same time as the Sunne The last is the Moone making one perfect reuolution from West toward East in 27. daies 7. howers 43′ 7″ yet all these are caried by violence of the first moueable from East to West as is before saide OF THE CIRcles of the Sphaere of Heauen and of their names and how they be made AStronomers to the end they might shewe the motions of Heauen and the straūge and wonderful conclusions of the Coelestiall bodies haue imagined certaine Circles in the bodie of the first Sphaere or first mooueable and principally ten whereof some be greater Circles of the Sphaere so called because the Center of these Circles is also the Center of Heauen euery such Circle diuideth the whole Sphaere into two aequall parts Of this sort be sixe the Aequinoctiall Zodiack Horizon Meridian and two Colures Some bee lesser Circles of the Sphaere so called because they haue not the Center of the world for their Center neither diuide the whole Sphaere aequally Of this kinde be fower the Tropicke of Cancer the Tropicke of Capricorne the Articke and Antarticke The Aequinoctiall called the aequator or girdle of Heauen is a great Circle of the Sphaere diuiding the Sphaere into two aequal parts and is aequally distant from ech Pole of the worlde And tooke his name of the aequator either because it is aequally in the middle of Heauen as Euclide saith in his Opticks or for that the Sunne comming to this Circle maketh the day and night aequall it is diuided in 360. aequall parts which parts are called degrees His Axe is the Axe of the world and Poles the Poles of the world The Zodiack is a great Circle of the Sphaere which crosseth the Aequinoctiall in two points the one being the head of Aries the other of Libra and swarneth from him in all other points leaning toward ech Pole of the world in the point of his greatest swarning 23. degrees 30. minutes This Zodiack is of breadth 12. degrees and of length that is to say in compas 360. degrees and according to his length is diuided into 12. aequal parts which are called the 12. signes Aries Taurus Gemini Cancer Leo Virgo Libra Scorpio Sagittarius Capricornus Aquarius and Pisces And ech signe contayneth of length 30. degrees in the midle bredth of the Zodiack we imagine a Circle to passe which we call the Ecliptick Circle or line For that that when the Sunne and Moone bee both vnder this line in a Diameter then the Moone is Eclipsed Vnder this Circle the Sunne mooueth dayly without declining any waies the quantity of one degree very neere in ech day the rest of the Planets are found some times on one side the Ecliptick some time on the other This Zodiack taketh his name of a greeke word signifying a liuing creature or as the Latens will is called Signifer for that that it beareth the 12. Signes the Axe of the Zodiack and the Ecliptick is all one being a line diuers from the axe of the world and the Poles bee two points alwayes so much distant from the Poles of the world as the greatest declination of the Ecliptick commeth vnto A Colure doth generally signifie any Circle passing by the Poles of the worlde and hath his name of his vnperfect shewing himselfe in the motion of heauen But now by the name of Colures we vnderstād two great Circles the one going frō the Poles of the worlde by the points where the Aequinoctiall and Zodiack cut them selues which be called the Aequinoctiall points and is called the Aequinoctiall Colure The other passeth from the Poles of the worlde by those points of the Ecliptick which swarue most of all others from the Aequinoctiall line which points are called the Solsticiall points and this is called the Solsticial Colure And here be you to know that these foure greater Circles which we haue defined be still the same through the whole worlde and are sayd to be moueable Circles for so much as in the motion of heauen they be also mooued of which some are moueable perfectly as the Aequinoctiall and Zodiack for they in the going about of heauen doe ascend by little and little till the whole Circle haue gone oure the Horison some vnperfectly moueable as the two Colures which neuer shewe the whole Circle in any crooked Sphaere the other two greater Circles which followe be called fixed for that they neuer mooue by the motion of heauen But they be changeable in euery Region The Horizon is a greater Circle diuiding the halfe of the Heauen which we see from the halfe which we see not and is called in Latine Finitor because it endeth our sight The Horizon maketh fower principal points East West North and South His Axe is a line imagined to fall from the point of heauen which is directly ouer our head where we be downe to the groūd like a plumme line and his Poles be the endes of that line called the Verticall point and point opposite to the Verticall The Meridian is also a great Circle passing from the Poles of the world by our Verticall point cutting the Horizon in the North and South points his Axe is a line going from the East point of the Horizon to the West and his Poles be the same points and these two Circles doe alwayes chaunge are diuers in euery Region for so much as the Verticall point of euery Region is diuers by the which the Meridian of necessitie must passe and is the Pole also of the Horizon OF THE LESSER Circles of the Sphaere and their names and of their making THe lesse Circles of the Sphaere in number be fower The Tropicke of Cancer the Tropicke of Capricorne and the two Artickes The Tropicke of Cancer is a lesse Circle of the Sphaere which is aequally distant from the Aequinoctial lying betwixt the Aequinoctiall and the North Pole and touching the Ecliptick in the beginning of Cancer This Circle is described by the bodie of the Sunne in the longest day of Summer at which time the Sunne is entred the solstitiall point or beginning of Cācer is called the Tropick of a Greeke word which signifieth a returning because the Sunne being brought to this point falleth in his noone height and returneth againe The Tropicke of Capricorne is a like Circle betwixt the Aequator the South pole and is described by the Sunne in the shortest day of Winter at which time the Sunne is in the beginning of Capricorne whereof it is called the Tropick of Capricorne The Articke Circle is a lesse Circle of the Sphaere described by the Northerne Pole of the Ecliptick Proclus saith it is described by the formost foote of the great beare and thereof taketh his name The Antarticke is a like Circle described by the South Pole of the Ecliptick is called Antartick of the Greeke worde which signifieth Opposition because it is opposite to the other Of the vse of the Circles of the Sphaere or Globle THE most
others whose cohaerence is not so naturall Propositio 31. An other way to finde the length of the Artificiall day or night FInde the time of the Sunne rising for your day proposed by the 12. propositioÌ„ then dubble all those howers and partes of time which be from Sunne rise till noone for it giueth the Artificiall day Or if ye nuÌ„ber all the howers and parts from Sunne rise to his setting it giueth the same Propositio 32. To finde the hower of the day PLace the Globe in the Sunne shine and rectifie him to his vse by the 4. proposition then finde the place of the Sunne by the 5. proposition Againe rectifie his Index by the 14. proposition Lastly 〈◊〉 the needle or pinne directly vp in the place of the Sunne then turne the Globe vp till the pinne cast no shadowe for then the Index sheweth what is then of the clocke Propositio 33. To finde the eleuation of the Pole in any place DRawe in the open ayre vpon some table that is leuell a Meridian line by the 1. proposition and place the Globe so on it that his Meridian Circle hang directly â—uer it then hauing the place of the Sunne set a pinne right vp in it and put the said place and pinne close to the Meridian circle Lastly lift vp the Pole and Meridian Circle till the pinne cast no shadowe for then the degrees betwixt the Pole and the HorizoÌ„ be the true eleuatioÌ„ of that place But this practise is to bee performed at noone onely or height of the day Propositio 34. An other way to doe the same TAke the height of any fixed Starre whom ye know by the 2. proposition at such time as he pointeth with the Meridian line then take the same Starre on the Globe and by helpe of your Quadrant or Meridian Circle cause him to haue the same Altitude in the Globe and withall to be vnder the Meridian of the Globe for theÌ„ is the Pole at his true Eleuation So did I finde the Pole Starre making my obseruation at Oxford the 11. of December 1584. by the plaine Sphaere to haue 55. degrees 59. minuts in Altitude being theÌ„ in the Meridian of Heauen and when I set him at the same in my Globe I found the Pole eleuated there 51. degrees 50. minuts And here ye are to knowe that when soeuer ye haue by any way the eleuation of the Pole in any place if ye subduct the same eleuation from 90. degrees it shall leaue and sheâ—… the eleuation of the aequator in the sayd place So then the eleuation of the aequator at Oxford is 38. degrees 10. minuts Propositio 35. An other way of working the same with more praecisenes FIrst learne by some good Ephemeris the precise place of the Sunne at noone in the day of your obseruation then againe learne the exact declination of the said place Lastly with your 〈◊〉 take the Meridian height of the Sunne that day And if the declination bee Northerne then subduct it from the Meridian Altitude but if it be Southerne then ad it to the Meridian Altitude so shall wee bring forth the Altitude of the aequator and this Altitude being subducted from 90. degrees leaueth the Altitude of the Pole but if the Sunne in the time of obseruation be in the Aequinoctiall point then is the Meridian Altitude the Altitude also of the aequator and it subducted from 90. degrees leaueth the Altitude of the Pole Propositio 36. To make a Horizontall Diall by the Globe A Horizontall Diall is such a one as is made in a plaine Superficies and lyeth leuell with the Horizon For making whereof ye are to consider that from one Pole of the Globe to the other goe twelue great Circles called hower Circles and diuide the aequator into 24. aequall parts And two of these bee two Colures Put therefore the Solstitiall Colure precisely vnder the Meridian of your Globe the Globe being first perfectly rectified and fixe the Globe so that he cannot mooue Now marke how many degrees of the Horizon are inclosed betwixt the Meridian and the next hower Circle toward the East which for distinction sake I call the second hower Circle so likewise betwixt the first third the first fourth the first and fifth the first and sixt the first and seuenth which is he that cutteth in the true East point and set them all downe in tables then drawe on some plaine thing a Circle and diuide it into fower quarters by drawing two crosse lines Now take the one ende of any of the two lines and terme it the North point so shall his other end be the South point and the endes of the other line East and West Againe diuide that quarter of this Circle which is betwixt the North point and East into 90. aequall parts and let 90. stand at the East So doe by the quarter betwixt North and West Lastly recken from the North point toward East so many degrées as your tables shewe to haue 〈◊〉 betwixt the first and second hower line and from the point where they ende drawe a line by the Center of the saide Circle and so doe by all the numbers of your tables for so shall ye haue your hower lines drawne for a Horizontall Diall In whose Center must be a stile exected according to the eleuation of your Pole But this I leaue obscure as meaning to set out an ample treatise of Dialling by it selfe Propositio 37. How the Starres may be knowne by the Globe of Heauen REctifie your Globe in the open ayre by the 4. proposition theÌ„ take the height of any knowne Starre by your Instrument afterward looke the same Starre on the Globe and by helpe of your Quadrant of Altitude put the same Starre at his height taken before and in the same Coast then fixe the Globe Now if ye would knowe any other Starre of Heauen then take the same Starre his height with your Instrument lastly turne your Quadrant of Altitude toward the same Coast of the Globe in which the Starre was in looke what Starre ye finde in that Coast to haue that Altitude the same is he whom ye seeke The like is to be done by all others Propositio 38. To finde the Longitude of any fixed Starre THE Longitude of a Starre is the portion of the Ecliptick line taken from the head of Aries according to the order of the Signes to the point of the Ecliptick cut by a Circle which passeth froÌ„ the Pole of the Ecliptick by the Center of the sayd Starre and is thus found Take the Globe from his Horizon and take of his Meridian Circle and fixe the same Circle by some meanes on the Poles of the Zodiack then turne the Starre whose Longitude ye seeke vnder the Circle and recken all the Signes and parts from the head of Aries to that point of the Ecliptick which is vnder the Circle with the Starre for so much is his LoÌ„gitude And the same point of the
aboue groūd at the sayd hower by the 41. proposition so shall the pointes be geuen as before Propositio 50. To find the bignes of the angle made betwixt the Meridian Circle and any Circle of position CIrcles of Position bee all such as are drawen from the North point of any Horizon by the Center of any starre and so to go to the South point of the same Horizon to returne to the North againe And euery one of these Circles doth make some with the Meridian and the sayd angle hath his bignes shewed by a portion of the fixed Verticall so that to find the bignes of the angle made betwixt the Meridian and any Circle of position is to find the portion of the fixed Vertical inclosed betwixt the Meridian and the said Circle of position that portion is thus found Put your quadrant of altitude to the true East point then raise vp your Brasse halfe Circle as high aboue the Horizon as yee please so that it may nowe represent some circle of position for then the degrees of the Quadrant of altitude from the Meridian to this circle be the bignes of the angle made betwixt the Meridian and the Circle of position but if your circle of position fall on the West side of the Meridian then put the Quadrant to the West point and worke as before Propositio 51. To find the beginnings and endes of the 12 howses of Heauen COncerning the erecting the scheme of heauen or as we commonly call it the twelue howsen though fower diuers waies haue bene receaued touching the howsen how they ought to bee taken yet it is not our entent to discourse of that question but to shewe howe they ought to be erected according to the most vsuall way set downe by Regiomontanus called reasonable Wherefore first ye are to knowe that in any Horizon wheresoeuer wee be wee doe imagine sixe circles to be drawen from the North point of the Horizon to the South of the same and diuiding the Aequinoctiall into 12 aequall partes and the 12. spaces betwixt these circles are called the twelue howses two of the 6. circles are alwaies the Meridian and Horizon in euery one of these howsen is inclosed some portion of the Zodiack and one portion is greater thē an other so that to erect the twelue howsen is to find out the portion of the Ecliptick inclosed in ech space to do it we thus proceede First find out the fower Cardinal points by the 49. proposition for those be the beginnings of 4. howsen of the twelue the Cardinall point vnder the Meridian aboue ground is the beginning of the tenth howse This done fixe the Globe then recken from the degree of the aequator being then vnder the Meridian 30. degrees toward the East point raise vp your brasse halfe circle to stand on the point of the aequator on which yee left For looke then what degre of the Ecliptick is cut then by the brasse halfe Circle the same is the end of the tenth howse and beginning of the eleuenth Againe yet recken 30. degrees more in the aequator toward the East and put the brasse halfe circle to it and thē take the degree cut in the Ecliptick for that is the end of the eleuenth howse and beginning of the twelfth Againe the Cardinall point of the East is the end of the twelfth howse and beginning of the first howse Now if in like sort ye goe from the degree of the aequator vnder the Meridian by ech 30. degree of the same toward the West point and still obserue the degres cut in the Ecliptick yee shall haue the beginnings and ends of the ninth eighth and seauenth howse Thus hauing erected sixe howsen the degrees of the Zodiack which are opposite to these in a Diameter one to an other bee the beginnings and ends of the other sixe howsen which were to be found And here must yee note that the first howse beginneth at the East point and goeth vnder the ground toward the Meridian Circle the second and the third succeede the fowerth beginning at the Meridian vnder ground comming toward West the fifth and sixth succeed the seuenth beginneth in the West and goeth aboue ground toward the Meridian the eight and ninth succeed Other conclusions lesse profitable I wittingly auoyded and the more excellent deferred to a more conuenient time FINIS Errata Pa 3. li 13. indicem lege iudicem Pa 23. li 1. same lege Sunne Pa 24. li 1. lege Ver. Pa 46. li 16. till ye lege till it
his Index stand on the hower which was knowen before Then fixe the Globe for remoouing Lastly turne your Quadrant of altitude to the Ecliptick line and looke what degree of the Ecliptick agreeth in your Quadrant with the height that was before knowen and that is the place of the Sunne on that day Propositio 20. The hower and place of the Sunne being giuen to find howe farre the Sunne is gone from the true East poynt THe place of the Sunne being giuen by supposition rectifie the Index by the 14. proposition then turne the Globe till the Index shew the hower giuen This being done fixe the Globe that he mooue not away and set the edge of the Quadrant of altitude to the place of the Sunne and withall marke howe many degrees of the HorizoÌ„ are inclosed betwixt the true East point and the edge of the Quadrant at such time as he staÌ„deth on the place of the sunne for so much is hee distaunt in the Horizon from true East Propositio 21. The distance of the Sunne being geuen from true East together with his height at the same time and the height of the Pole for the same region to finde the true place of the Sunne at any time TO the ende wee make not vnnecessarie repetitions of the first principles know this that in all the propositions following we alwayes suppose before the working the Globe rightly rectifyed as is specified in the beginning For the performance therefore of this practise first consider diligently in what quarter of the yere ye be in that is whether it be betwixt the aequinoctiall of March and height of Summer or betwixt height of Summer and aequinoctial of September Likewise whether betwixt aequinoctial of September and dept of Winter or betwixt dept of winter and aequinoctiall of March. For then set the edge of the quadrant of altitude at the true distance of the Sunne from the East and turne the Globe till that quarter of the Ecliptick come vnder him which serueth for the quarter of the yeere in which ye be and see what degree of that part of the Ecliptick agreeth with the height proposed For that is the place of the Sunne at that time Note therefore here that to the Spring which is from the aequinoctiall of March till the height of Summer answereth the part of the Zodiack from Aries to CaÌ„cer To summer which is from the height till the aequinoctiall of September answereth the part from Cancer to Libra The Autume is guided by the quarter from Libra to Capricorne and Winter by the signes from Capricorne to Aries Propositio 22. The distance of the Sunne being geuen from true East and the place of the same to find the height of the Sunne which he hath at the same time PLace the quadrant of altitude at the true distance from East so shall hee cut the place of the Sunne by the 21. proposition and therefore the portion of the Quadrant betwixt the place of the Sunne and the Horizon is his height Propositio 23. The distance of the Sunne from true East being geuen and his place to find the hower of the day FIrst hauing his place rectifie your Index by the 14. proposition again setting the Quadrant of altitude in the distance from true East reduce the place of the sunne till he fall in the edge of the Quadrant for then the Index doth shewe the hower Propositio 24. The distance of the Sunne being geuen from true East and his height to find the time of his rising THe distance being giuen find his place by the 21 proposition and then rectifie the Index by the 14 proposition Lastly put the place of the Sunne to the East side of the Horizon for then the Index will shew the Sunne rising Propositio 25. The distaunce of the Sunne being giuen from true East and his height to finde his Declination THE distaunce being giuen his place is fouÌ„d by the 21. proposition his place being knowne giueth his Declination by the 6. proposition So may wee likewise by the said distaunce finding his place finde his right or crooked ascention or difference of ascentions and length of Artificiall daies Propositio 26. The declination of the Sunne being knowne to finde the place of the Sunne COnsider first diligently in what quarter of the yeare ye be in as was expressed before then take that quarter of the Ecliptick which answereth to your quarter of the yeare and mooue it still vnder the Meridian of your Globe till ye finde no more of the Meridian inclosed betwixt the aequator and Ecliptick then the declination that is giuen commeth vnto for then looke what degree of the Ecliptick is vnder the Meridian that is the place of the Sun As the declination of the Sunne in the quarter of the yeare betwixt the Aequinoctiall of March and height of Summer was giuen to bee 11. degrees 50. minuts And to this quarter of the yeere aunswereth the quarter of the Ecliptick froÌ„ Aries to Cancer Therefore moouing the said quarter vnder the Meridian I found the first of Taurus to aunswere to this declination and therefore that was the place of the Sunne Propositio 27. The declination of the Sunne being knowne to finde the day of the Moneth BY the declination giuen finde the place of the Sunne by the 26. proposition theÌ„ take the said place in the Horizon of your Globe for looke what day aunswereth against it that is the day of the Moneth Propositio 28. The day of the Moneth being knowne to finde the length of the Planetarie hower THE Artificiall day is from Sunne rise to Sunne set and the 12. part of this day whether it be longer or shorter then an hower by the clocke is the Planetarie hower and may thus be knowne The day being giâ—en finde the length of that day by the 10. proposition and diuide all by 12. The Quotient is the length of a Planetarie or Artificiall hower of that day As the day being 15. howers by the clocke I diuide it by 12. the Quotient is one hower and a quarter and so much is a Planetarie hower of that day Propositio 29. The day of the Moneth being giuen to finde the dawning of the day BY the day knowne finde the place of the Sunne by the 5. proposition and then rectifie your Index by the 14. proposition Againe take the degree of the Ecliptick which is opposite in a Diameter to the place of the Sunne and mooue him toward the West together with the Quadrant of Altitude till ye haue 18. degrees of height for then the Index sheweth the beginning of the dawning or spring of the day Propositio 30. To finde the length of the whole dawning FInde the beginning of the dawning by the 29. proposition and then the Sunne rise by the 11. or 12. proposition for the difference of those times is the whole dawning And thus farre haue I followed such conclusions as haue a more orderly cohaerence it remaineth now to shewe some