Equinoctiall Colure that which passeth by the poles of the world and the Solstitiall poynts is called the Solstitiall or Tropicall Colure the portion thereof lying betwéene the two Tropickes is the distance of the Tropickes whose halfe is the Sunnes greatest declination otherwise called the Obliquitie of the Zodiacke which by obseruation made with large instruments is in this our age found by great Artes-men to be 23. degrées and 30. minutes whose report it shall be sufficient to accept of and commit to memorie without taking or trying it by any small instrument though some writers of the vse of the Astrolabe haue made that one of their speciall conclusions The Equinoctiall and the Eclipticke are circles of chiefe accompt the first being the rule and measure of the first motion or the motion of Primum mobile otherwise called the Diurnall reuolution and the other as it were the Standard whereby all secondarie motions are examined therefore the degrées of these circles haue peculiar names called in the Equinoctiall Tempora times because they be the first measures of time euery 15. degrées ascending making an houre and so the whole reuolution of 360. which is performed euery naturall day make 24. houres Astronomers begin to accompt the parts or degrées as well in the Equinoctiall as in the Eclipticke from that poynt common to them both which is called the Vernall section and though in the Equinoctiall there be no chaunge of names yet in the Eclipticke or Zodiacke euery thirtie degrées is called a signe and hath a peculiar name The first 30. immedtatly following the Vernall section is called Aries the next 30. Taurus the third 30. Gemini the fourth 30. whose first point begin a new quadrant and toucheth the Summer Tropicke is termed Cancer the fift 30. Leo the sixt Virgo These sixe Signes make vp the semicircle of the Zodiacke which leaneth or declineth from the Equinoctiall toward the North pole The first 30. after this semicircle beginning at the Autumnall section make the seuenth signe named Libra the next or eight 30. is the signe Scorpio the ninth 30. is Sagittarius the tenth 30. beginning a new quadrant with the first poynt which toucheth the winter Tropicke is Capricornus the eleuenth 30. is Aquarius and the twelfth 30. is Pisces There be characters vsed to expresse euery Signe with which are found in euery Almanacke The Sunne passeth in the Ecliptick from poynt to poynt making his continuall reuolution in it without swaruing to the one side or the other other Starres for the most part decline from it but yet haue their places determined by Longitude and Latitude in respect thereof thus By any poynt or Starre a greatest circle being drawne from the pole of the Ecliptick to his circumference the section there made or the portion of the Ecliptick betwéene that section and the Vernall section is the Longitude of the poynt or Starre by which the greatest circle is drawne his Latitude is that portion of the same greatest circle lying betwéene the Starre and the Eclipticke The Sunne being in any poynt of the Eclipticke and the poynt it selfe with all other Starres wheresoeuer placed besides are in like manner compared to the Equinoctiall and in respect therof not onely their declination which hath béen touched before but also their right Ascension is considered A greatest circle being drawne from the Poles of the world to the Equinoctiall by any poynt or Starre his right Ascension is that portion of the Equinoctiall taken betwéen that poynt where the greatest circle cutteth and the Vernall section The declination is the portion of the greatest circle so drawne which lieth betwéene the Equinoctiall and the Starre which as before was noted is also determined by a Parallel to the Equinoctiall passing by the Starre The right Ascension is so called because vnder the Equinoctiall that is in a Situation where the Equinoctiall passeth by the Zenith and the Horizon by the Poles of the world the Horizon by which once in 24. houres euery poynt ascendeth doth the office of any greatest circle so drawne as is appoynted and agréeth with it most exactly This Situation is called Sphaera recta the right Sphere and the Horizon in that Situation Horizon rectus the right Horizon but when the Equinoctiall declineth from the Zenith and the Poles bée one aboue the other beneath the Horizon that Situation is called the Oblique or Declining Sphere and the Horizon the Oblique Horizon which neuer agréeth with the foresayd greatest circle drawne by the Poles of the world and therefore with the Starre there is another poynt of the Equinoctiall in the Horizon betwéene which and the Vernall section is contained that portion of the Equinoctiall that is called the Starres Oblique Ascension and the portion of the Equinoctiall betwéene the ends of the right and Oblique Ascension is called the Difference Ascensionall But for helping the conceit of these things I will vse a linearie example taking the former figure where E C is the Meridian line and the Diameter on which the Horizon standeth now in the middest of winter the Sun being lowest in the Meridian in the point K by the Diurnall reuolution describeth a Parallel standing vpon the Diameter K M which cutteth the Horizon from the East towards the South it continually groweth higher and higher in the Meridian pan riseth in the Horizon néerer and néerer the East till about the 11. of March at noone it commeth to G the section of the Equinoctiall and the Meridian and then by the Diurnall reuolution describeth a circle iust answering the Equinoctiall which passing by the poynts of East and West in the Horizon standeth vpon the Diameter G F from thence a◠Summer commeth on it ascendeth in the Meridian and riseth more Northerly vpon the Horizon til about the 12. of our Iune being at the highest in N it describeth a Parallel standing vpon the Diameter N Z in which it riseth vpon the Horizon furthest frō the East to the Northward from thence it descendeth againe by G to K and passeth in the Horizon by the true East to the furthest Southward then it ascendeth againe till it come to N continually returning from the highest to the lowest from the lowest to the highest whereof the two Parallels standing vpon the Diameters K M L N be called Tropickes By these changes it was easily gathered that the Sunne besides the Diurnall reuolution made another proper to it selfe in a circle standing vpon the Diameter K L drawne from Tropicke to Tropick by A the center of the Sphere by reason whereof this circle called the Eclipticke and the Equinoctiall diuide the one the other into two semicircles The Eclipticke is sometimes called the Zodiacke though properly the Zodiacke be a superficies lying on either side of it as you sée the superficies O P Q R parted by the line Z K. The common Diameter of the Equinoctiall and the Ecliptick standing in A perpendicular to the plaine of the circle B C D E
in P make O K equall to the distance R P and laying a ruler on A and K it will cut the lymbe in L the Circumference B L is the height of the Pole The 40. Conclusion By two knowne Starres whereof the one is in the Meridian the other in the Horizon to knowe the height of the Pole or Latitude LEt the declination of that which is in the Horizon be equall to either of the Circumferences E F C G draw the line G F cutting the Axis A B in O and let R P A be the Synicall arch of the line GF and let the right ascension of that which is in the Meridian be distant from the néerest Equinoctiall section so much as Q is from E now laying a ruler on A and Q it will cut R P A the Synicall arch of the line F G in P make O K or ON it skilleth not which equall to R P a ruler laid on K and A will cut the lymbe in L the Circumference B L is the height of the Pole The 41. Conclusion In a Countrey of knowne Latitude the height and declination of the Sunne being giuen to knowe the houre of the day or what it is a clocke LEt the Circumferences E F C G be equall to the declination of the Sunne and B L and D T the height of the Pole make either of the Circumferences L S T H equall to the height giuen a ruler layd on S and H will cut F G in V in R P A the Synicall arch of F G applie from R to W a distance equall to O V a ruler laid on A and W will cut the lymbe in X. Before Noone the obseruation being taken and if the Axis of the world fall betwéene V and the Horizon then in the quadrant C D taking from C a Circumference equal to EX you shal haue the houre pointed forth but if V fall betwéene the Axis and the Horizon then take in the Quadrant B C from C a Circumference equall to E X and the houre shall be poynted out The obseruation being taken after Noone you must vse the Quadrants E D and E B in like manner A Caution BEcause when the Sunne draweth néere the Meridian you cannot perfectlie discerne whether it bée before Noone or after Noone you must helpe that matter thus Take two Obseruations with some pretie distance betwéene and if the last be greater then the first thou was the first before Noone but if the last be lesser then was the last after Noone The 42. Conclusion In a Countrey of knowne Latitude the Azimute and declination of the Sunne being giuen to find the houre of the day BY the Azimute and declination giuen you may by the 14. Conclusion finde the height thereof that being had by it and the declination you shall by the former conclusion finde the hower The 43. Conclusion In a Countrey of knowne Latitude the height and declination of any Starre being giuen to find the houre of the night LEt the Circumferences E F C G be equall to the declination of the Starre drawe the line F G cutting B A in O let either of the Circumferences L B D T bee the height of the Pole and make the Circumferences L S T H equall to the height giuen on S and H laying a ruler it will cut F G in V in R W A applie from R to W a distance equall to O V and laying a ruler on W and A you shall cut the lymbe in X if the obseruation be taken before the Starre come to the Meridian which you shall know by the caution of the 41. Conclusion then take a Circumference equall to EX on the one or the other side of C according to the falling of the poynt V shewed in the 41. Conclusion and so shall you haue the distance of the Starre from the Meridian or the howre of the Starre which imagine you finde to be poynted out by T from T toward the poynt E take a Circumference TEG equall to the Starres right ascension and from G towards B take a Circumference G M equall to the Suns right ascension a ruler laide on A and M in the howre circle poynteth forth the howre The 44. Conclusion In a Countrey of knowne Latitude the Azimute and declination of any Starre being giuen to know the houre of the night THe Azimute and declination being giuen you may by the fourtéenth Conclusion finde the height then by the height and declination by the former Conclusion you may finde the houre The 45. Conclusion Any day of the yeare in a Countrey of knowne Latitude to finde the beginning continuance and ende of the Crepusculum that is the dawning in the morning and twy-light in the euening LEt B L be the height of the Pole and either of the Circumferences E F C G equall to the declination of the Sunnes place for the day giuen draw the line F G vpon A and L laying a ruler it will cut F G in K and the lymbe on the other side in T from L and T take vnder the Horzon that is towards C and D the Circumferences L Y T Z of eyghtéene degrées apéece vpon Z and Y laying a ruler it will cut F G in 2 in R P A the Synicall arch of F G applie from R to P a distance equall to O K againe from R to 4 applie in R P A a distance equall to O 2 now a ruler layd vpon A and P will cut the lymbe in Q but layd on A and 4 will cut it in 6 the Circumference Q 6 in the houre circle will shew the continuance of the Crepusculum This added to the Sunnes rising which you are taught to know by the 38. Conclusion Cor. sheweth when it beginneth in the morning and added to the time of his setting sheweth when it endeth in the euening I néed not tell that it endeth in the morning with the rising of the Sunne and beginneth in the euening with his going downe The 46. Conclusion In a Countrey of knowne Latitude any day in the yeare at any houre assigned to know the height of the Sunne LEt B L be the height of the Pole and the Circumferences E F C G equall to the Sunnes declination for the day giuen and let E X be the houres distance from sixe on X and A laying a ruler it will cut R P A the Synicall arch of the line G F in W with your compasse take the distance R W and setting one foot in O marke in the line F G a point toward G if in the morning it be before sixe or in the euening after sixe but if it be after sixe in the morning or before sixe in the euening then towards F as here it is supposed in the morning after sixe and therefore let it be V on A and V laying a ruler it will cut the lymbe in 5 make the circumference T 7 equall to L 5 and draw the line 7 A in it take
a line A 3 equal to A V and laying a ruler on V 3 it will cutte the lymbe in S and H either of the circumferences L S or T H are the height desired The 47. Conclusion In a Countrie of known latitude for any day of the yeere to finde in what Azimute the Sunne is in BY the former conclusion you learned how to finde the height for the time assigned in the 13 conclusion was taught by the height and declination giuen in a countrie of knowne latitude to finde the Azimute and so by these two conclusions you may performe that which is here propounded The 48. Conclusion In a countrie of knowne Latitude any day of the yeare at any houre assigned to know how far any determinate point is distant from the Meridian LEt the houre assigned be M and from M by B Eastward take a circumference M B G equall to the Sunnes right ascension for the time giuen againe from G by E take a circumference G E T equall to the right ascension of the point or starre giuen the circumference T D is the distance thereof from the Meridian which you desired The 49. Conclusion In a Countrey of knowne Latitude at any houre assigned any day of the yeere to know the height of any knowne Starre TAke the distance of the point or starre at the time giuen from the Meridian and so consequently from the houre of sixe which let be E X and let E F C G be equall to the starres declination draw the line F G cutting A B in O then vpon A and X laying a ruler it will cut R W A the Synicall arch of F G in W with your compasse take the distance R W and in the lyne F G from O towards G if the distance from the Meridian be more then sixe houres but if lesse then sixe houres as here it is supposed then towards F take V O equall to R W then laying a ruler on A and V it will cutte the lymbe in 5 make the circumference T 7 equall to L 5 and draw the lyne 7 A therein take A 3 equall to the distance A V and laying a ruler on V and B it will cut the lymbe in the points F and G eyther of the circumferences E F C G is equall to the height you desire The 50. Conclusion In a Countrey of knowne Latitude at any houre assigned any day of the yeare to know the Azimute of any knowne Starre BY the former conclusion you knaw how to finde the height for the time assigned and by the height and declination the 13. conclusion will teach you to finde the Azimute as you desire The 51. Conclusion In a Countrie of knowne Latitude to finde the difference Ascensional or the difference of the right and oblique ascension of any poynt of the Eclipticke or any knowne Starre LEt E W be the height of the Pole and let either of the Circumferences W I and W H be equall to the complement of the declination giuen draw the line HI cutting the Horizon E C in Y and the Axis of the world A W in 4 let 6 Z A be the Synicall arch for the line H I and therein from 6 to Z applie a distance equall to 4 Y vpon A and Z laying a ruler it will cut the lymbe in 5 the circumference E 5 is the difference Ascensionall which you require The 52. Conclusion In a Countrey of knowne Latitude to finde the oblique ascension of any poynt of the Eclipticke or any knowne Starre LEt the right ascension of the poynt taken by the 20. Conclusion be the Circumference E B G accounted from E the beginning of Aries and the difference ascensionall of the poynt whose line of declination is H I let be E 5 now if H I be betwéene the apparant Pole and the Equinoctiall take from G towards E a Circumference G 1 equall to E 5 and E B 1 shall be the oblique ascension but if H I be betwéene the Equinoctiall and the hidden Pole then from G towards C take the Circumference G 3 equall to E 5 and then shall E G 3 be the oblique ascension sought for A Corollary IF you adde a semicircle to the oblique Ascension found that is if you lay a ruler on 1 or 3 and A it will in the opposite quadrant E D poynt out the oblique descension of the poynt that is opposite to the poynt whose oblique Ascension you looke Another Corollary YOu may also finde the oblique descension of any point by this Conclusion if you adde when here you are appoynted to subtract and subtract when you are appoynted to adde The 53. Conclusion The oblique Ascension of any poynt of the Eclipticke or any knowne Starre being giuen to finde the Latitude LEt W be the Pole of the world W I and W H the complements of the poynts declination draw the line H I cutting A W the Axis of the world in 4 and let the difference Ascensionall which you may knowe by comparing of the right and oblique Ascensions be E 5 a ruler layde on the Center A and 5 will cut 6 Z A the Synicall arche of the line H I in Z in the line H 4 take Y 4 equall to the distance 6 Z then laying a ruler vpon A and Y it will cut the lymbe in E the Circumference E W is the height of the Pole or the Latitude sought for The 54. Conclusion In a Countrey of known Latitude any day assigned to knowe what poynt of the Eclipticke is in the Meridian in the morning TAke the oblique ascension for that poynt of the Eclipticke wherein the Sunne is that day which is assigned as for example the poynt V then opening your Compasse to the distance B C set one foote in V and with the other from the West towards the East or according to the succession of the degrées or times of the Equinoctiall marke in the lymbe T that poynt is the poynt of the Equinoctiall which is in the Meridian now if by the 22. Conclusion you take the poynt answerable to that right ascension in the Eclipticke it shall be the same that is in the Meridian The 55. Conclusion In a Countrey of knowne Latitude any day of the yeere at any houre assigned to finde what poynt of the Eclipticke is in the Meridian LEt the right ascension answering the degrée of the Eclipticke which serueth the day giuen be E B V accounted from E the beginning of Aries now take the houre distance of the Sunne from the Meridian which let be B W if the Sunne be not yet come to the Meridian from V towards C or from West towards East according to the succession of the degrées of the Equinoctiall take a Circumference V 7 equall to B W 7 sheweth the poynt of the Equinoctiall that is in the Meridian the place of the Zodiacke answerable to the right ascension is also in the Meridian with it But if the Sunne be past the Meridian you
my fingers Scorpio falleth on my little finger so I say that the Sunne entreth Scorpio in October then taking the verses and setting the words one by one in like manner on my fingers I finde in the second going ouer Faustos on my little finger now telling in the crosse row the letters from A to F I finde sixe this sixe I subtract from 20. so rest 14. which the day of October the Sunne entreth Scorpio Parergon secundum To know the Sunnes place in the Zodiacke vpon any day giuen FInde the Signe answering your moneth and the word likewise then to the day of the moneth put ten and the number the first letter sheweth in the crosse row if this be lesse then 30. the number is the degrée of the Signe next before that which the Sunne entreth in your moneth if more cast away 30. and the residue is the degrée of the Signe entred in your moneth Example I would know where the Sunne is the 9. of October I finde in October he entreth Scorpio and the word for it to be Faustos whose first letter F is the sixt in the crosse row I take ten and 6. vz. 16. which I put to 9. there is made 25. therefore I say the Sun is in the 25. degree of the Signe before Scorpio which is Libra If I would know for the 18. day putting 16. to 18. there would amount 34. from which abating 30. the 4. remaining sheweth me that the Sunne is in the 4. degrée of the Signe belonging to October which is Scorpio Parergon tertium The place of the Sunne being giuen to finde the day of the moneth TAke the day and moneth the Sun entreth the Signe giuen the number of the degrées giuen put to the day wherein the Sunne entreth the Signe that product being lesse than the dayes in your moneth shew the day but being more cast away the dayes of your moneth the residue is the day of the moneth following Example I finde the Sunne in the 4. degrée of Scorpio I would know what day of the moneth it is I finde that the Sunne entreth Scorpio the 14. of October I put 4. to 14. there amounteth 18. so I say it is the 18. day of October Againe let it be in the 25. of Libra I finde that the Sunne entreth Libra 13. Septembris I put 13. to 25. there amounteth 38. from which I take 30. the dayes of September and there remaineth 8. the day of October These are but gesses as you may see much after the way commonly taught by the backe of the Astrolabe Let him that desireth exactnes seeke the Sunnes place in some Ephemerides or in the Regiment of the Sunne published by E. W. painfully calculated vpon his owne diligent and exact obseruations The end of the first Section THE SECOND SECTION OF THE NEW HANDLING THE PLANISPHERE SHEWING HOW THE CONclusions of the Astrolabe may readily and exactly for any Countrie be performed onely with Ruler and Compasses ALthough for working the conclusions following any circle diuided or to transferre out of any diuided quadrant the giuen circumferences would be sufficient yet for the easier dispatch I would a plate of Latten to be prouided according to the figure which you sée on the other side There vpon one center A be sixe circles described one within another of which the two outtermost cōtaineth the narrowest space which must be diuided into 360. equall parts or degrées as the common manner is At euery 30. degrées in the space contained vnder the second and third circles make diuisious and beginning at E write Ari or Aries at the next Tau or Taurus and so for the rest of the 12. Signes this circle shall be called the Zodiacke The third space contained vnder the third and fourth circle must bee diuided at euery 15. degrées beginning at B you must set downe 12. at the next diuision toward C set downe 1. at the next 2. and at euery diuision the numbers in order till comming to D you are to set downe 12. againe and so in the other semicircle DEB set 1. at the diuision next D at the second 2. till comming to the next before B you are to set downe 11 this fourth circle shall be called the houre circle The fourth space contained vnder the fourth and fift circle must be diuided at euery 10. degrées at the first diuision from E towards B set 10. at the second 20. and so encreasing continually at euery diuision by 10. till you come againe to E where you are to set downe 360. this circle shall be named the Equinoctiall The space contained vnder this and the sixt or innermost circle must from E by D vnto C haue diuisions at euery 20. degrées and at euery diuision a number set encreasing by 10. til you come to 90 in the quarters B C B E you must make diuisions at euery 10. degrees at the first from B towards E set 10 and likewise at the next vnto C towards B at the next 20. and so in order till comming to E and B you are there to set 90 this inner circle shall be called the limbe If you will set two sights on the outter edge so that the line drawne from lope to lope be parallel to the line subtending the arch B C and hang a plummet from B you may by your plate begin The first Conclusion To take the height of the Sunne or any Starre aboue the Horizon TVrning your plate towards the Sunne lift it vp and downe till his beames shine through both the lopes of your sights or if it be a Starre till you see it through them the thréed sheweth in the semicircle E D C how many degrées the Sunne or Starre is aboue the Horizon The second Conclusion To finde the distance of the Sunnes or any Starres Azimute from any determinate poynt in the Horizon LEt your plate be fixed leuell with the Horizon and direct E to any poynt then a ruler being turned and lift vp by a stéele or wier standing plumbe vpright from the center A till you see the starre by the edge of it or rather through two sights set vpon the edge or if it be the Sun till his beames passe through the lopes then without stirring the end next your eye bring it close to the center the edge sheweth in the Equinoctiall the distance of the Azimute from the poynt respected by E. The Azimute is sayd simply without adition to bee giuen when his distance from the Meridians North end is giuen The third Conclusion From a point giuen in the circumference of a circle at any side assigned to applie or subtend a distance or a right line not greater than the Diameter LEt the poynt giuen be C from which vpon the side towards D I am to applie a line equall to A Q draw the Diameter C A E now if the line A Q be equall to the Diameter I haue done that which is required but being lesse I take the
must take a Circumference equall to B W contrarie to the succession of the Equinoctials degrées as from V the Circumference B V and then the poynt of the Eclipticke which answereth the right Ascension B shall be in the Meridian and the same is to be vnderstoode of the opposite poynts The 56. Conclusion In a Countrey of knowne Latitude any day of the yeere to know what time any poynt of the Eclipticke or any knowne Starre riseth or setteth TAke the oblique Ascension of the poynt which let be E B G and the right Ascension answering the poynt wherein the Sunne is the day giuen which let be E B T from the houre of the Sunnes rising according to the succession of the houre circle take a Circumference equall to G T and it shall poynt out the houre when the Starre commeth to the Horizon The 57. Conclusion In a Countrey of knowne Latitude to know with what poynt of the Eclipticke any knowne Starre commeth to the Meridian TAke the right ascension of the Starre and then the poynt of the Zodiacke that is answerable thereunto and that shall be the poynt wherewith the Starre commeth to the Meridian The 58. Conclusion The oblique ascension being giuen to know the situation of the Equinoctiall sections in respect of the Meridian LEt the oblique ascension giuen be E B 1 with your compasse take the distance B C and setting one foote in 1 with the other marke a poynt L which is the poynt of the Equinoctiall in the Meridian now for as much as E is beyond the Meridian it is in the West quarter aboue the Horizon if it had fallen betwéene L and 1 it should haue béen in the East the opposite section is alwaies in the opposite Quadrant The 59. Conclusion In a Countrey of known Latitude to know the Horizontall angle made by the Section of the Horizon and Eclipticke in any poynt giuen TAke the oblique Ascension of the poynt giuen and by it finde the situation of the Equinoctiall section Now if the Section be on the East side of the Meridian take the complements of the oblique ascension and the poynt giuen as Latitudes the Sunnes greatest declination is the difference of their Longitudes and by the 30. Conclusion séeke the Horizontall angle as the bearing of the oblique ascension from the poynt of the Eclipticke that is in the Horizon and so haue you the Horizontall angle but if the Equinoctiall Section be on the West side you must take the complements to the opposite poynts of the Eclipticke and oblique ascension and with them worke by the Conclusion as is aforesaide To the Reader THere remaineth for perfecting this Section almost 20. Conclusions more wherof many depend vpō this probleme viz. In a Countrey of knowne Latitude any oblique Ascension being giuen to finde the poynt of the Eclipticke Coascending which yet I haue not found how to perfourme generally otherwise then by taking such helpe of an Eleipsis as is vsed in the fouretéenth Conclusion in which manner of working the construction will very often exceede the compasse of the lymbe for which and some other causes I omitte it and the rest at this present Notwithstanding if I perceiue hereafter that those matters be much desired they shall be adioyned at the next impression the meane while I must intreate the reader to take thus much in good part The end of the second Section THE THIRD SECTION OF THE NEW HANDLING OF THE PLANISPHERE WHICH IS A SVPPLEMENT Organicall CHAP. 1. To make a Quadrant whereby you may readisie know what Degrees and Minutes are contained in any Circumference giuen VPon the Center A describe a quadrant A B C whose lymbe you must diuide as the common manner is into 90. equall parts or degrées euery degrée into halfes in the lymbe take the quantitie of 30. degrées which let be C D and drawe the line A D. In either of the lines A D or A C take some reasonable distance from the lymbe as A E or A F and vpon the Center A at that distance describe the Circumference F E then inlarging your compasse a little describe another Circumference as you sée at F and E againe opening your compasse somewhat larger describe another Circumference G H then extending or contracting the distance of your compasse describe a Circumference néere it as you sée at G H. In like manner describe two other Circumferences somewhat néere together and distant from G H as you sée at I K and so make betwéene E C F D 30 such lists as you sée at F E G H and I K. Then take an arch of 59 degrées which you must diuide into 60 equall parts the sixtie part of which diuision will diuide two degrées into two vnequall parts take the two degrées next D and from that poynt towards D take a Circumference equall to the greater segment you made by diuiding 59 degrées in 60 parts and vpon that poynt and the Center A laying a ruler where it cutteth the lyst next the lymbe as that beneath L M is drawe a line diuiding the lyst beneath L M and from that deuision applie so many degrées in order as the circumference will admit till you come so neare 1 as you can Then take 58 degrées and deuide that circumference into 60 equall parts the sixtie part of this deuision falling betwéene two degrées deuideth them into two vnequall parts againe taking 2 degrées next D from that point towards D take the greatest portion and laying a ruler on that point and A where it cutteth the second lyst from the limbe draw a line cutting that lyst and from that deuision marke so manie degrées in that lyst as the residue of the circumference will receiue then deuide 57 degrées for the third lyst 56 for the fourth lyst and so the degrées in order till you come to thirtie degrées and the thirtieth list although if the limbe be deuided into halfe degrées the thirtieth lyst the deuision of thirtie degrées is néedles Hauing thus deuided 30 lystes in the space without the quadrant to the side A C draw two parallell lines including two spaces extend one circumference of euery fift lyst to the vttermost parallell in the space next the side of the quadrant A C at the lyst next the limbe set one or 1. at the next circumference extended from the fift lyst set fiue or 5 in the same space vnder that which is extended from the tenth set 10 and so increasing by 5 to thirty then descending in the second space at the fift list set 35 at the tenth 40 and so in order by 5 to 60 then may you thus vse the quadrant To finde what degrees and minutes are contained in any circumference giuen VPon the center A describe in the quadrant A B C an arch N P O hauing A N the semidiameter equall to the semidiameter of the circumference giuen take from it so manie degrées that you haue a remainder lesse then