouable heauens, which is one more than all the other Astronomers haue hereto∣fore set downe. And he calleth the highest or eleuenth heauen, the first mouable, describing the same as hereaf∣ter followeth: next to which is placed in his Theoriques the tenth heauen, then the ninth and eight heauen, and vnder that, the seuen Planets, that is, first Saturne, then Iupiter, Mars, Sol, Venus, Mercurie, and Luna, which is the lowest heauen of all. Of which his Theoriques I thought good to make a breefe Extract, because that more tearmes belonging to the Prutenicall Tables are therein both defined and demonstrated, than are set downe either by Purbachius or by Mes••elyn in their The∣oriques.

And according to the number of this eleuen Heauens, I haue deuided this Extract into 11 chapters.

CHAP. I.

The description of the eleuenth Heauen or first mouable, to∣gether with such definitions as are contained therein.

THe first mouable is the greatest or highest heauen, which carieth all the inferior heauens round about from East to West in 24 houres. The concaue su∣perficies whereof is imagined to be traced with certaine circles, whereof some be greater and some lesser.

2. The greater circles cheefely seruing for our pur∣pose, are these, the Aequinoctiall, the Eclipticke, and the two Colures, the one called the Colure of the Equino∣xes, and the other the Colure of the Solstices.

3. The Aequinoctiall is a great circle supposed to be in the convex superficies of the first mouable, deuiding the same superficies into two equall parts, the poles of which circle are the poles of the world, vpon which poles the said first mouable continually mooueth, making his reuolution in 24 houres.

4. The Eclipticke of the first mouable is also a great circle, deuiding the superficies thereof into two equall parts, & cutteth the Aequinoctiall in two opposit points, which points are called the Equinoxes, one of them be∣ing called the Vernall Equinox, and the other the Au∣tumnall Equinox: and the poles of this Eclipticke are alwaies distant from the poles of the world 23 degrees, ⁱ ₄₀· and doe neuer alter. And this Eclipticke is called the meane Eclipticke.

5. The Colure of the Equinoxes, is a great circle

passing through the two Equinoxes, and the two poles of the world.

6. The Colure of the Solstices, is also a great circle deuiding the superficies of the first moouable into two equall parts, and is drawne both through the poles of the world, and also through the poles of the meane Eclipticke.

CHAP. II.

Of the tenth Heauen.

THe tenth Heauen is a great Orbe next vnto the first mouable, hauing contrarie motion to the first moouable, that is, from West to East vpon the poles of the Eclipticke of the first moouable or meane Eclipticke, and maketh his reuolution in 3434 Aegyptian yeares, and 10 daies.

2. In this heauen are imagined to be described such like greater circles, as are before described in the first mouable: for the Aequinoctiall of this heauen and the two Colures are in one selfe plaine, right vnder the Ae∣quinoctiall and Colures of the first moouable: but the Eclipticke of this heauen is mouable, by reason of the vnstabilitie of the poles of the Eclipticke of the said tenth sphere: for the better vnderstanding of which vn∣stabilitie, Maginus setteth downe this figure.

[illustration]

In which, imagine the letter A to be the pole of the meane Eclipticke of the first moouable, and also the pole of the tenth heauen, about which pole the tenth sphere maketh his reuolution in 3434 Aegyptian yeares, and 10 daies. And vpon the point A imagine also a lesser circle to be drawne, whose semidiameter is A B, containing in length ⁱ _•° and imagine the same lesser cir∣cle to be the circle B D F, in the circumference where∣of, suppose the centre of another lesser circle equall to that, to be placed in the point D, and let the semidiame∣ter 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 neuer to change his place, but to mooue about the pole A, as the tenth heauen mooueth about the same pole A. And so likewise suppose the second lit∣tle 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 colure of the first mo∣uable; which Colure 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 where∣soeuer that happeneth vpon the line C G, is the pole of the Eclipticke of the tenth heauen, whose pole doth con∣tinually alter his place, and therefore the place of the Eclipticke of the said tenth heauen, must needs alter, be∣ing sometimes farre from the meane Eclipticke, and sometimes neare vnto it, and sometimes vnited there∣with. 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 Eclipticke, & the poles of the first moouable: for the poles of the Eclipticke of the tenth heauen can neuer exceed ⁱ ₁₂· and the Ecliptick of this tenth heauen is called the true Eclipticke, whose poles doe differ from the poles of the meane Eclipticke ⁱ ₁₂· as haue been said before.

3. And such distance is called the equacion of the ob∣liquitie of the Eclipticke, which the former figure doth plainely demonstrate: for the letter A is supposed to be the pole of the meane Eclipticke, and H the pole of the true Eclipticke: and this equacion of the obliquitie is to be found in the 16 Cannon of the Prutenicall tables, by helpe of which equacion or Prosthapherisis, you may find at any time the obliquitie of the true Eclipticke, as is taught in the 13 precept of the said tables. But now be∣cause the said Prosthapherisis cannot bee found but by the Anomalia of the obliquitie, you are to know first what that Anomalia is, which the foresaid figure dooth

also shew. 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 alwaies fixed in the point A: and the other end marked with E, by the motion of the tenth heauen, describeth the great circle C E G.

4. And this circle is called the circle of Anomalia of the obliquitie of the true Eclipticke.

5. And the arch or portion of this circle, marked with the letters C E, is the Anomalia of the obliquitie of the true Eclipticke: the motion of which Anomalia you shall find at any time by the Prutenicall tables in the 14 Cannon vnder the title Anomalia Aequinoctiorum in such order as the eight precept teacheth.

CHAP. III.

Of the ninth Heauen.

THe ninth Heauen is a sphere situated next and im∣mediatly vnder the tenth heauen: the motion of which ninth sphere is from North to South vpon his proper poles, which are fixed in the two Aequinocti∣all points, called the true Aequinoctiall points of the tenth heauen, about which poles he maketh his reuolu∣tion in 1717 Aegyptian yeares and 5 daies.

In this sphere are imagined certaine circles both greater and lesser to be drawne, as in the former two hea∣uens: but the greater circles whereof we shall haue most vse, are these, that is, the Eclipticke and the Aequinoctiall.

2. The Eclipticke of this ninth sphere is alwaies in the plane of the Eclipticke of the tenth sphere, and ther∣fore doth not differ from the true Eclipticke, because it neuer swarueth from the same: but the Aequinoctiall

line of this ninth sphere is mouable, according as the two Aequinoctiall points in which it crosseth the true Eclipticke, are moouable, being caried both backward and forward, and sometimes are conjoined together with the Aequinoctiall points of the tenth heauen, and some∣times againe are remooued from the said true Aequino∣ctiall points of the tenth sphere, and the greatest distance that the said two points can haue from the Aequinoctiall points of the tenth sphere is 1 degree, ⁱ ₁₂· ⁱⁱ ₂₂· ⁱⁱⁱ ₃₀·

The motion of which Aequinoctiall points, and also of the sphere it selfe, you shall more easily vnderstand by this figure here following.

[illustration]

IN which, the point A signifieth the Vernall Aequino∣ctiall point, as well of the tenth heauen, as of the first mouable, which point we will hereafter call the true ver∣nall Aequinox, in which point one of the poles of the ninth sphere is supposed to be fixed, and the other pole

is in the opposit point, which is the true Autumnall Ae∣quinoctiall point. Now vpon the centre A imagine a little circle to be drawne, whose semidiameter is A B, containing in length vpon the superficies of the said ninth sphere, ⁱ _•5· ⁱⁱ ₄₁· ⁱⁱⁱ ₁₅· and in the same convex superfi∣cies imagine a second little circle to be drawne, equall vnto 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 con∣taine in length 1 degree, ⁱ ₁₁· ⁱⁱ ₂₂· ⁱⁱⁱ ₃₀· and suppose the right line K G to be the true Eclipticke, and the right ouer∣thwart line I F to be the AEquinoctiall line of the tenth heauen and also of the first mouable. Now the circum∣ference of the second little circle wil crosse the true Eclip∣ticke K G in some one point or other, as in the point E, which point of Intersection, wheresoeuer it happeneth to be, is the place of the Vernall Aequinoctiall point of the ninth sphere: which Vernall Aequinoctiall point we will henceforth call the meane Equinox, as the point A is the true Equinox. So that hereby you may perceiue, that the meane Equinox is nothing els but that point in which the Aequinoctiall line of the ninth sphere cros∣seth the Eclipticke line of the said ninth sphere or true Eclipticke.

3. The Prosthapheresis of the Equinox is the distance which is betwixt the true and meane Equinox, as is the line A E: and this Prosthapheresis you shall find in the 16 Cannon, vnder the title Praecessionis Aequinoctiorum, the manner of finding whereof is taught in the 10 Pre∣cept. But because the said Prosthapheresis cannot bee found but by helpe of the Anomalia of the Equinox.

4. I will therefore shew what the said Anomalia of the Equinox is. For the vnderstanding whereof, resort to the former figure, in which you see how the tip or extreame 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 alwaies reckoned: and the distance be∣twixt the point L and the point D, is the Anomalia of the Equinox it selfe, and is alwaies double vnto the Ano∣malia of the obliquitie of the true Eclipticke, and there∣fore we vse to doe no more but to double the Anomalia of the said obliquitie, otherwise called the simple Ano∣malia, which is to be found by the 14 Cannon, vnder the title, Anomalia Aequinoctiorum, in such order as the eight Precept teacheth.

CHAP. IIII.

Of the eight Heauen.

1. THe eight Heauen is situated vnder the ninth Hea∣uen, and moueth from West to East contrarie to the motion of the first moouable, vpon the poles of the true Eclipticke, making his reuolution in 25816 Aegyp∣tian yeares, and dependeth wholly vpon the meane Equinox.

2. In this sphere are imagined also an Aequinoctiall and an Ecliptick line: and the Ecliptick line of this Heauen is alwaies in the same plane with the Ecliptick of the 9 and 10 Heauens, and swarueth not from the true Ecliptick at all. But the Aequinoctiall points of this sphere do moue from the true Equinoxes, sometimes forward, and some∣times

times backward, euen as the meane Equinox of the ninth sphere moueth.

3. This sphere is apparent to the eye, by reason of the multitude of starres which are therein: the moouing of all which starres, and all other the inferior lights, is ac∣counted or reckoned from the first starre of the Rams horne, as from a visible beginning, although the same be vnstable, by reason of the changeable moouing of the Precession of the meane Vernall Equinox.

4. The Precession of the Equinox is a portion of the true Ecliptick, comprehended betwixt two great circles, whereof the one passeth through the first starre of the Rams horne, and the other through the Equinox; which if it be the true Equinox, then the arch of the Eclipticke, comprehended betwixt the two said circles, is called the true Precession: but if it passe through the meane Equi∣nox, then it is called the meane Precession of the Ver∣nall Equinox.

[illustration]

As for example, suppose in this figure the line K G to be the true Eclipticke, and I F to be the Aequinoctiall of the first moouable, crossing one another in the point A, which representeth the true Equinox, vnto which point when the Sunne commeth, it is Equinox throughout all the world: and suppose M to be the first star of the Rams horn, through which a right perpendicular line passeth, signifying a great circle drawne through the first starre of the Rams horne, & also through the poles of the true Eclipticke: and suppose L H to be another great circle drawne through the true Aequinoctiall point A, and through the poles of the true Eclipticke, so shall M A be the true Precession of the Vernall Equinox. In like manner suppose the line D E to bee another great cir∣cle, passing through the point E, signifying the meane Equinox, and also through the poles of the true Eclip∣ticke, so as the arch of the true Eclipticke, which is com∣prehended betwixt M and E, is the meane Precession of the vernall Equinox. And this meane Precession is readily found by the 14 Cannon, as the 8 Precept tea∣cheth, and the title thereof in the said 14 Cannon, is Praecessionis Aequinoctiorum. But the true Precession is to be found by helpe of the Prosthapheresis, which was defined in the third definition of the third chapter.

And although that there be many other circles both great and little, which the Astronomers vse, as the circles of Positions, Azimuths, and many others, yet will I only speake of such circles, arches, and points in the Heauen as are belonging to our present purpose (because I haue spoken of the others in my sphere) shewing what is the longitude, latitude, and declination of any star or point in this Heauen.

5. The longitude of any starre is an arch of the Eclip∣ticke, comprehended betwixt the true Vernall Equinox, and the circle of latitude of the said starre or point.

6. The circle of latitude is a great circle passing through the poles of the true Eclipticke and the centre of the starre. Of which circle, that part which is betwixt the centre of the starre and the true Eclipticke, is called the latitude of the starre.

7. The circle of declination is a great circle, passi••g through the poles of the world, and through the centre of any starre or other point in the firmament: and that part of this circle which is contained betwixt the said starre and the true Aequinoctiall line, is called the decli∣nation of the starre.

CHAP. V.

Of the seuenth Heauen, that is, the heauen of Saturne.

1. THe seuenth Heauen is situated next vnder the eight Heauen or Sphere, and mooueth from West to East, and is onely proper to Saturne, which is the highest Planet: whose orbes and motions thereof, this figure here following doth plainely shew.

¶The first figure belonging to the Theorique of Saturne, together with the description thereof.

[illustration]

In this figure, consisting of certain circles & right lines, you see that the three outermost great circles drawn vpon the p••int A, signifying the centre of the world, do enclose two w••••••te seuerall spaces, and in each space are set down

the caracters of the 12 signes: of which two spaces, the outermost representeth the Eclipticke both of the 10 and 9 Heauen, the beginning of which Ecliptick is mar∣ked on the right hand with the letter D, signifying the true Vernall Equinox: and the next space vnder that re∣presenteth the Eclipticke of the eight Heauen, whose be∣ginning is marked with a little starre, ••ignifying the first starre of the Rams horne.

2. And the two blacke orbes doe represent the defe∣rents of the Auge, which Auge is marked with the letter I, & the opposit Auge with the letter R, which deferents doe moue regularly, and doe make their reuolution in 35333 Aegyptian yeares: and betwixt the two balcke orbes is another white orbe, signifying the orbe Excen∣trique, drawne vpon his owne centre, marked with the letter B, in the middest of which broad white circle is another circle described by the centre of the Epicicle, marked with the letter E, vpon which point E is drawne a little circle, signifying the Epicicle it selfe, which carri∣eth the body of the Planet, in the circumference wherof is a little starre, representing the body of Saturne. You see also that there is another circle which crosseth the foresaid middle circle of the Excentrique in two points opposit, drawne vpon his owne 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 helpe of the let∣ters hereafter declared: for the right line which is drawne from the point A vnto the point I, and so foorth to the Eclipticke, is called the line of Auge: and the point or degree of the Eclipticke, into which the line of the Auge falleth, is called the place of the Auge, which for exam∣ple

sake suppose to be in the first point of Gemini, mar∣ked with the letter F. And the arch comprehended be∣twixt the point F and the first starre of the Rams horne, signified by the little starre set downe on the right hand in the true Eclipticke is called the meane motion of the Auge. And the right line A B is called the excentrici∣tie of the Excentrique, containing in length 3 degrees, ⁱ ₂₅· and the right line A C is the excentricitie of the cir∣cle Equant, containing in length 6 degrees, ⁱ ₅₀·

3. The Auge is that point in the superficies of the Ex∣centrique which is furthest distant from the centre of the world, marked with the letter 1. But the opposit Auge is that point in the superficies of the said Excentrique, which is nearest vnto the centre of the world, marked with the letter R.

4. The place of each point is shewed by a right line drawne through the centre of the world & also through the Auge of the Excentrique vnto the Zodiake of the eight Heauen, marked with the caracters of the twelue signes, and the line so drawne, is called the line of Auge.

5. The meane motion of the Auge is an arch of the Eclipticke, proceeding from the first starre of the Rams horne vnto the place of the Auge, and is found in such order as is shewed in the eight Precept, by helpe of the 13 and 14 Cannons in that Colume, whose title is Apo∣gaea Saturni.

6. But the true motion of the Auge is an arch of the Eclipticke, beginning at the true Vernall Equinox, and ending at the place of the Auge: the manner how to find the same, is shewed in the 33 Precept.

7. The orbe Excentrique, is an orbe of one equall thicknesse, compassing the centre of the world, in which

Excentrique the Epicicle is alwaies caried, and maketh his reuolution in 29 Aegyptian yeares, 183 dayes, and almost 5 houres, the Diurnall 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 vnto the concauitie of the Ex∣centrique, are equall.

9. The distance betwixt which centre and the centre of the world is called the excentricitie of the Excen∣trique: 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 vpon the point C in the plane of the Excentrique, in regard of the centre wherof, the motion as well of the Excentrique as of the Epicicle, is regular and equall. And this circle is sometimes called the circle of equalitie, sometimes the Equator, and other times the Excentricall 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 cen∣tre of the world is called the Excentricitie of the circle Equant.

11. The Epicicle is a little orbe, whose centre is mar∣ked with the letter E, which the Excentrique carrieth a∣bout, which Epicicle notwithstanding hath his proper motion, for the higher part thereof hath his moouing according to the succession of the signes, and the lower part contrarie to the succession of the signes. The daily motion of the Epic••cle about his owne centre, is ⁱ ₅₇· ⁱⁱ ₇· ⁱⁱⁱ ₄₄· and maketh one ent••e reuolution in 378 dayes, 21 houres, ⁱ ₃₆·

12. But because that the accounting of the motions by the circle Equant is troublesome, therefore the Astro∣nomers doe vse to reckon the fame vpon the Eclipticke, by imposing a line to be drawne from the centre of the world vnto the Eclipticke, in such sort, as the same may be paralel vnto the line before drawne: as in the foresaid figure, the line A G being paralell vnto the line C E, is called the line o•• the meane moouing of the Epicicle or of the Planet.

13. The meane Anomalia of the Excentrique is an arch of the Ecliptick, beginning at the line of the Auge, and so proceeding according to the succession of the signes, vntill at end at the line of the meane moouing, as in the foresaid figure the line A F is the line of the Auge, and A G is the line of the meane moouing. Now the arch of the Eclipticke, which is comprehended betwixt the two lines, A F, and A G, that is to say, the arch F G is called the meane Anomalia of the Excentrique, and of some it is called the meane or equall centre.

14. But if the said arch bee reckoned from the first starre of the Rams horne, vnto the line of the meane mouing, marked with A G, then the said arch is called the equ••ll motion of longitude, which you may find by the Tables at any time, supposed by the 13 and 14 Can∣nons in the Colume, whose title is Longitudinis Saturni, in such order as is shewed in the eight Precept.

The equall or meane moouing of the longitude of Saturne, is daily ⁱ ₂· ⁱⁱ ₀· ⁱⁱⁱ ₂₇· ⁱⁱⁱⁱ ₁₈· and the yearely motion thereof is 12 degrees, ⁱ ₁₂· ⁱⁱ ₄₆· ⁱⁱⁱ ₄· and the whole reuoluti∣on is in 29 Aegyptian yeares, 174 dayes, 4 houres, ⁱ ₅₈· ⁱⁱ ₂₄· for in that time it returneth to the first starre of the Rams horne.

15. The line of the true mouing of the Epicicle is a right line drawne from the centre of the world, passing through the centre of the Epicicle vnto the Eclipticke, 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 Excen∣trique (which is called by the Alphonsines the true cen∣tre) is an arch of the Eclipticke, 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 fore∣said 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 Eclipticke, beginning at the first starre of the Rams horne, and endeth at the true place of the centre of the Epicicle, as in the foresaid figure, the arch from the Rams horne, marked with a little starre in the Eclipticke of the eight sphere, to L, is called the true mouing of the longitude of the Epicicle.

18. The Prosthapheresis or Equacion of the centre, is the difference betwixt the meane Anomalia and the coequated Anomalia of the Excentrique, or the diffe∣rence betwixt the equall mouing and the true moouing of longitude. As the arch L G is called the equacion of the centre, and this equacion is neuer greater than 6 degrees, ⁱ ₃₀· ⁱⁱ ₃₀· and is alwaies greatest when the equall mouing of the centre of the Epicicle from the Auge of the Excentrique, is 11 Sex. 33 degrees, whether the same bee reckoned according to the succession of the signes, or contrarie to the succession of the signes: and from thence it decreaseth vntill the line of the said mean moouing commeth into the line of the opposite Auge.

The finding of which Equacion is taught in the 34 Precept, by helpe of the 19 Cannon in the Colume, whose title is Eccentrici, and is to be added or subtracted according as the words Subtrahe and Adde at the head or foot of the said Colume, doe shew.

19. The two points in which the Prosthapheresis of the Excentrique is greatest, are called the meane longi∣tude of the Excentrique: and these two points are shew∣ed by a right line perpendicularly drawne vpon 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 deuided into two equall parts, as in the point Q, and through the same point Q a right line be drawne, cros∣sing the line A F with right angles, and is produced as well towards the right hand as towards the left, vnto 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 meane longitudes of the Excen∣trique: in which meane longitudes the centre of the Epicicle is, when the equall motion of Saturnes longi∣tude is 93 degrees or 267 degrees.

20. The meane 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 cir∣cle Equant vnto the circumference of the Epicicle, through the centre of the said Epicicle, as in the former figure the right line C E being produced vnto the cir∣cumference of the Epicicle, sheweth the meane 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 vnto the centre of the Epicicle, and produced vnto the circumference ther∣of, as the right line A E being produced vnto the cir∣cumference of the Epicicle, meeteth with the same cir∣cumference 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 vnto the cen∣tre of the Epicicle, and so produced vnto the circumfe∣rence of the Epicicle: as if the line B E bee produced vnto the circumference of the Epicicle, viz. vnto 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 meane Auge of the Epicicle, and ending at the place of the Planet in the Epicicle: and this arch is alwaies reckoned, according as the Pla∣net moueth. As the arch H * of the Epicicle is called the Anomalia of commutation, and is otherwise called of some the meane Anomalia of the orbe or Epicicle, and of others the meane argument: the finding of the Anomalia of Commutation is taught in the 8 Precept, by helpe of the 13 and 14 Cannons in his proper Col∣lum, 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 Orbe, and others call it the true Ar∣gument.

25. The Prosthapheresis or equacion of the centre in the Epicicle, is an arch of the Epicicle, which is compre∣hended betwixt the meane and true Auge of the Epici∣cle: as in the former figure the point K is the true Auge, and the point H is the meane Auge of the Epicicle, the distance betwixt which two Auges is the arch K N H, and that is the equacion of the centre in the Epicicle: and this equacion is alwaies equall vnto the equacion of the centre, before defined in the 18 definition of this chap∣ter: Only this rule is generally to be obserued, 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 againe if it bee subtracted in the former, then it must be added in the latter.

26. The line of the true motion of the Planet is a right line drawne from the centre of the world vnto the Eclipticke, 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 it selfe of the Planet is an arch of the Eclipticke, comprehended betwixt the true Ver∣nall 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 equacion of the Argument, which Copernicus calleth the Parallax of the orbe, and others call the same

the Prosthapheresis of the Epicicle, is an arch of the Eclipticke, 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 equacion of the argument. This equacion is found by helpe of the coequated Anomalia of Commutation, in such order as is shewed in the 34 Precept, and in the 19 Cannon in the Colume, whose title is Paralaxis Orbis. The greatest equacion that Saturne can haue, when the Epicicle is in the Auge of his Excentrique, and the Pla∣net is distant from the Auge of the Epicicle 96 degrees, is 5 degrees, ⁱ ₅₅· ⁱⁱ ₃₃· But the greatest equacion belonging to him when the Epicicle is in the opposit 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 excesse of the equacion of the Argument, which the Alphonsines call the diuersitie of the diameter, is an arch of the Eclipticke, whereby the equacion of the Epicicle being in the opposit Auge of the Excentrique, exceedeth the said equacion, when the Epicicle is in the Auge of his Excentrique. As you shall more plainely perceiue by this figure following.

[illustration]

In which figure, the middle point A signifieth the centre of the world, & B the centre of the Excentrique, and C the centre of the Equant. The middle circle mar∣ked with the letters E F G, signifieth the Excentrique, in which are placed three other little circles, signifying the Epicicles of Saturne, in euery of which circles the point H signifieth the Auge of the Epicicle, and O the true place of the Epicicle in the Eclipticke: and N signi∣fieth the place of the starre in his Epicicle, and L his true place in the Eclipticke: and the arch O L the equacion of the argument, which equacion is least when the Epi∣cicle is in the Auge of the Excentrique, marked with the letter E: but the said equacion is greater when the centre

of the Epicicle is in the point F, and greatest of all when the said centre is in the point G, that is, in the opposit Auge of the Excentrique. Now if you take the arch of the Eclipticke O L, which is the equacion of the Ar∣gument, when the Epicicle is in the Auge of his Ex∣centrique out of the arch O L (which is the equacion of the Argument) when the Epicicle is in the opposit Auge, the remainer wil be the arch P L, which remaineris called the excesse of the equacion of the Argument. The fin∣ding of which excesse is taught in the 34 Precept, by help of the 19 Cannon in the Colume, whose title is Excessus.

30. The proportionall minutes are the 60 parts of the excesse, by helpe whereof the equacions of the Epicicle, being not in the Auge, nor in the opposit Auge of the Excentrique are equated or corrected. As in the former figure the arch P L, which is the excesse, is supposed to be deuided into 60 equall parts, by helpe of which diuisi∣on the proportionall minutes are found in what place of the Excentrique soeuer the epicicle is placed. As suppose the true place thereof to be in the point F, in which situ∣ation of the Epicicle, the arch O L is the equacion of the Argument, which equacion is greater than it was when the Epicicle was in the point E, and the diffe∣rence betwixt these two equacions is the arch I L. Now if you suppose the arch P L to bee deuided into 60 equall parts, looke how many of those parts the arch I L doth containe, so many proportionall minutes are belonging to the equacion of the argument of the Epi∣cicle, when the place of the said Epicicle is in the point F. The finding of these proportionall minutes is taught in the 34 Precept, and are set downe in the 19 Cannon in the Colume, whose title is Scrupula Proportionalia.

31. The absolute equacion is an arch of the Eclip∣ticke, which is compounded of the equacion of the Ar∣gument, and the excesse answerable vnto the proportio∣nall minutes. And this absolute equacion is either added or subtracted vnto the true mouing of the Epicicle, and the summe of such addition or the remainer of the sub∣traction will shew the true distance of the Planet from the first starre of the Rams horne: whereunto if you adde the true Precession of the Equinox, the summe of that addition will shew the true longitude of the Planet.

CHAP. VI.

Of the sixt Heauen, or the Heauen of Iupiter.

THe sixt Heauen, which is of Iupiter, consisteth of like orbes as doth the Heauen of Saturne, & ther∣fore the demonstrations belonging to this Hea∣uen, doe not differ from those which were set downe in the heauen of Saturne, but only in the time of their mo∣tions & in the quantitie of some arches: for the deferents of the Auge and opposit Auge in the heauen of Iupiter doe make their reuolution in 109756 Aegyptian yeares. And the Excentrique of this Heauen maketh his reuo∣lution in 11 Aegyptian years, 318 daies, and one houre almost. And the excentricitie of the Excentrique of Iu∣piter is 2 degrees, ⁱ ₄₅· and the excentricitie of the circle Equant is 5 degrees, ⁱ ₃₀· The Epicicle of this Heauen maketh his reuolution in 398 dayes, 21 houres, ⁱ ₁₃· ⁱⁱ ₁₅· ⁱⁱⁱ _••° and the daily motion thereof is ⁱ ₅₄· ⁱⁱ ₉· ⁱⁱⁱ ₄· The grea∣test equacion of the centre which belongeth vnto Iupi∣ter, is 5 degrees, ⁱ ₁₃· ⁱⁱ ₅₉· and that is when the centre of the Epicicle is distant from the true Auge of the Excen∣trique

93 degrees, whether it be according or contrarie to the succession of the signes. And the greatest equaci∣on 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, ⁱ ₃₀ almost. And the greatest equacion of the said Argument, when the Epicicle is in the opposit 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 equall or meane moouing of Iupiters longitude from the first starre of the Rams horne, is daily ⁱ ₄· ⁱⁱ ₅₉· ⁱⁱⁱ ₈· and the yearely motion thereof is 30 degrees, ⁱ ₁₉· ⁱⁱ _4•° ⁱⁱⁱ ₆· & maketh one entire reuolution in 11 Aegyptian years, 214 dayes, 21 houres, 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 needfull for that purpose are set downe in the said fift Chapter, differing nothing from the manner which was therein shewed, except it bee in the number of the Cannon, which for Saturne was the 19, and for this Planet it is the 20 Cannon.

CHAP. VII.

Of the fift Heauen, or Heauen of Mars.

THe fift Heauen belonging to Mars, hath like num∣ber of orbes, as hath the Heauen of Saturne, and the said orbes are placed euen as they were in Sa∣turne. And therefore I shall not need to make any per∣ticular relation of the orbes or lines of this sphere, but to referre you to the fift Chapter, shewing only here the

difference of the motions. The deferents of the Auge in the Heauen of Mars doe make their reuolution in 45088 Aegyptian yeares, so as their daily motion is ⁱⁱⁱ ₄· ⁱⁱⁱⁱ ₄₃· and their yearely motion is ⁱⁱ ₂₈· ⁱⁱⁱ ₄₄· ⁱⁱⁱⁱ ₃₇·

The Excentrique of this Heauen maketh his reuolu∣tion in one yeare, and 322 daies almost, so as his daily motion is ⁱ ₃₁· ⁱⁱ ₂₆· ⁱⁱⁱ ₂₆· ⁱⁱⁱⁱ ₁₅· and the yearely motion therof is 191 degrees, ⁱ ₁₅· ⁱⁱ ₄₉· ⁱⁱⁱ ₄₄· ⁱⁱⁱⁱ ₃·

The Epicicle of this Heauen maketh his reuolution in 2 yeares, 49 dayes, 19 houres, ⁱ ₄₃· and the daily moti∣on thereof is ⁱ ₂₇· ⁱⁱ ₄₁· ⁱⁱⁱ ₄₀· and his yearely motion is 168 degrees, ⁱ _2•° ⁱⁱ ₃₀· ⁱⁱⁱ ₄₂·

The greatest equacion of the centre belonging vnto 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 Excen∣trique 95 degrees and ⁱ ₃₀· be it according or contrarie to the succession of the signes.

The greatest equacion 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 equacion of the Argument, when the centre of the Epicicle is in the opposit 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 meane mouing of the longitude of Mars is eue∣ry day ⁱ ₃₁· ⁱⁱ ₂₆· ⁱⁱⁱ ₃₁· and the yearely motion thereof is 191 ⁱ ₁₆· ⁱⁱ ₁₈· ⁱⁱⁱ ₂₉· and maketh one entire reuolution in one yeare, 321 dayes, 23 houres, ⁱ ₃₂·

All other lines and arches belonging to Mars are defi∣ned in the fift Chapter: and the Cannon seruing for the finding of them and their places, is the 21 Cannon in number.

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.

CHAP. IX.

Of the third Heauen, or Heauen of Venus.

THe next Heauen vnder that of the Sunne, is the Heauen of Venus, which hath his proper mouing from West to East.

This Heauen hath foure orbes, as the Heauen of the three higher Planets haue, that is to say, two, which are called the deferents of the two Auges, then the Orbe

Excentrique, or the deferent of the Epicicle, and the Epicicle it selfe, in the circumference whereof the Planet is alwayes carried. And because I haue defined the said orbes in the fift Chapter, I thinke them needlesse to be here againe repeated: and therefore I referre you to that Chapter: For the Orbes of Venus doe not differ from the Orbes of Saturne in shape and position, but onely in the quantitie of their motions.

The deferents of the Auge and opposit Auge in the Heauen of Venus do continue without any motion, and the place of her Auge, which is in the Eclipticke of the eight Heauen, is alwaies 48 degrees, ⁱ ₂₁· reckoning from the first starre of the Rams horne: and the opposit Auge is alwaies 3 Sex. 48 degrees, ⁱ ₂₁· from the first starre of the Rams horne, accounting the said distance according to the succession of the signes. The Excentrique of Ve∣nus mooueth according to the succession of the signes vpon his proper centre, which is differing from the cen∣tre of the world, and the poles and axletree of this Orbe are moouable, sometimes approching neare vnto the poles of the Eclipticke, and at other times are further off. Howbeit this Excentrique maketh one entire reuoluti∣on, beginning at the first starre of the Rams horn in 365 dayes, 6 houres, ⁱ ₉· ⁱⁱ ₃₉· so as the moouing of this orbe is equall vnto the simple equall mouing of the Sunne, be∣fore defined in the 19 definition of the 8 Chapter. And therefore the line of the meane moouing of the centre of Venus her Epicicle, is alwaies in the same place of the Zodiake, in which the line of the meane mouing of the Sunne is: so as in seeking for the meane mouing of Ve∣nus her longitude, you are to find the simple equall mo∣uing of the Sunne in such order as the eight Precept tea∣cheth:

from which if you subtract 48 degrees, ⁱ ₂₁· the remainer will shew the meane Anomalia of the Excen∣trique, or meane centre, before defined in the 13 defini∣tion 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 remai∣ner 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 swarueth from the plane of the Excentrique.

The semidiameter of the Epicicle is 43 degrees, ⁱ ₁₀· such like degrees, as the semidiameter of the Excen∣trique containeth 60 degrees. And because that the line of the meane moouing of her centre is all one with the line of the meane moouing of the Sunne, it may easily appeare, that the starre or Planet will be twice conjoined with the Sunne in one reuolution of her Epicicle, that is to say, once in the Auge, and once in the opposit Auge of the Epicicle. But if she be neither in the Auge nor in the opposit Auge of the Epicicle, then in her ascending from the opposit Auge of her Epicicle vnto the Auge thereof she goeth before the Sunne, and is our morning star, called of the Latines Lucifer. But in descending from the Auge of her Epicicle vnto the opposit Auge therof, she goeth after the Sunne, and is our euening star, called of the Latines Hesperus.

The daily mouing of the Anomalia of Commutati∣on (which was defined in the 23 definition of the 7 chap∣ter) is ⁱ ₁₆· ⁱⁱ ₅₉· ⁱⁱⁱ ₂₈· and the yearely motion thereof is 3 Sex. 45 degrees, ⁱ ₁· ⁱⁱ ₄₅· ⁱⁱⁱ ₂₁· and maketh one entire reuolution

in one yeare 218 dayes, 21 houres, 15 minutes.

The greatest equacion 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 bee 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 opposit Auge of the Excentrique, and that the Planet be distant 2 Sex. 17 degrees from the Auge of the Epicicle, then is the grea∣test equacion of the argument of Venus 46 degrees, ⁱ ₅₁· ⁱⁱ ₂₉· What other points, lines, and arches are needfull to be known for the calculating of her motion at any time, are set downe before in the 7 Chapter, vnto which I re∣ferre you, onely the finding of the equacions belonging vnto 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 Heauen, or Heauen of Mercurie.

NExt vnder the Heauen of Venus is the Heauen of Mercurie, which consisteth of six orbes, that is to say, 2 deferents of the Auge of the circle Equant, two deferents of the Auge of the Anomalia of the Ex∣centrique, the fift orbe is the Excentrique, and the sixt is the Epicicle.

The fiue first orbes are in all respects like vnto the fiue orbes of the Sun, whereof wee spake in the 8 Chapter. And the sixt orbe, which is the Epicicle, is like vnto the Epicicle in the other Planets whereof we spake in the fift Chapter. Notwithstanding I think it not amisse for your better vnderstanding to set downe the said orbes in this figure here next following.

¶The first figure belonging to the Theorique of Mercurie.

[illustration]

IN this figure the two outermost circles, in which are set the caracters of the twelue signes, doe signifie the two Ecliptickes, one of the first mouable, the other the Eclipticke of the eight Heauen. The two broad & black circles doe signifie the two deferents of the Auge of the

circle Equant, and the two shaddowed circles do signifie the deferents of the Auge of the Excentrique, and be∣twixt them is a broad white circle, which representeth the Excentrique: in the middest whereof is the circum∣ference 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 cir∣cumference signifieth the circle Equant. Againe, in the Excentrique is another litle circle, representing the Epi∣cicle, the centre whereof is the point H, and in the cir∣cumference thereof is a little starre, which signifieth the Planet of Mercurie. The point in the middle of ••••is Fi∣gure, which is marked with the letter A, signifieth the centre of the world, and C is the centre of the Excen∣trique, and B is the centre of a litle circle, in the circum∣ference whereof the centre C alwaies moueth 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 vnto the motion of the deferents of the meane Auge of the Sun, for it is equall and regular vpon the centre of the world according to the succession of the signs, that is to say, from West to East vpon their own proper poles, which are equally distant from the poles of the Eclipticke: and the daily motion of these orbes is ⁱⁱⁱ ₉· ⁱⁱⁱⁱ ₃₁· and their yearely motion is ⁱⁱ ₅₇· ⁱⁱⁱ ₅₀· ⁱⁱⁱⁱ ₃₈· and so do make one entire reuolution in 22700 Aegyptian yeares.

The excentricitie, 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 drawne through the centre of the world, and also through the centre of the little circle, marked with B, euen as the line of the meane Auge of the Sunne is wont to be drawne, 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 opposit Auge of the said cir∣cle Equant. And the arch of the eight Eclipticke, marked with the first starre of the Rams horne, and with the let∣ters M N, is the motion of the Auge of the Equant vn∣der the eight sphere. But the arch D M N is the moti∣on of the said Auge vnder the first mouable or from the true Equinoctiall point, marked in the said Eclipticke of the first mouable with the letter D.

The deferents of the Excentrique doe moue regular∣ly about the centre of the little circle, contrarie to the succession of the signes, as the orbes of the Anomalia of the Auge of the Sunne doe mooue namely vpon their proper poles and axletree, and do make their reuolution in 365 dayes, 6 houres, 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 meanes of which motion, the excentricitie of the Planet changeth euery day, and is greatest when the cen∣tre of the Excentrique is in the Auge of the little circle, and the said excentricitie is least when the centre of the said Excentrique is in the opposit Auge of the said little circle, and the said excentricitie is meane when the cen∣tre of the centre of the Excentrique is in the middle point betwixt the Auge and opposit Auge of the said

little circle. All which things were shewed in the 7, 8, and 9 definitions of the 8 Chapter.

The Excentrique hath his proper motion vpon his owne poles, which are also moouable, and the motion thereof is according to the succession of the signs, which motion although it be irregular and vnequall in respect of the centre of the world, yet is the same regular and equall 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 reuolution in 365 dayes, 6 houres, ⁱ ₃₃· ⁱⁱ ₈· And this mo∣tion is found by subtracting the daily motion of the de∣ferents of the Auge of the Equant (which is ⁱⁱⁱ ₉· ⁱⁱⁱⁱ ₃₁·) out of the daily motion of the longitude of Mercurie, which is ⁱ ₅₉· ⁱⁱ ₈· ⁱⁱⁱ ₁₁· ⁱⁱⁱⁱ ₂₂· for so the remainer wil be ⁱ ₅₉· ⁱⁱ ₈· ⁱⁱⁱ ₁· ⁱⁱⁱⁱ ₅₂· which summe is the daily motion of the Excentrique, counting from the line of the Auge of the Equant. And you haue to note, that the motion of the longitude of Mercurie is equall vnto the simple equall mouing of the Sunne, so as when you are to find out the equall longitude of Mer∣curie, you haue to seek in the Prutenical tables the equal simple mouing of the Sunne for the time giuen: and as for the moouing of the Anomalia of the Excentrique, you are taught how to find the same at any time by the 8 Precept, by helpe 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 shewed, in the 15 definition of the 8 Chap.

The Epicicle of Mercurie hath his proper motion vpon his mouable axletree, and the daily motion therof is 3 degrees, ⁱ ₆· ⁱⁱ ₂₄· ⁱⁱⁱ ₁₄· ⁱⁱⁱⁱ ₅· ^v ₃₆· and maketh one entire reuo∣lution in 115 dayes, 21 houres, ⁱ ₃· ⁱⁱ ₂₆· ⁱⁱⁱ ₅₄· and the semi∣diameter 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 alwaies equall vnto the equall simple mouing of the Sunne, it cannot be but that this Planet must be alwaies neare vnto the Sunne; sometimes going before the same, and then it may be seene in the morning before the Sunne riseth; and sometimes it followeth the Sun, and then it may be seene in the euening.

Lastly, the greatest equacion of the Argument of Mercurie, 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 op∣posit Auge of the Excentrique, then is the greatest equacion 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 Mercurie, because they doe not differ from those which we haue shewed in the 5 Chapter, I therefore referre you to that Chapter: and as for the particular equacions, you shal find them set down in the 23 Cannon of the Prutenicall Tables.

CHAP. XI.

Of the first Heauen, or Heauen of the Moone.

THe last or lowest Heauen is the Heauen of the Moone, and it consisteth of foure orbes, whereof the first is called the orbe or circle of Nodes, or the deferent of the head and taile of the Dragon.

The next orbe is called the deferent of the Epicicles.

The third orbe is called the first Epicicle.

And the fourth is the second Epicicle.

All which orbes are set down in this figure following.

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

[illustration]

You shall find the two Epicicles of the Moone more plainely set downe in the third figure here following.

IN the former figure, the two outermost circles do sig∣nifie the two Eclipticks, as in the Heauen of Mercurie. Next vnto them is another white circle, in which are set the caracters of the head and taile of the Dragon, sig∣nifying the deferent of the Nodes, and in the middle thereof is the circumference of a circle, in which the two Nodes doe continually moue. Next vnto that is a great broad and blacke orbe, signifying the deferent of the Epicicles: in which orbe is a shadowed circle, which representeth the first Epicicle, whose centre is marked with the letter E: and vpon the perpendicular line C B are placed two other little circles, one aboue, and ano∣ther beneath the centre E, both whose centres are mar∣ked with the letter F, and these two little circles beeing white within, doe signifie the second Epicicles. And in the circumference of either of them is set the caracter of the Moone. 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 opposit Auge of the said first Epicicle.

1. The deferent of the Nodes is an orbe in the The∣orique of the Moone, in which the Nodes doe continu∣ally moue, marked in the former figure with the head and taile of the Dragon, describing the middle circle of the said orbe. This orbe is concentricall, that is, hath one selfe centre with the Zodiake: and the motion of this orbe is regular and equall in respect of the centre of the earth, vpon the axletree and poles of the Zodi∣ake, contrarie to the succession of the signes, and the daily motion thereof is ⁱ ₃· ⁱⁱ ₁₀· ⁱⁱⁱ ₄₇· and in one yeare

mooueth 19 degrees, ⁱ ₁₀· ⁱⁱ _3•° ⁱⁱⁱ ₄₄· and so maketh one entire reuolution in 18 Aegyptian yeares, 223 dayes, 6 houres, ⁱ ₁₂· and by the violence or strength of his motion, he carrieth the other orbes round about with him.

2. The deferent of the Epicicles is the foresaid blacke Orbe in the Theorique of the Moone, in which the E∣picicles of the Moone are carried continually about. And this blacke orbe hath his owne proper motion, which is according to the succession of the signes, and is regular in respect of the centre of the world, marked with the letter A, and mooueth vpon his owne axletree, which cutteth the axletree of the Eclipticke in the point A, the centre of the world, and the poles thereof are al∣wayes no more but fiue degrees from the Eclipticke: whereby it happeneth, that the plane of this Orbe cutteth the plane of the Eclipticke in two points, which are called the Nodes, or the head and taile of the Dra∣gon. For the vnderstanding whereof I haue set downe this other figure next following.

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

[illustration]

IN which figure the circle F C E K signifieth the plane of the Eclipticke, 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 circum∣ference whereof is the centre of the first Epicicle, mar∣ked with the letter L; and in the circumference thereof is the centre of the second Epicicle, marked with the let∣ter M, and in the circumference thereof is the character of the Moone: and the centre of the deferent of the Epi∣cicle, is the same which the Eclipticke hath, that is to say, the centre A; and this circle crosseth the Eclipticke in two opposit 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 caracter 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, and the other is called the taile of the Dragon, marked with this cara∣cter

〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉. Vnto either of which two Nodes when the Moon commeth, then she is in the Eclipticke, and in her moo∣uing from either of the said two Nodes shee goeth fur∣ther and further from the Eclipticke, vntill 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 neuer more distant from the Ecliptick than fiue degrees, but from the Nodes each limit is di∣stant 90 degrees.

4. And hereby you may gather, that the two Nodes are nothing els but two points, in which the plane of the deferent of the Epicicles dooth crosse the plane of the Eclipticke. And the one of these Nodes is called the ascending Node or head of the Dragon, and the o∣ther is called the descending Node or the taile of the Dragon.

5. The head of the Dragon is that Node, vnto which when the Moon commeth, she beginneth to go North∣ward from the Eclipticke: and that Node is marked with this caracter 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉.

6. The taile of the Dragon is that Node, vnto which when the Moone commeth, she beginneth to go South∣ward from the Ecliptick, which Node is marked with this caracter 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉.

7. The line of the mean or true mouing of the Nodes is a line drawne from the centre of the world vnto any of the said Nodes: as in the former figure the line A F signifieth the line of the mouing of the head of the Dra∣gon, and the line A E signifieth the line of the mouing of the taile of the Dragon.

8. The meane mouing of the Nodes is an arch of the

Eclipticke, beginning at the first star of the Rams home or at the first true Vernall Equinox, and endeth at the line of the mouing of the Node, so as the said arch bee reckoned contrarie to the succession of the signes.

9. The true moouing of the Nodes is an arch of the Eclipticke, beginning at the first starre of the Rams horn, if the same be reckoned in the Eclipticke of the eight Heauen, or at the true Vernall Equinox, if the same bee reckoned in the Eclipticke of the first mouable, and en∣ding at the line of the mouing of the Node, so as the said arch be numbered according to the succession of the signes.

10. The line of the meane mouing of the Moone is a line drawne from the centre of the world through the centre of the first Epicicle, and so forth vnto the Eclip∣ticke. As for example, in the first figure the right line A E B is the line of the meane mouing of the Moone.

11. The place of the centre of the first Epicicle in the Eclipticke, is that point in which the line of the meane mouing of the Moone falleth in the Eclipticke. As in the said first figure the point B in the Eclipticke is the place of the centre of the first Epicicle.

12. The meane simple moouing of the Moones lon∣gitude, is an arch of the Eclipticke, beginning at the first starre of the Rams horne, 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, equall, or simple mouing of the Moones longitude: and the daily mouing of this simple longitude is 13 degrees, ⁱ ₁₀· ⁱⁱ ₃₄· ⁱⁱⁱ ₅₃· and according vnto this motion the Moone maketh her reuolution in 27 dayes, 7 houres, ⁱ ₄₃· ⁱⁱ ₇· for in this time shee returneth vnto the first starre of the Rams horne, and this is called

the Periodicall moneth. As in the first figure the arch * H K is the equall simple mouing of the longitude of the Moone.

13. But if the said motion dooth begin at the meane place of the Sunne, that is, at the line of the meane mo∣uing of the Sunne, then is it called the equall or meane longitude of the Moone from the Sunne, and then the daily motion is 12 degrees ⁱ ₁₁· ⁱⁱ ₂₆· ⁱⁱⁱ ₄₁· and according vn∣to this, the Moone maketh her reuolution in 29 dayes, 12 houres, ⁱ ₄₄· ⁱⁱ ₃· and the time of this reuolution is called the Synodicall moneth. So as if you subtract the equall simple moouing of the Sunne out of the equall simple moouing of the Moones longitude, the remainer will shew the meane longitude of the Moone from the Sunne. As in the said first figure suppose the arch * H to be the equall simple mouing of the Sunne, and the arch * H K to be the equall simple moouing of the Moones longitude. Now if you subtract * H out of * H K, the remainer will be H K, and that is the meane longitude of the Moone from the Sunne. And the finding of this at any time giuen, is taught in the 8 Precept, by helpe of the 13 and 14 Cannons, in the Collume whose title is Longitudo media à Sole.

14. And againe, sometimes the meane moouing of the centre of the first Epicicle or of the Moone, is ac∣counted to begin at the North limit, and then is it called by Ptolomey and Copernicus the mean motion of the lati∣tude of the Moone; because that after the same be corre∣cted, it sheweth the true latitude of the Moon: & the fin∣ding of this motion at any time is to be found in such or∣der as is shewed in the 8 Precept, by help of the 13 and 14 Cannons in the Colume, whose title is Latitudinis Lunae.

15. But Alphonsus and his followers make the begin∣ning of the said motion to be at the head of the Dragon, and is called by them the Argument of the latitude of the Moone, and the daily motion of the Moons latitude is 13 degrees, ⁱ _1•° ⁱⁱ ₄₅· ⁱⁱⁱ _•9· and according vnto this moti∣on she maketh her reuolution in 27 dayes, 5 houres, ⁱ ₅· ⁱⁱ ₃₆· And the Argument of the Moones latitude is to be sound at any time giuen, by adding of 90 degrees vnto the mean motion of her latitude: the manner of the fin∣ding whereof was shewed in the 14 definition of this Chapter.

16. And you haue to note, that according to the mo∣tion 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 mouing of the centre; and this circle is signified in the first figure by the white circle in the middle of the blacke deferent of the Epicicle, described by the centre of the first Epicicle.

17. The first Epicicle is an orbe in the Theorique of the Moone, which continually carieth about the second Epicicle of the Moone. This orbe hath his owne proper motion about his owne poles and axletree, which axle∣tree is perpendicular vnto the plane of the deferent of the Epicicle, and is paralell vnto the said axletree of the said deferent: wherby it commeth to passe, that the plane of this first Epicicle is alwaies in the plane of his deferent. And the motion of this Epicicle is contrary to the suc∣cession of the signes, and the daily motion thereof is 13 degrees, ⁱ ₃· ⁱⁱ ₅₃· ⁱⁱⁱ ₅₆· and maketh one entire reuolution in 27 dayes and 13 houres almost: and the semidiameter of this Epicicle is 6 degrees, ⁱ ₃₅· whereof the semidiameter

of the mouing 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 cen∣tre of the earth. And the opposit Auge is that point which is nearest vnto the centre of the earth. And the Auge and opposit Auge is determined by a right line drawne from the centre of the earth vnto the circumfe∣rence 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 opposit Auge thereof.

19. The meane Anomalia of the Epicicle, which is otherwise called the meane Argument, is an arch of the first Epicicle, containing the distance betwixt the centre of the second Epicicle, and the Auge of the first Epici∣cle. And this is determined by a right line drawne from the centre of the first Epicicle vnto the centre of the se∣cond Epicicle, as this figure next following sheweth.

¶The third figure belonging to the Theorique of the Moone.

[illustration]

IN which figure, the outermost circle representeth the Eclipticke, and the lesser circle within that is a circle which the centre of the first Epicicle is imagined to de∣scribe. 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 opposit Auge thereof: the point F signifieth the centre of the second Epicicle, and the arch B F is the meane Anomalia of the Moon: and this is called Anomalia motus in the Prutenicall ta∣bles, the finding whereof is taught in the 8 Precept by helpe of the 13 and 14 Cannons, in the Colume, whose title is Anomalia Lunae.

20. The first Epicicle is imagined to be deuided into two parts, whereof the one part is called the higher or vpper part, and the other is called the lower part of the Epicicle. And these two parts are shewed by two right lines, drawne 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 drawne from the centre A, and doe touch the first Epicicle in the points L and M: and that part of the Epicicle, which is aboue 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 Orbe in the Theorique of the Moone, in the circumference whereof the bodie of the Moone is alwaies carried about.

The plane of this Epicicle is alwaies in the plane of the first, and the axletree thereof is perpendicular vnto the plane of the first Epicicle, and therfore the axletrees of the two Epicicles and of the deferent of the first Epi∣cicle, are paralels one to another.

And the mouing of this second Epicicle is contrarie vnto the moouing 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 vnto the centre of the first Epicicle: and the op∣posit Auge thereof is furthest from the centre of the said Epicicle: for these Auges haue 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 Moone, is an arch of the second Epicicle, beginning at the Auge of the said second Epi∣cicle, and ending at the body of the Moone. 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 caracter in the circumference thereof, and the arch of the said little circle, contained betwixt R and the caracter of the Moone, is called the Anomalia of the Excentrique, or centre of the Moone. And this Anomalia is called in the Prutenicall Tables Longitudo Duplicata, or the double longitude of the Moone from the Sunne: 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 Moone in the second Epicicle is dou∣ble vnto the motion of the centre of the first Epicicle, from the line of the meane moouing of the Sunne. For according vnto this motion the Moone maketh her re∣uolution in 14 dayes, 18 houres, ⁱ ₂₂· ⁱⁱ ₁· and her daily mo∣tion is 24 degrees, ⁱ ₂₂· ⁱⁱ ₅₃· ⁱⁱⁱ ₂₃· and is found in the Prute∣nicall tables, by doubling the meane longitude of the Moone from the Sunne.

25. The line of the true Anomalia of the Moone is a right line drawne from the centre of the first Epicicle vn∣to the body of the Moone. As in the third figure of this

Chapter the right line E G, and the caracter of the Moone is called the line of the true Anomalia, because it is drawne from the centre of the first Epicicle, which is marked with the letter E, vnto the body of the Moone, marked with the caracter of the Moone.

26. The true Anomalia of the Moone, which the Al∣phonsines doe 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 equa∣ted Anomalia, or the true Argument of the Moone.

27. The equacion of the centre, which in the Prute∣nicall tables is called the equacion of the second Epici∣cle, is an arch of the first Epicicle, whereby the true and meane Anomalias do differ the one from the other. As in the said third figure the arch B G is the true Ar∣gument of Moone, and the arch B F is the mean Ano∣malia or Argument of the Moone, or of the Epicicle, de∣fined 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 helpe of the 18 Cannon, in that Collum whose title is Secundi Epicycli. And this equaci∣on is to be added or subtracted from the mean Anoma∣lia, as is shewed in the said 24 Precept, to the end that the true Argument or Anomalia may bee had. And the greatest equacion that can be, is 12 degrees, ⁱ ₂₆· ⁱⁱ ₅₇· which then happeneth, when the Moone is in either of the Touch-points of the second Epicicle: which Touch-points are determined by two right lines drawne from the centre of the first Epicicle: and touching the cir∣cumference

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, throgh the body of the Moon vnto the Ecliptick, & the point in the Eclip∣ticke, where that line endeth, is the true place of the Moone: as in the third figure the line A G T signifieth the line of her true mouing, and the point T is the true place of the Moone.

29. The true or apparent motion of the Moone is an arch of the Eclipticke, beginning at some knowne place of the Eclipticke, and ending a•• the true place of the Moone: which arch dooth begin either at the first starre of the Rams horne, or at the Vernall Equinox, either meane or true, or els at the line of the meane place of the Sunne. As in the said third figure the arch * T is the apparent or true moouing of the Moone from the first starre of the Rams horne.

30. The equacion of the first Epicicle is an arch of the Eclipticke, contained betwixt the line of the meane mo∣uing of the Moone, and the line of her true mouing. As for example, in the third figure of this Chapter the line A V is the line of the meane mouing of the Moon, and the line A T is the line of her true mouing, and the arch of the Eclipticke, contained betwixt these two lines, that is to say, the arch T V, is called the equacion of the first Epicicle, or the equacion of the Argument. And the fin∣ding of this equacion at any time giuen, is taught in the 24 Precept, by helpe of the 18 Cannon, in the Collum, whose title is Primi Epicycli. But because this equacion doth varie, and is sometimes greater and sometimes les∣ser, therefore the absolute and perfect equacion is to be

found by the proportionall minutes, and the excesse, which were defined before in the 29 definition of the fift Chapter, and therefore I need not here again to define the same, but onely to tell you, that the proportionall minutes are to be found in the 18 Cannon, in the Col∣lum, whose title is Scrupula Proportionalia: and the excesse is to be found in the said 18 Can∣non, in the Colume, whose title is Excessus.

Here endeth my Extract of Maginus his Theoriques: And if this my labour shall content you, then looke shortly for the vse of the Prutenicall Tables.