center then the center of the earth and therefore that the circle or Orbe wherein the Sunne is moued is an Eccentricke CHAP. VII Of the vses of the Sunnes eccentricall Orbe THerefore the vses of the Sunnes eccentricke may bee these 1. First to shew the reason of the apparent inequalitie which seemeth to bee in the motion of the Sunne for although the Sunne moâ—e equally in his owne Oâ—be and about his owne center yet to them that are at the center of the world or vpon the earth he shall seeme to moue vnequally that is swiftly when he is in that part of his eccentricke which is nearest vnto the earth and slowly when he is farthest from the earth And therefore in sommer when the Sunne is about his Apogaeum and in his greatest distance from the earth he seemeth to moue little aboue 57. min. in one day But in winter being about his Perigaeum and nearest vnto the earth he seemeth to moue more then 16. minutes whereas notwithstanding he moueth equally in his Eccentricke euery day about nine and fifty minutes and 8. seconds and so finisheth his reuolution in 365. dayes and six houres almost 2. The second vse of the Sunnes Eccentricke may be to shew the reason why the Sun appeareth greater at one time then at another for the Sun being in those parts of the eccentrick that are nearest vnto vs seemeth greatest and when he is in those parts of his eccentrick that are furthest from vs he appeareth to be least 3. And lastly the inequality of the Sunnes distance from the earth caused by his eccentrick is one especiall cause of the inequalitie of the Eclipses both of the Sunne and Moone CHAP. VIII The definitions of certaine Astronomicall wordes of art for the better vnderstanding of the Theorick of the Sunne 1. WHat the Aux or Apogaeum of the Sunne is it hath beene partly shewed already that â—â—mely it is that part or rather point of the Orbe carying the Sunnes Apogaeum wherein the said Orbe is thinnest or narrowest Or it is that point of the eccentrick which is furthest distant from the earth and is alwayes shewed by a right line vnderstood to be drawn from the center of the world by the center of the eccentrick vnto the Orbe carying the Sunnes Apogaeum Which line is therefore called the line of the Sun his Aux or the line of the Sunnes Apogaeum 2. The motion of the Aux or of the Apogaeum of the Sunne which is also called the Sunnes Aux in the second signification is nothing els but the arch of the Ecliptick conteyned betweene the beginning of Aries and the line of the Sunnes Apogaeum drawne forth to the Zodiack where this line also sheweth the place of the Sunnes Apogaeum 3. The middle or meane place of the Sunne in the Zodiack is shewed by a line drawne from the center of the world vnto the Zodiack equidistant from the center of the Eccentricke and of the Sunne 4. This line is therefore called the line of the meane or middle place of the Sun 5. The middle or meane motion of the Sunne is the arch of the ecliptick betweene the beginning of Aries and the middle place of the Sun 6. The true place of the Sunne is shewed by a streight line drawne from the center of the earth by the center of the Sun vnto the Zodiack which line is therefore called the line of the true place of the Sun 7. The true motion of the Sun is the arch of the eclipticke from the beginning of Aries vnto the true place of the Sun 8. The argument of the Sun at the 〈◊〉 â—erme it or the motion of the Sunnes Anomalie as Copernicus calleth it is the arch of the ecliptick conteyned betweene the place of the Sunnes Apogaeum and the middle place of the Sunne according to the order and succession of the Signes This arch is called the argument or motion of the sunnes Anomalie or irregularitie because that by it is alwayes found how much the suns true motion which is vnequall and irregular differeth from his middle motion which difference they call the Suns equation or prosthapheresis 9. The equation or prosthapheresis of the Sun is nothing els but the arch of the ecliptick conteyned betweene the true and middle places of the sunne This arch is called the sunnes equation because it maketh the suns middle motion equal to his true motion being added to it or subtracted from it as occasion requireth for which cause it is more significantly and fitly called Prosthaphaeresis that is as much to say as that which is to be added to or subtracted from the middle motion that so we might haue the true motion For so long as the Sunne is in the semicircle of his eccentrick discending from his Apogaeum to his â—â—â—gaeum so long this Prosthapheresis is to be subtracted from the middle motion but the Sunne being in the other halfe of his eccentrick ascending the Prosthapheresis or equation of the Sun must be added to the middle motion that 〈…〉 motion and place of the Sunne may be found Because that in the first semicircle of the eccentricke descending the middle place of the Sunne goeth before the 〈◊〉 and the middle motion is 〈…〉 greater 〈…〉 the Sun and therefore the difference of these 〈◊〉 motions that is to say the 〈◊〉 or Prosthaphaeresis must be subtracted to findeth 〈…〉 for the true place of the Sunne goeth alwaies 〈…〉 motion and place of the same CHAP. IX Of the vppermost Orbe of the Sphaere of the Moone carying the Dragons head and tayle NExt within the Orbes of the Sun in this Sphaere are conteyned the Orbes of the Sphaere of the Moone which 〈…〉 in number The vppermost of them which in this Sphaere is next vnder the Orbe that caryeth the Suns Perigaeum and is coloured with red is called the Caryer of the Dragons head and tayle or 〈…〉 which is as much to say as the Caryer of the knots that is of the two intersections or pointes wherein the rest of the Orbes of the Moone doe crosse ouer-thwart this Orbe This Orbe is deuided into foure nineties of degree for the easier reckoning of the motion and place of the Dragons head or tayle in this Sphaere And it is moued about in 18. Iulian yeares 224. dayes 3. houres and 5. minutes almost from the East Westwards vnder the ecliptick By reason of this motion it commeth to passe that the Eclipses or rather the places wherein the eclipses of the Sunne or Moone doe happen in the Heauens are remoued continually more backwards in the Zodiack contrary to the order and succession of the Signes As for example the eclipse of the Moone hapning this present yeare 1600. the 20. of Ianuarie neare vnto the Dragons tayle about the 9. degree and 40. min. of Leo the next eclipse that shall happen neare the same intersection of the Dragons taile in the yeare 1601. the 29. of Nouember shall be in 17. degrees and an halfe of
Gemini And that eclipse which shall be the next yeare after neare the same intersection the 19. of Nouember in the morning shall be about the 6. degree and 40. minutes of Gemini c. All this remouing of the Eclipses backwards commeth to passe by reason of the motion of this Orbe carying the Dragons head and tayle contrary to the course and order of the Signes This Orbe continueth alwaies right vnder and euen with the Orbes of the Sphaere of the Sunne which abide alwaies in all parts iust vnder the ecliptick line and hath his center agreeing and all one with the center of the world and of the ecliptick And therefore the poles and axtree about which this Orbe is turned agree iustly with the axtree of the Ecliptick The rest of the Orbes of the Moone that are conteyned within this haue all theire playnes agreeing in one and lying euen one with another But the one halfe of all their playnes ariseth aboue the playne of the former Orbe and of the Ecliptick towards the North pole of the Zodiack and the other halfe descendeth beneath the playne of the ecliptick toward the South pole euen as the one halfe of the Zodiack ariseth aboue the Equinoctiall circle towards the North and the other halfe descendeth towards the South And as the angle of intersection or obliquitie of the ecliptick with the Equinoctiall circle is 23. degr and an halfe or little more so the angle of intersection or obliquity of the playnes of these Orbes of the Moone from the plaine of the Ecliptick and of the former Orbe carying the Dragons head and taile is 5. degrees or according to Tigâ—â— Brahe his obseruation 5. degr and a quarter almost sometimes and sometimes lesse then 5. degr That point or intersection of these Orbes with the former from which they begin to arise about the playne of the ecliptick towards the North proceeding East-wards is called the Dragons head and is signified by this character ☊ and the other point or intersection diametrally opposite vnto this is called the Dragons tayle which is also signified by the former character turned vp side downe after this manner ☋ The two points of these Orbes that are furthest distant from the plaine of the 〈◊〉 are called the bounds or limites of the Moones latitude and they are 90. deg from the Dragons head and tayle and 5. deg and a quarter almost from the playne of the Ecliptick according to the obliquity or greatest declination of the playnes of these Orbes from the playne of the ecliptick Of these two points that which is in the north side of the ecliptick is called the North limit or bound of the Moones latitude and contrariwise the other point opposit to this on the south side of the Ecliptick is called the South limite of the Moones latitude And when the Moone commeth to eyther of these two points she hath her greatest latitude CHAP. X. Of the Orbes carying the Moones Apogaeum and Perigaeum NExt within the Orbe carying the Dragons head and tayle is contayned the Orbe called Deferens Apogaeum lunae which is the point wherein the Moone is furthest distant from the earth And vnder this Orbe is placed the Moones Eccentrick which is also called Deferens Epiculum Lunae that is the Orbe carying the Moones Epicycle Againe within this eccentrick of the Moone is conteyned the least and lowest Orbe of all that are in this Sphaere Which they call Diferens Perigaeum Lunae that is the Orbe carying the Moones Perigaeum which is the point wherein the Moone commeth nearest to the earth The vppermost and nethermost of these three Orbes that is to say the Orbes carying the Moones Apogaeum and Perigaeum both which Orbes in this Sphaere are coloured with blew are alwaies placed in such sort that the narâ—â—west part of the one is continually answerable to the broadest part of the other whereby it commeth to passe that the Sphaere of the Moone is made concentricall that is to say to haue the same center with the world which also is one especiall vse why these Orbes were deuided Another vse of these Orbes is to shew the reason of the motion of the Moones Apogaeum and Perigaeum Therefore both these Orbes are moued togither with one motion equally about the center of the world in the same time from the East Westwards in the space of 32. dayes 3. houres and 5. minutes almost So mouing in one day 11. deg 12. min. and 1. third part almost The axtree about which these Orbes are moued equally passeth through the center of the world and of the ecliptick but the poles of these Orbes differ from the poles of the Ecliptick and of the Orbe carying the Dragons head and tayle by the space of 5. degr and a quarter or thereabouts which poles are caryed about the poles of the Orbe carying the Dragons head and tayle with the motion of the same Orbe in the space of 19. yeares almost Whereby it commeth to passe that the poles of the Orbe carying the Apogaeum and Perigaeum of the Moone describe certaine litle circles about the poles of the Orbe that carieth the Dragons head and taile euen as the Arctick and Antarctick circle in the ordinary Sphaere are described by the motion of the poles of the Ecliptick caryed about dayly with the motion of the first and highest moueable Sphaere in the space of 24. houres almost CHAP. XI Of the eccentricke of the Moone THe Eccentrick of the Moone contained betweene the two former Orbes and coloured with a sad yealow colour in this Sphaere is moued equally about the center of the same Orbes from the West towards the East finishing his motion vnder the Zodiack in the space of 27. dayes and 8. houres almost and with this motion it caryeth about the Moones Epicycle equally vnder the Zodiack Therefore the motion of this Orbe about his owne center must needs be vnequall that is to say swifter in those parts that are about the Apogaeum and slower in the lower parts about the Perigaeum Because that greater arches of the Eccentrick doe answer to equall arches of the Zodiack about the Apogaeum then about the Perigaeum of the Eccentrick The axtree about which this Orbe is moued is alwaies in all places equidistant from the axtree of the Orbe carying the Apogaeum of the Moone and the poles of the axtree of the Moones eccentrick are fastned in the Orbe carying the Moones Apogaeum equidistantly from the poles of the same Orbe therefore these poles together with the whole axtree of the eccentrick are caryed and equally moued about the poles and axtree of the Orbe carying the Apogaeum from the East towards the West With this motion therefore the poles and center of the eccentrick describe certaine litle circles of equall bignes about the poles and center of the Orbe carying the Apogaeum from the East West-wards And therefore also the Apogaeum of the eccentrick is moued about equally vnder the ecliptick contrary to the
order of Signes from the East West-wards Whereby it commeth to passe that both the Apogaeum and center of the eccentricke are somtimes vnder the Ecliptick that is when they are vnder the Dragons head or taile but for the most part they are beside the plaine of the ecliptick either towards the North or else towards the South Hereby also it appeareth that the plaine of the Ecliptick doth not alwayes deuide the plaine of the eccentricke into epqall parts or halfes but then onely when the Center and Apogaeum of the Eccentrick is right vnder the Dragons head or tayle for then onely the plaine of the Ecliptick deuideth the plaine of the Eccentrick by the center therof and consequently deuideth it precisely into two halfes Otherwise if the Apogaeum of the eccentrick be not vnder the Dragons head or tayle looke on which side of the plaine of the ecliptick the Apogaeum is for on the same side of the ecliptick is the greater part of the eccentrick CHAP. XII In what proportion the Moones eccentrick and Orbe carying her Apogaeum are moued NOw the Eccentrick of the Moone and the Orbe carying her Apogaeum are moued in such sort that the middle place of the Sunne is alwayes right in the midst betweene the center of the Epicycle caried in the eccentrick and the Apogaeum of the Eccentrick except it be when the center of the epicycle is in coniunction or opposition to the middle place of of the Sunne For in euery middle coniunction and opposition of the Sunne and Moone the center of the Epicycle and the Apogaeum of the eccentrick are vnited together But in the coniunction they are both conioyned with the middle place of the Sun and in the opposition they are both together opposite to the same Whereof it followeth that in the first and last quarters of the Moone the center of her epicycle is diametrally opposite to the Apogaeum of her eccentrick Hereof it commeth to passe that although the Moone haue the same position in her epicycle at the time of the new and full Moone and of the first and last quarters yet the equation or prosthaphaeresis of the Moones Argument as they call it that is the difference betweene the true and middle places of the Moone is alwayes greater in the first and last quarter then in the full and new Moone Hereby likewise it appeareth that in the time contayned betweene new Moone and new Moone which they call Mensem synodicum that is the moneth coniunctional or the time from coniunction to coniunction the center of the epicycle maketh two complete reuolutions vnder the Orbe carying the Apogaeum of the Moones eccentrick And therefore in euery moneth the center of the epicycle commeth twise to the Apogaeum and twise to the Perigaeum of the eccentrick and so the monthly motion of the center of the epicycle describeth an oual figure the ends whereof are alwayes towards the place of the full and new Moone and the â—ides towards the places of the first and last quarter By this that hath beene spoken it is also manifest that if the middle motion of the Sunne be subtracted out of the middle motion of the Moone there remaineth the middle motion of the Moones longitude from the sunne and that if this longitude againe be doubled you shall haue the motion of the center of the Moones Epicycle from the Apogaeum of her eccentrick which motion they call the center of the Moone CHAP. XIII Of the Epicycle of the Moone and how it is moued THe little Orbe placed in the Eccentrick is called the Epicycle of the Moone in the circumference whereof is also placed the body of the Moone represented by the round Beade set into the Moones Epicycle in this Sphaere The plaine superficies of this epicycle agreeth euen with the plaine of the eccentrick and the axtree about which it is moued is perpendicular to the plaine of the eccentrick This Epicycle is moued equally from his middle Apogaeum about his owne center and axtree from the East Westwards contrary to the motion of the eccentrick carying forwards the body of the Moone with this motion 13. degrees and almost 4. min. euery day and finishing his reuolution in 27. dayes 13. houres and 19. minutes almost The middle Apogaeum of the Epicycle is shewed by a right line imagined to be drawne from that point of the little circle described by the motion of the center of the Moones eccentrick which is opposite to the center of the Eccentrick by the center of the Epicycle vnto the vpper part of the Epicycle But the true Apogaeum of the Epicycle is shewed by a right line vnderstood to be drawne from the Center of the earth by the center of the Epicycle vnto the vpper part of the circumference thereof By the motion of this Epicycle it may easily be conceiued why the Moone seemeth to moue sometimes swifter and somteimes slower For seeing that the vpper part of the Epicycle moueth contrary to the motion of the Eccentrick from the East Westwards when the Moone commeth in that part shee must needs seeme to moue more slowly to them that are at the center of the world But when the Moone commeth in the nether part of the Epicycle the Eccentrick caryeth the Epicycle and the Epicycle caryeth the body of the Moone both one way that is from the West East-wards and therefore at that time the Moone seemeth to moue more swiftly According as you may see in Ephemerides the dâ—â—â—ne motion of the Moone to be sometimes little more then 11. degrees and sometimes againe little lesse then 15. degrees The true motion of the Moone seemeth then to be swifter when the Moone is in the Perigaeum of her Epicycle and the Epicycle in the Perigaeum of the Eccentrick because then she is not onely caryed forwards the same way both by her Epicycle and Eccentrick but she is also at that time nearest vnto vs for which cause her motion shall seeme swifter then when the Epicycle is in other parts of the Eccentrick 〈…〉 CHAP. XIIII The definitions of certayne Astronomicall wordes of Art for the better vnderstanding of the Theoricke of the Moone 1. THe line of the Moones middle motion is a line vnderstood to be drawne from the center of the earth by the center of the Moones Epicycle vnto the Zodiack 2. This line sheweth the middle place of the Moon in the Zodiack 3. And the middle motion of the Moone is the arch of the Zodiack from the beginning of Aries vnto the same line 4. So likewise the line of the true motion or of the true place of the Moone is drawne from the center of the world by the center of the Moone to the Zodiack 5. This line therefore sheweth the true place of the Moone in the Zodiack 6. And the true motion of the Moone is the arch of the Zodiack from the beginning of Aries vnto the true place of the Moone 7. The middle longitude of the Moone from the Sunne
beginning of any yeare from this present yeare 1600. till the yere 1620. The second part sheweth how much the Dragons head moueth in any number of moneths of the yeare the third part giueth you the motion of the Dragons head in any number of dayes of the moneth The place of the Dragons head  Yeare Sign Deg. Mt. Moneths Complete De. Mi. Da. De. Mi. 1600 Aquarius 0 45 Ianuary 1 38 1 0 3 1601 Capricorn 11 21 February 3 8 2 0 6 1602 Sagittar 22 2 March 4 46 3 0 10 1603 Sagittar 2 42 Aprill 6 22 4 0 13 1604 Scorpio 13 22 May 8 0 5 0 16 1605 Libra 23 59 Iune 9 36 6 0 19 1606 Libra 4 39 Iuly 11 14 7 0 22 1607 Virgo 15 19 August 12 53 8 0 25 1608 Leo 25 59 Septemb. 14 28 9 0 29 1609 Leo 6 35 October 16 7 10 0 32 1610 Cancer 17 15 Nouemb. 17 42 11 0 35 1611 Gemini 27 55 Decemb. 19 21 12 0 38 1612 Gemini 8 35   13 0 41 1613 Taurus 19 12   14 0 44 1614 Aries 29 52   15 0 48 1615 Aries 10 32   16 0 51 1616 Pisces 21 12   17 0 54 1617 Pisces 1 49   18 0 57 1618 Aquarius 12 29   19 1 0 1619 Capricorn 23 9   20 1 4 1620 Capricorn 3 49   21 1 7       22 1 10       23 1 13       24 1 16       25 1 19       26 1 13       27 1 26       28 1 29       29 1 32       30 1 35 CHAP. XXI To finde the place of the Dragons head or tayle by the former table FInde out in the former table the moneth next going before the moneth giuen finde out also the day of the moneth Adde together the numbers of degrees and minutes answerable to that moneth and day of the moneth and subtract the same out of the place of the Dragons head at the beginning of the yeare adding thereto 30. degr â—â—at is the whole signe next going before resolued in to degr if the Sunne aforesayd be greater then the number of degr shewing the place of the Dragons head at the beginning of the yeare so shall you haue the place of the Dragons head for the time giuen And the point of the Zodiack opposite to this is the place of the Dragons taile Take for example The 29. of Nouember 1601. I find therefore against October the moneth going next before Nouember 16. degrees 7. minutes and against the 29. day 1. degree 32. minutes the summe of both these added together is 17. degrees 39. min. the place of the Dragons head for the beginning of the yeare 1601. is 11. deg 21. min. of Capricorne which because they be lesse then 17. deg 39. min. I adde vnto them 30. deg that is the whole signe of Sagittarie and the summe of both is 41. deg 12. min. out of which subtract 17. deg 39. min. and there shall remaine 23. deg 42. minutes of Sagittarie the place of the Dragons head at that time And the point of the Zodiacke which is opposite hereto that is the 2◠〈◊〉 42. minutes of Gemini is the place of the 〈◊〉 tayle CHAP. XXII To know at what time there shall be an Eclipse of the Moone THe place of the Dragons head being thus knowne finde out the same place vpon the horizon of the Sphaere and see what day and moneth answereth thereto finde out also the place of the full Moone which hapneth next before or after that day which place if it chance to bee within 11. or 12. deg eyther before or after that point of the Zodiack which is opposite to the Dragons head there must needs be for the most part in Eclipse of the Moone Likewise if you finde what day and moneth is answerable to the place of the Dragons taile vpon the horizon of the Sphaere if the place of the full Moone which hapneth next before or after that day chance to be within 11. or 12. degrees of the Dragons head for the most part there shall bee an Eclipse of the Moone As for example The 20. of Ianuarie last this present yeare 1600. the place of the Dragons head was found by the former Chapter to haue beene in 29. deg 41. min. of Capricorne whereto there answereth in the horizon the 10. day of Ianuarie the place of the full Moone hapning next after vpon the 20. of the same moneth in the morning must needs be in the place opposite to the place of the Sunne the same 20. 〈◊〉 Therefore because 〈◊〉 Sun that day is in 9. deg 〈◊〉 one halfe of Aquarius therefore the place Why this Circle is called the Equinoctiall or Equator The scituation of the Orbe carying the Dragons head and tayle The scituation of the rest of the Orbes Why the Moone seemeth sometimes to moue swifter sometimes slower To finde the Moones proportionall minutes What the proportionall minutes of the Moone are â—t the begining of the 〈◊〉 of our â—â—rd
more yeares it returneth againe into Aries The reuolution of one Trigon contayneth almost 200. yeares after which time the same great conjunctions remoue into the next trigon CHAP. IX The vse of the Zodiack 1. THe Zodiack is the measure of the second motions as the Equinoctiall is the measure of the first motion 2. For in this Circle wee reckon the longitudes and from it we count the latitudes of all the Starres For the longitude of a Starre is nothing else but the arch of the Ecliptck conteyned betweene the beginning of Aries and the circle of the Starres latitude And the latitude is the Arch of a great circle drawne by the poles of the Ecliptick conteyned betweene the Starre and the Ecliptick 3. According to this circle the whole Heauen yea the whole world is deuided into twelue Signes Whereof it commeth that because of this Circle aswell the fixed as the wandring Starres which we call Planets yea and those Starres also that appeare of a sudden as blazing Starres or Comets and other Meteors are said to be in this or that signe and that three manner of wayes First to be in a signe is to be vnder some one of the 12. parts of the Ecliptick Thus the Starres which are vnder the Ecliptick but especially the Sunne which runneth alwayes vnder it are said to be in the Signes Secondly because the Zodiack hath latitude those Starres are said to be in a signe which although they be beside the Ecliptick yet are vnder the Zodiack and so any of the other Planets which for the most part wander beside the Ecliptick may be said to bee in some signe Thirdly if we vnderstand six great Circles to bee drawne by the beginnings of the twelue signes and by the poles of the Eclipticke by these circles the whole heauen or rather the whole world is deuided into twelue parts which with a generall name are called signes Thus all the Starres aswell fixed as Planets and Comets which are without the Zodiacke in any of these parts may be said to be in some signe 4. In this circle are noted the degrees of the signes with which the Starres doe rise and set as well in a right as in an oblique Sphaere For because this circle is the chiefest all Caelestiall apparances or at least the most part of them are referred vnto it and not vnto the Equinoctiall But the Equinoctiall measureth the times of their risings and settings 5. The obliquitie of the Ecliptick is the cause of the inequalitie aswell of naturall dayes in both Sphaeres as of artificiall dayes in an oblique Sphaere For seeing it is moued vnequally because it is moued vpon other Poles then his owne the Sunne which is the author and maker of times mouing vnder it must needs make vnequall dayes 6. The chiefe times are defined by this circle as the time of a yeare by the motion of the Sunne the time of a moneth by the motion of the Moone through the whole compasse of this circle Also the foure quarters of the yeare Spring Summer Autumne and Winter whereto may be added Plato his great yeare which is the time wherein the fixed Starres make one reuolution about the axtree and poles of the Zodiack if God would haue the world to last so long 7. The Eclipticke line sheweth the places and times of the Eclipses For the Sunne and Moone are Eclipsed onely vnder it or neere vnto it 8. As the description of the Tropicks dependeth on the obliquitie of the Eclipticke so the polar Circles are described by the Poles thereof 9. Hereof it commeth that by reason of the same obliquitie the Zones and Climats are set forth and bounded 10. This Circle is of especiall vse in Astrologie for it distinguisheth the points of the 12. Houses and in it the Aspects and configurations of the Planets are obserued The chiefest judgement aswell in casting Figures as in reuolutions and directions is taken from this circle CHAP. X. The description of the two Colures THe two circles crossing each other at right Angles in the poles of the Sphaere are called the Colures whereof the one that passeth by the common meeting of the Eclipticke and Equinoctiall is called Colurus aequinoctiorum that is the Equinoctiall Colure or the colure of equall dayes and nights The other passing by the poles of the Eclipticke and the Solstitiall points is called Colurus solstitiorum the Solstitiall colure or colure of the Sunne-standings Vses common to both Colures 1. By meanes of these two Colures all the mouable circles of the materiall Sphaere are framed together that so they might be turned about like as the whole Heauens are moued 2. The Poles are fastened in the common meeting of these two Circles and the Poles are also shewed by the same common meetings 3. They shew the foure principall points of the Eclipticke that is the two Equinoctiall and the two Solstitiall points 4. These circles shew those points of the Eclipticke wherein the Sunne is either equally distant from both poles of the Sphaere or commeth neerest to either of them In which points the Sunne maketh the dayes longest or shortest or of a meane length betweene both these in an oblique Sphaere 5. They deuide the Ecliptick into foure quarters in which the Sunne maketh foure quarters of the yeare the Spring the Summer Autumne and Winter 6. They deuide the Ecliptick and Equinoctiall into such foure quarters as in a right Sphaere doe rise together in equall time CHAP. XI Vses of the Equinoctiall Colure 1. THe section of this Circle with the Ecliptick sheweth the Equinoctiall points wherein the Equinoctiall and the Eclipticke doe deuide and crosse each other In which points the Sunne maketh equality of dayes and nights throughout the whole world whereof this circle is also called Colurus Aequinoctiorum that is the colure of equall dayes and nights or the Equinoctiall colure 2. It deuideth the Eclipticke into the North and South halfes 3. It deuideth the Signes wherein the Sunne maketh the dayes longer then the nights from those signes wherein the dayes are made shorter then the nights 4. It sheweth which halfes of the Eclipticke and Equator doe arise together in equall time in an oblique Sphaere 5. It sheweth the two high Sunne-standings in a right Sphaere in the time of which Sunne-standings the Sunne passeth by the Zenith CHAP. XII Vses of the Solstitiall Colure 1. THe common meetings of this circle with the Ecliptick shew the Solstitiall or Tropicall points in which points the Sunne seemeth to stand and then returneth backe againe for which cause this circle is called the Colure of the Sun-standings These points are called tropicall which is as much to say as turne-points or points of returne because that when the Sunne going alwayes vnder the Eclipticke commeth to these points which are furthest distant from the Equinoctiall circle it returneth againe towards the same circle But they were called Solstitiall or Sun-ding points because that whilest the Sunne is about those
when hee is in Aries or Libra PROP. XXXIII To finde by the Sphaere how much the naturall dayes are longer at one time of the yeare then at another FOr this purpose it will be best to take a good number of dayes together as for example take the whole moneth of December and the whole moneth of March both which moneths consist of the same number of 31. naturall dayes find the place of the Sunne for the beginning and ending of both moneths which you may finde by the second Proposition to be for the beginning of March this present yeare 1600. about 20. degrees and 13. minutes of Pisces and for the ending about 20. degr 48. minutes of Aries Also for the beginning of December the same yeare 18. degr 46. minutes of Sâ—gitarie and for the ending 20. degrees 24. minutes of Capricorne Then seeke out the right ascensions of the same places of the Sunne for the beginnings and endings of both those moneths by the fourth Proposition and the differences of ascension answerable to the motion of the Sunne in each moneth by the sixt Proposition which you may finde by the Sphaere to be about 33. degrees 24 minutes for December and 28. degrees 39. minutes for March. Lastly finde out the difference of these differences of ascension by substracting the lesser out of the greater which in this example is 4. degrees 45. minutes which resolued into minutes of an houre by taking for euery degree 4. minutes of an houre and for euery 15. minutes of a degree one minute of an houre shall amount to 19. minutes of an houre that is a quarter of an houre and 4. minutes And so much is the moneth of December longer then the moneth of March Notwithstanding both of them consist of the same number of 31. naturall dayes The third Part. Of the Orbes whereof the SPHAERES of the Sunne and Moone haue beene imagined to bee made and of their Motions and Vses CHAP. I. Of the Orbes whereof the Sphare of the Sunne is made WIthin the Sphaere or Orbe contayning all the Circles that wee haue hitherto spoken of and representing vnto vs the Primum mobile that is the first and highest moueable Heauen that hath been imagined by the Astronomers to shew the reason of that daily motion which appeareth to bee in all the Heauens and of all the apparences that follow thereupon are included the Sphaeres and Orbes of the Sunne and Moone The sphaere of the Sunne contayneth three Orbes The vppermost of them which in this Sphaere is signified by the yellow Circle that commeth next within the compasse of the Zodiacke is called Deferens apogaeum Solis that is the Orbe which carrieth about that point wherein the sunne is furthest distant from the earth Next within this Orbe is placed the Eccentrick carying about the body of the Sunne which in this Sphaere is represented by the greene coloured circle that commeth next vnder the Deferens apogaeum Againe within this Eccentrick is included the third Orbe of the Sphaere of the Sunne called Deferens Perigaeum solis that is the Orbe carying about that point wherein the Sun is nearest to the Earth This is the nethermost of the three Orbes of the sunne and in this Sphaere is represented vnto you by the yellow coloured circle next vnder the sunnes Eccentricke CHAP. II. Of the vppermost and nethermost Orbes of the Sphaere of the Sunne more particularly IN the vppermost and nethermost of these three Orbes there be 4. points especially to bee considered That is the points where they bee narrowest and where they be broadest and where they are of a meane bredth betwixt the narrowest and broadest For at the narrowest part of the vppermost Orbe where you may see written Aux solis and the broadest part of the nethermost Orbe is the place of the sunnes Apogaeum so that whensoeuer the Sun commeth there he is furthest distant from the earth As you may easily try if with a payre of Compasses or otherwise you take the distance betwixt the Earth and the Sunne being brought about to that place and compare the same with the distances that the Sun hath from the Earth in other places This point is called Aux Solis and Longitude longior that is the point of the sunnes furthest distance from the earth But vnder the broadest part of the vppermost and vttermost Orbe where you see printed PERIGAEVM and right aboue the narrowest part of the nethermost Orbe is the place where the Sun commeth nearest to the Earth as you may easily find with your Compasses or otherwise in like sort as before was shewed The point where the Sun commeth nearest to the earth is called oppositum Aâ—gis and longitudo propior that is the point opposite to the Apogaeum and the nearest distance And at those parts of this Orbe which are in the midst betweene the former the Sunne hath a meane distance from the earth a meane I say betweene the least and greatest distance The very point wherein this meane or middle distance hapneth is shewed by the points that are iust in the middest betweene the short lines AB and IK which are drawne ouerthwart on eyther side of this Orbe These points are called longitudines media that is the meane distances of the Sunne because the sunne comming to these points hath a meane distance betweene the least and the greatest About these points also the true motion of the sun is as it were in a meane between the slowest which hapneth the sunne being about the Apogaeum and the swiftest which hapneth about his Perigaeum Moreouer the lines A and K shew the places wherin there is the greatest Prosthaphaerisis or Equation of the sunne that is the greatest difference betweene the true and middle or meane place of the sunne Lastly the distance betweene the lines I and K or A and B shew how much the eccentricitie of the sunnes eccentricke is that is how farre the Center of the eccentricke is distant from the Center of Earth CHAP. III. To finde how much the Sunne is nearer or further from the earth at one time then at another BY meanes of this Circle you may easily find with your Compasses how much the Sunne is nearer to or further from the earth at one time then at another for hauing set one foot of the Compasses vpon the vtmost edge of the Deferens Apogaeum vnder the place of the Sunne in the Zodiacke found by the second Prop. stretch out the other foot to the innermost edge of the same Orbe for then if you set one foot of your Compasses vpon the vtmost edge of this Orbe at the Apogaeum the other foot turned inwards towards the center of the Sphaere will shew you how much the Sunne is nearer to the Earth at that time then when he is in his Apogaeum for so much as that foot reacheth within the inner edge of the Orbe so much is the sunne nearer Likewise if you set one foot of your Compasses vpon the