proposition then subduce the lesse from the greater for the remaines is the difference of ascention Propositio 10. To finde the length of the Artificiall day in any Region or Countrie FInde out the difference of ascention of the place of the Sunne by the 9. proposition and dubble the same then conuert is all into howers and parts of howers allowing for one hower 15. degrees and for a halfe 7. degrees 30. minuts c. This time which commeth of the difference of ascention adde to 12. howers if the place of the Sunne bee any degree betwixt Aries and Libra or subduct it frō 12. if he be betwixt Libra and Aries for the number made or left is the length of the day As the Sunne being in the first of Tanrus his difference of ascention is 15. degrees 6. minuts this dubble and conuerted into time maketh 2. howers and 12. Aequinoctial minuts And because Tanrus is a Northerne Signe ye must ad this difference to 12. howers so do ye make 14. howers and 12. Aequinoctiall minuts for the length of that whole day Propositio 11. To finde the hower of the Sunne rising or of his setting KNowe the length of the Artificiall day by the 10. proposition and take halfe of the same day for that sheweth the hower of Sunne setting But if ye recken so much from noone forward it giueth Sunne rise As the Sunne being in the first of Taurus the day is 14. howers and 12. minuts The halfe is 7. howers and 6. minuts I say then the Sunne setteth after 7. of the clocke 6. minuts Againe thus much taken from noone forward sheweth the Sunne to rise before 5. of the clocke 6. minuts Propositio 12. An other way to finde the same more mechanically FInde the place of the Sunne by the 5. proposition and turne the saide place directly vnder the Meridian thē put the Index of the hower Circle precisely on 12. of the clocke Lastly turne the saide place of the Sunne to the East side of the Horizō for when he is there then shall the Index shewe the time of the Sunne rising And contrariwise putting the place of the Sun to the West it sheweth his setting Propositio 13. To finde how farre the Sunne riseth or setteth from the true East or West point any day FIrst finde the place of the Sunne by the 5. proposition then turne the same place to the East side of the Horizon til he touch the same for then the number of degrees in the Horizon inclosed betwixt the true East point and the place of the Sunne shewe how farr he riseth and setteth from the true East And this portion of the Horizon is called his bredth of rising and is called Northern bredth if the Sunne rise beyond the East point toward the North Southern if contrary Likewise are ye to knowe that of the Ecliptick two points Aries and Libra haue no bredth of rising Two points also as Cancer and Capricorn haue greater then any other and of the rest fower points haue the like Propositio 14. To rectifie the Index of the hower Circle euery day as he ought FInde the place of the Sunne euery day in which ye vse the Index by the 5. proposition and put the said place vnder the Meridian this being done thē put the Index on 12. of the clocke for afterward in the motion of the Globe he will goe true as he ought Propositio 15. To finde the noone height of the Sunne for any day to come or gone in any place whose eleuation is knowen THe height of the Sunne is the portion of the verticall Circle inclosed betwixt the Center of the Sunne and the Horizon But for as much as at noone the Meridian and the Verticall of the Sunne bee all one Circle therefore his noone height is the portion of the Meridian betwixt the Center of the Sunne and the Horizon this height is thus to be knowen Find the place of the Sunne for the day proposed and turne the same place vnder the Meridian for then the portion of the Meridian betwixt the sayd place and the Horizon is his noone height Thus found I the height of the Sunne at noone in Oxford whose Pole is raysed 51. degrees 50. min. on the 2. day of May to be 59. degrees 47. mi. and on the twelfth of Iune to be 61. degrees 41. minuts Propositio 16. To find the depression of the Sunne at midnight AS the Meridian altitude is the portion of the Meridian from the Center of him to the Horizon when hee is aboue the earth so is his depression the part of the Meridian betwixt the Center and the Horizon when he is vnder ground and may thus bee knowen Finde the place of the Sunne and put it to the Meridian vnder the Horizon for then the portion of the Meridian betwixt it the Horizon sheweth his depression So find I the depression of the Sūne at Oxford his place being the first of Taurus to be 27. degrees 40. min. but his place being the first of Scorpius to be 50. degrees 0. min. Propositio 17. To find what height the Sunne shall haue at any certaine hower of any artificiall day TAke the place of the sunne by the 5. proposition rectifie the Index by the 14. pro. then turne the Globe till the Index of the hower circle be on the hower for whom ye desire the height of the Sunne and scopping the Globe there put the quadrant of altitude to the place of the Sunne for his portion betwixt the place of th◠Sunne the Horizon geueth his height So find I the height of the Sunne at Oxford at 9. of the clocke the 7. day of March. to be 24. dedrees 25. min. and at one of the clocke the same day to be 34. degrees 51. min. Propositio 18. By any height of the Sunne geuen and his place to find the hower of the day LEt it bee that either ye take the height of the Sunne at some time of the day by the second proposition or that yee haue some height of him giuen by supposition and ye would knowe by it what it is of the clocke that day at that time Finde therefore the place of the Sunne for that day by the 5. proposition rectifie the Index by the 14. proposition Lastly put the place of the Sunne to the Quadrant of Altitude and mooue them both vp and downe till ye allowe him the same height in your Quadrant as ye found or supposed him in trueth to haue For then the Index of the hower Circle sheweth what was or is of the clock as finding the height of the Sunne before Noone on the seauenth of March at Oxford to be twentie fower degrees 25. min. I founde it to haue beene then nine of the clocke Propositio 19. By the hower knowen and the height of the Sunne at that hower together with the Index rectified as he ought to find the place of the Sunne at that tyme. MOoue your Globe till
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
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
principall cause why Artificers inuented the Aequinoctiall was first because it is the measure of the first Heauen by a conuenient perpetual and aequal swiftnesse Secondly it measureth and limitteth the time of rising of the Signes as also the length of the Artificial daies and times of the Aequinoctials with declinations and right ascentions of Starres together with Longitudes of Regions Lastly for the exection of the twelue howsen of Heauen In like maner the Zodiack serueth for Latitudes Longitudes of Starres for distinction of the times of the yeare for the motions of all the Planers and effects of the same Not vnlike be the vses of the Colures and Meridian ech shewing the greatest declination of the Ecliptick but especially the MeridiaÌ„ which giueth as well al declinations of Starres their noone height and distinguisheth the daies and nights into two aequal parts and serueth for the Horizon of the right Sphaere It beginneth likewise and endeth all Longitudes of Regions and sheweth Latitudes and Eleuations of the Pole It helpeth to diuide the 12. howsen In like maner sundrie and diuers be the vses of the Horizon As in seperating the hidden part of Heauen from that which is seene and sheweth the place of rising and setting of any Starre how farre from East or West with his height All which points are respected of Astronomers as the Sphaere is secondarily diuided that is to say as he is a right or a crooked Sphaere which bee his properties and affections ment in the diuision afore specified By a right Sphaere is ment such a kinde of position of Heauen as that neither Pole bee râ—ised aboue ground but that ech lye in the face of the earth And such a kinde of position haue they which dwell in Bersera and the Islands of Molucca or such like Contrariwise it is sayd to bee a crooked Sphaere when any one of the Poles is raised aboue ground Such a Sphaere haue we at Oxford and London and generally all which dwell not vnder the line All which thinges for our better conceate are shewed to the eye in the materiall Globe whose names and diuisions appeare at the first vewe two things only being waied First that the mechanicall or materiall Globe which representeth the first mooueable beareth in him the fixed Starres not because the Starres bee in the first mooueable but because their motion is so litle in their own Sphaeres in many yeares that they may seeme not to haue mooued at all in a man 's his age from their places vnder which they be of the first moueable therefore they may bee supposed to stand in it Secondly the Globe representeth the Starres to vs in his connexitie which appeare in Heauen in the concauitie For that our eye is not in the Globe but without Furthermore in the Globe besides the aforenamed Circles bee found three others of brasse the one being a perfect Circle of a litle quantitie placed about the Pole which is eleuated is called the hower Circle whose stile is called the Index An other is a thinne rule of brasse representing one quarter of a whole Circle called the quadrant of Altitude and is alwaie to be fixed when ye vse the Globe on the middle of the halfe of your Meridian which is aboue the Horizon that is to say 90. degrees aboue the Horizon The third and last is a great halfe Circle lying at the Horizon seruing aswell for the erection of the scheme of Heauen as any Circle of position All which things being aduisedly considered of ye may proceede in the vse of the Globe As followeth HOW THE Globe is to be placed readie for his vse and practise THe placing of the Globe ought to be such that the Horizon of the Globe may stand parallele or leuied to the true Horizon and the Meridian of the Globe stand in the Superficies of the true Meridian of Heauen and the Poles of the Globe and his Axe answere exactly to the Poles and Axe of Heauen Now to the leuying of the Horizon there ought to bee at your Globe a hanging plummet and for the Meridian a Needle touched of the lode stone and touching the rectifying of the Poles and Axe of the Globe the eleuation of the Pole of heauen is first to be knowen the meanes to performe and accomplish the same being such as followe Propositio 1. To finde a Meridian line in any place appoynted SEt vp on your Horizon or some plaine leuied boarde a Gnomon of any reasonable length then at such time as the same shineth describe from the top of your Gnomon a Circle by the tippe of his shadowe and make a marke in the Circle where the shadowe ended at your obseruation which must be before noone Then marke in the afternoone at what time the ende of the shadowe returneth into the same Circle againe and make a marke at his point of falling so shall ye haue a portion of the sayde Circle inclosed betwixt the two points If then ye diuide this portion into two aequal parts and drawe a line from this middle point by the point in which the Gnomon standeth it shal be a Meridian line Propositio 2. To take the height of any Starre FRrom the point of Heauen which is directly ouer our heads being called the Verticall point or Zenith are imagined diuers Circles to fall by euery degree and minute of the Horizon all which Circles are called Verticals serue for the height of Starres for so much as the altitude of Sunne or starre is the portion of the Vâ—…ticall Circle inclosed betwixt the Center of the Sunne or Starre in the time of his obseruation and the Horizon which height is thus found Take your Astrolabe and let him hang freely by his ring then turne vp his Dioptral so long that ye see the Starre whose height yee seeke thorowe his sights for then howe many degrees and minutes are inclosed betwixt the Dioptrall and the line of your Astrolabe which is parallele to the Horizon so many hath that Starrs of height as the seauenth day of Ianuarie Anno. 1585. vnder the Meridian of Oxford at 9. of the clocke I sought the height of the Sunne taking then my Astrolabe and hanging him towarde the Sunne and raising his Dioptrall till I espyed the Sunne I found betwixt the Dioptral and the line representing the Horizon seauen degrees and 16. minutes so much was the height of the Sunne at that time Propositio 3. To take the altitude of the Pole in in any place or countrey THe altitude of the pole is the portion of the MeridiaÌ„ Circle inclosed betwixt the Pole and the Horizon and is thus found Find a Meridian line and drawe him in the Horizon by the first proposition then take the height of any fixed Starre which setteth not and that at the fore part of the night at such time as he is pointed vppon your Meridian line by the second proposition Again the next morning or any other morning take the height of
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
Ecliptick which is so vnder the Circle shal be called the place of that Starre And the Starre is sayd to bee vnder that Signe of whom the aforesaid point is a part The Longitude may also be taken if ye doe but fixe the Quadrant of Altitude in the Pole of the Ecliptick and stirre not at all the Meridian Circle Propositio 39. To finde the Latitude of any Starre THE Latitude of a Starre is the portion of the Circle that passeth from the Poles of the Ecliptick line by the Center of any Starre which is inclosed betwixt the Ecliptick line and the Center of the Starre and is found thus Your Circle standing in the Poles of the Zodiack as before turne the Starr vnder the said Circle for then the portion of that Circle betwixt the Starre and the Ecliptick is his Latitude And this Latitude is Northern when the Starre is North from the Ecliptick and Southerne of contrary Propositio 40. To finde what Starres be aboue ground at any time of the day or night IF ye would know it in the day time whē the Sunne shineth then take the height of the Sunne by the 2. proposition afterward finde his place by the 5. proposition lastly by help of the Quadrant of Altitude set the Sunne at his owne height Coast and then all the Starres aboue the Horizon doe appeare in the Globe Now if it be in the night and the Starres appeare then take the height of some knowne Starre and place the same Starr at his due height in the Globe so shall ye see the same Propositio 41. To doe the same without Sunne or appearaunce of any Starre YE must knowe what it is of the clocke at that time when ye would worke this conclusion then rectifie the Index by the 14. proposition Lastly turne the Globe till the Index come on the same hower as is giuen by the clocke for then the Starres appeare as they should Propositio 42. To finde what Starres will passe directly ouer our heads in the motion of the heauen AFter that the Quadrant of Altitudes is fixed in his due place as is spoken of before so that he now doe shewe the Zenith or Verticall point then mooue about the Globe and marke what Starres passe vnder the Zenith in this motion for those bee such as goe by our heads are called sometimes Culminant starres sometimes Verticall starres and haue their cheefest vse in Astrologie Propositio 43. To knowe with what degree of the Ecliptick any Starre rised commeth to the Meridian or setteth MOue the Globe till the Starre whom ye propose ascend aboue the Horizon and then marke the degrée of the Ecliptick that riseth with him Againe mooue him to the Meridian and marke the degree of the Ecliptick so doe by him in the West side of the Horizon and ye shal haue your intent Propositio 44. To knowe the hower of any Starres rising REctifie the Index by the 14. propositiō then turne the Globe til the said Starre whose time of rising ye desire touch the East side of the Horizon for then the Index giueth his time of rising And if ye turne him to the Meridian the Index will shewe his time of comming the ther or if ye turne him to the West side of the Horizō the Index sheweth his setting Propositio 45. To find in how long time any whole signe ariseth REctifie the Index by the fowerteenth proposition then put the beginning of the signe whose time of rising ye seeke to the East part of the Horizon and marke what the Index standeth on then againe put the last degree of the sayde signe to the Horizon and see what the Index sheweth for the differēce of the two times by the Index is the time in which that signe riseth Propositio 46. To find in what coast any starre is and how many degrees from the Meridian FInde the Starres aboue ground by the 40. proposition then the Globe beeing fixed put the Quadrant of altitude to any State Then shall the foote of the Quadrant shewe in the Horizon how farre the same Starre is from East West North or South But if ye first rectifie your Index by the 14. proposition and then finde the starres aboue by the 40. propositiō Agayn at the same time marke where the Index standeth lastly put any Starre vnder the Meridian and againe note the standing of the Index the differēce of those two times shewed by the Index is the distance of that starre from the Meridian in the time of your obseruation Propositio 47. To find what Starres rise or set any day Cosmically Achronically or Helically SVch starres as bee neare to the sunne in any day and ascende aboue the Horizon a little before the appearance of the same are said to ryse helically and such Starres as set very little after the Sunne are sayd to set helically Againe such Starres as ascend together with the Sunne and such as set at the same time are sayd to rise and set cosmically Lastly such starres as set together with the Sunne and such as rise at the same time are sayde to set and rise achronically and such may bee thus found Rectifie the Index by the 14. proposition and turne the place of the Sunne to the East side of the Horizon for the starres going immediatly before the Sunne rise helically and those in the Horizon rise cosmically and they that are in the Horizon in the west doe set cosmically and such as immediatly rise after the Sunne doe sette helically Lastly turne the Sunne to the West point of the Horizon and looke what starres touch the Horizon with him such set achronically and such as are at the same time rising in the East rise Achronically Propositio 48. To knowe the hower of the night at any time by the Starres REctifie the Index by the 14. proposition then againe finde what starres bee aboue ground at the same time when yee would know the hower by the 40. proposition for then the Index will shewe the hower Propositio 49 To find the fower Cardinall points of heauen at any time of day or night THe fower Cardinall points bee the fower degrees of the Ecliptick where of one is in the East rising an other is in the South or vnder the Meridian aboue at the same time the third in the West setting and the fourth vnder the Meridian beneath ground all at one instant in the time of any geniture or motion of any question and are thus knowen If yee seeke them in the day the Sunne shining then find the starres aboue ground by the 40. proposition and with all marke the degree of the Ecliptick in the East so likewise in the South West and North for those be then the Cardinall points Againe if it be in the night then find the starres aboue by the same 40. proposition and the pointes shall likewise appeare Lastly if nether the Sunne shine or starre then knowe the hower by the clock and afterward find the starres
A perfect and easie Treatise of the vse of the coelestiall Globe written as well for an Introduction of such as bee yet vnskilfull in the studie of Astronomie as the practise of our Countriemen which bee exercised in the Art of Nauigation Compiled by Charles Turnbull And set out with as much plainnes as the Author could to the end it might of euery man be vnderstood Psalm xix The heauens declare the glorie of God and the firmament sheweth the worke of his handes Day vnto day vttereth the same and night vnto night teacheth knowledge ¶ Imprinted at London for Symon Waterson INSIGNISSIMO VIRO AC OMNI VIRtutum genere clarissimo Magistro Henrico Nocllo Carolus Turnbullus salutem ac foelicitatem perpetuam comprecatur CVM antiquissimorum scriptorum singularem industriam in studijs Mathematicis iam ante seriùs accuratiúsque cognouerim recentium quorundam deprauatam lectionem summa cura summáque diligentia viderim obseruauerim ne infestus error damnum inferret grauius curaui vir insignissime ea faciliùs explicare quae si fideliter discantur omnis erroris tollent difficultatem Eorum verò te patronum esse volui vt meo exemplo ad eadem vota multos inuitem tanquam indicem te in florentissimo hoc regno non solùm tanti negotij virum celeberrimum sed omnium regiarum virtutum laudúmque patronum Itaque minusculam opus hoc Aâ—… qualecunque sit quod scio quam sit indignum tibi dedico vt qui imposterum non solum obseruationes astronomicas elaboratas magis minúsque vsitatas siue sint theorica siue horalogica sed opticas quoque qua sunt geometriae communis praecepta vt tempus postulat sis receptarus Quibus vt es spiritus nobilissimi ita mirificè quoque delectaris Vnum hoc interim precibus etiam atque etiam obsecrans vt qua humanitate erga me semper vsus es cum maxime possis eadem iam indies confirmata magis libertissime quoque velis patrocinari Vale. To the Reader MEn which are more desirous of publique Fame and Renow ne then studious of coÌ„mon profit with great curiositie set a glasse vpoÌ„ such things as being discouered would shew dismeÌ„bred mishapen As for my selfe I seeke no higher dignitie then to be reported to set forth a trueth and therefore without any wrested cloquence I make bold to offer the vse of the Globe to the exquisite vewe of your curious eyes though farre inferiour as I suspect to some mens expectation to the end such grosse enormities might bee amended as often times in diuers haue bene discouered Who for want of right conceat of things by them attempted haue in the ayer built such fortresses as haue without assalts wounded their louing enemies But happely such men wil now retire and arme them selues better against the next assault lest they be like to the dogs in the capitall of Rome which were placed to the end that if by night spoylers should ariue they might sound a warning For true it is that by night these barke out false Allaromes at their enimies but if by day they barke likewise at friends I hope ye wil iudge them worthy to haue their legs broken which things I leaue to your gentle interpretation Nothing misdoubting but if in this tract either anything bee escaped contrarie to my will or omitted not satisfying your expectation ye wil aequally suffer the same For if ye receaue the fruites of my labor and care of your commoditie I require no more Wherefore my trauaile I bequeath to your discreet consideration and your selues to the protection of almightie God Farewell DEFINITIONS to be praemised necessarie for the vnderstanding of the Globe THe Sphaere or Globe is a perfect round sollide bodie contained vnder one superficies or face in whose middle is a point from which point all lines that are drawne to the superficies and face of the same are aequall the one to the other The Center of the Sphaere is the middle point of the same The Axe of the Sphaere is a right line passing from one side of the same by his Center to the contrary side about which line the Sphaere is caried but the line it self standeth still The Poles of the Sphere be the endes of his Axe The Pole of any Circle is a point without the compasse of the same and yet is aequally distant from all points of the circuit or borders of the Circle whose Pole it is from which the same Circle is drawne OF THE NAME of the Sphaere and his diuers and sundrie kindes of diuisions together with the motion of ech one in his kinde THE NAME OF the Sphaere is taken either generally or particularly Generally and so it is said to containe all perfect round bodies whether they be sollide or not whether contained vnder one onely Superficies or moe And so may euery Orbe be called a Sphaere But if wee take the worde Sphaera in his particular and proper signification then nothing is a Sphaere but a perfect round bodie being sollide contained vnder one c. as the former definition declared This Sphaere is diuided either according to his substaunce or according to certaine properties and affections which he is capable of According to his substance he is diuided into two parts the one Elementall the other Aethercall The Elementall containeth the fower Elements Fire Ayre Water and Earth and is subiect to alterations by reason of their effectual working The Aethercall compasseth in round the Elementall part in his hollownesse and is lightsome by nature and vnchaungeable and containeth ten Sphaeres The first and highest from the earth being called the first moueable containeth in his hollownesse al the other and by his natural motion is moued directly from the East to the West and so to East againe in the space of 24. howers continually and carieth about with him by violence al the other Sphaeres The next vnder this is the ninth Sphaere called the Christall heauen and by his naturall motion is caried from West toward East but very slowly in many yeares passing but one degree and this motion hath caused the Starres to alter their LoÌ„gitudes The third Sphaere is the Firmament or Sphaere of the fixed Starres whose motion by nature is vpon two little Circles the one being described about the head of Aries and the other of Libra which motion is called the motion of Trepidation The other seauen Sphaeres be of the seauen Planets the highest of Saturne which moueth by nature from West toward East and that in 30. yeares one perfect reuolution The next of Iupiter moouing froÌ„ West to East by nature and that in twelue yeares The other of Mars making his reuolutioÌ„ from West toward East in two yeares Vnder Mars is the Sunne moouing by nature from West toward East making one perfect reuolution in 365. daies and 6. howers almost Vnder the Sunne is Venus and then Mercurie moouing from West to East about the