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
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
which cutteth I P in 2 the line G 2 in the Meridian answereth the point Z or is the 45 degrée Now hauing marked these sections for euerie degrée in the quadrant transfer them one after another into your ruler or the side of your quadrant that is at one end of your quadrant take a line equall to that which answereth one degrée adde to it that which answereth the second to that put that which answereth the third and so till you come to the end of that line which not being able to receiue all draw another line and prosecute the like construction in that and so in the third and forth till you haue transferred all the lines answering your degrées If in this transferring your deuisions agrée not iust with the ends of your lines you must take onelie the ouerplus of the last deuision in the beginning of the next line and so procéed as is aforesaid Now hauing your lines thus deuided and another deuided to the same parts that the side of your quadrant is being parallell to them all perpendicular to one right line you may readilie know what equall partes are contained betwéene any two of your degrées taken howsoeuer whereby you may performe all the vses of Mercators Directorium Thus for example The Longitudes and Latitudes of any two places being giuen to finde their direction commonlie called the Rumbe TAke the equall parts contained as well in the difference of the latitudes as in the diffrence of their longitudes and see whether both be lesse then the side of your quadrant or no first suppose they be lesse and let the geater be X G the lesser G M draw the line X M deuide G X into two equall parts in V then opening your Compasse to the distance V G and kéeping one foote in V with the other marke T in M X on T and G laying a ruler it will cut the limbe in 4. Now if the difference of the Latitudes be lesse then the difference of the longitudes 4 Y is the distance of the rumbe from the Meridian but if the difference of the longitudes be lesse then is 4 P the distance of the rumbe from the Meridian But now suppose that one or both the differences be greater then the side of your quadrant then by the rule of proportions you must finde a line vnto which the lesser is as the greater is to the side of the quadrant or make the side of the quadrant to another line as the greater is to the lesser namelie let G Y be vnto G Q as the greater difference is to the lesse and draw the line Q Y deuide G Y into two equall partes in W then opening your Compasse to the distance W G and kéeping one foote in W in Y Q marke R a ruler laid on G and R will cut the limbe in 3 now as before if the difference of the longitudes be the greater then is H 3 the distance of the rumbe from the Meridian South if the place respected be South North if it be North and so likewise East or West CHAP. 5. Of the backe of your plate To inscribe in the backe of your plate the fixed stars according to their Longitudes and Latitudes or declinations and right ascensions as you please LEt the vtter edge of the backe side of your plate be deuided into 360 degrées which you may vse for the Zodiacke or the Equinoctiall the Zodiacke if you inscribe the Starres according to their Longitudes and Latitudes or the Equinoctiall if you will place them according to their declinations and right asceÌ„sions which is the best for those are oftnest in vse both are done after one manner thus From the beginning of Aries reckon the right ascension as from E by B vnto T and draw the line A T then from B to V reckon the declination B V laying a ruler on V and A it will cut the Synicall arch of the limbe A S C in S in the lyne A T take A Q equall to the distance A S and the point Q is the place of the starre according to his right ascension and declination this being done set downe by it the name and S or N to signifie whether it decline North or South This may be done so sleightlie that you may rub it out when you will with a wet pumice and yet déepe enough to continue a great while for your vse To finde the longitude and latitude or the declination and right ascension of such stars as bee placed on the back of the plate VPon the center of the plate and the point of the star lay a ruler where it cutteth the limbe is the right ascension reckoned from the vernall Section or the longitude if they be placed for the Zodiacke As for example Place this figure in steade of the figure in folio 35. lay a ruler on A and Q it will cut the limbe in T the circumference E B T is the right ascension of Q. Now if in A S C the Synicall arch of the limbe you applie from A to S a distance equall to A Q and lay a ruler on A and S it will cut the limbe in V the circumference B V is the declination of the starre placed at Q or the latitude if they were placed according to the longitudes latitudes by the letter S or N you shall know whether it bee North or south And that you may be furnished for these two last problemes I haue set downe on the other side a table out of Clauius contayning certaine fixed starres both with their longitudes and latitudes and their declinations and right ascensions calculated for this yeare 1600. And thus much at this time for the Planisphere which hereafter I meane to increase with more conclusions problemes and could haue now enlarged it with handling mensurations Synicall calculations and dialling but those thinges séemed somewhat farre from my principall purpose and therefore I will intreate the reader to accept thus much onely as now is deliuered and so for this time I end The end of the new handling of the Planisphere A Table of fixed Starres out of Claâ—â—ius calculated for the yeere 1600. compleat Bignes Names Place in the Zodiacke or Longitude Their Latitude The part The declination The part The righâ— Ascension 3 The Rams former horne Aries 28 5 7 20 N 17 39 N 23 20  Medusaes head Taur 21 5 23 0 N 40 5 N 40 55  Bulles eye Gem. 4 5 5 10 S 15 56 N 63 6  Orions right shoulder Gem. 23 25 17 0 S 6 21 N 83 41  The Goate Gem. 16 25 22 30 N 45 9 N 72 6  The great dogge Can. 9 5 39 10 S 15 â—4 S 97 19  Hydraes bright Starre Leo. 21 25 20 30 S 5 4 S 137 19  Lions hart Leo. 23 50 0 10 N 13 44 N 146 19  Lions tayle Virg. 15 55 11 50 N 16 26 N 171 49  The Virgins spike Lib. 18 5 2 0 S 8 58 S 195 55  Arcturus Lib. 18 25 31 30 N 21 49 N 209 23  Scorpions heart Scor. 4 5 4 0 S 24 57 S 241 16  Harpe Cap. 8 45 62 0 N 38 40 N 275 15  Last in Aquarius water Aqu 28 25 23 0 S 33 24 S 339 56  Swannes tayle Pisc 0 35 60 0 N 44 8 N 307 22  Pegasus legge Pisc 23 35 31 0 N 25 44 N 341 0 Errata Page 3. line vlt. Analemma p. 6. l. 6. Maurolycus p. 10. l. 9. Frisius p. 13. l. vlt. Motus raptus p. 14. l. 33. Zenith appearing p. 16. l. 33. from the Zenith which p. 17. l. 2.5.7 for Z make L. p. 22. l. 1. blot out pan and l. 11. N L. p. 23. l 13.25 for Z make L. ibid. l 20 Tropickes p. 24. l. 26. there makâ—th angles p. 25. l. 12. and by two of those p. 26. l. 9. setting Ianuarie p. 32 l. 26.27 for Q make 7. p. 33. l. 10. for 3 3 make 8 8. ibid. l. 13. for G make E. p. 34 l. 4.5 for T make V. l. 13 for F make E. l. 27. which let be C 1 1 l and l K. l. 8 29. for B make P. p. 26 l. 2.7 for B make P. l. 5. for 12. make 2. l 8. for 2. and D make P. p. 38. l. 18. and H l cutting p. 40. l. 23. for K make B. in the figure of the 39. page place 3. on the other side of D.
many exquisite arguments which I meane not to prosecute but hoping from the testimonie of sense in such manner to deduce the positions that any meane capacitie may haue so reasonable a conceit of them that with probabilitie they may easily be admitted I will referre their exact and more subtile demonstration with the reproofe of such as impugne them to some others handling or to some other place Therefore requiring first the reader not to cast vntimely doubts nor hastily to iudge of any part by it selfe before he hath considered and in some manner vnderstood the whole discourse I will according to Hippocrates his counsell begin with the notablest and easiest things Whosoeuer doth but cast vp his eyes vnto heauen presently perceiueth that it compasseth him round about in manner of halfe a globe or an Hemisphere and if he stand vpon some high place or be at Sea farre from land where nothing can be séene but water and the Skie his eye if he turne himselfe about will represent vnto him at the lowest bounds or limits which he seeth the fashion of a circle vpon whose plaine as vpon a base this visible Hemisphere seemeth to be placed therefore that Circle was first in Gréeke and is now commonly in English called the Horizon that is to say bounding or limiting vz. the compasse of your sight The largenes of this Circle euen as it falleth vnder view is of so great a compasse as you neede not restraine the center thereof according to the precise Mathematicall definition to one determinate exquisite indiuisible and very poynt or pricke but without sensible error as your eye will plainly testifie any one at pleasure may bee taken in the place where you stand From a center so taken if there be or be imagined a plumbe line or line perpendicular to the plaine of the Horizon extended vnto the heauen the place which there it toucheth is commonly called by an Arabian name the Zenith being in truth the pole of the Horizon and the line it selfe his Axis By this Axis and any lines crossing it if plainnes be euery way extēded reaching vnto heauen they marke out their circumferences or semicircles cutting one another in the Zenith but in the Horizon their sections are right lines cutting one another in his center Those circles are named Azimutes and are imagined by Astronomers to be cut by other circles parallel to the Horizon which they terme Alinicantars and circles of Altitude because the portion of the Azimute which is betwéene the Horizon and the Parallel sheweth how his aboue the Horizon that poynt of the Parallel is by which the Azimute passeth Furthermore in a cléere night beholding the bright shining Starres you shall euidently perceiue how they change their places continually some to rise and shew themselues other to goe downe vnder the Horizon and to be hidden from your sight onely if you place your selfe so that your right hand be towards their rising and your left hand toward their going downe looking right foorth and somewhat vpward you shall behold certen Starres which are all times of the night to bée seene and neuer Charles Wayne pole star Little Beare go down amōgst some of which placed after this fashion there is one commonly called the Pole star which being the last in the tayle of the constellation called the little Beare lyeth in māner directly as it were in a right line with those two in the hindermost whéeles of Charles his wayne This Starre seemeth little or nothing to remoue out of his place and indeede not farre from it there is a poynt or pricke which remaineth in one and the same place alwaies immoueable The Azimute passing by the Horizons Axis and a right line drawne frō this immoueable point or the pole starre is properly called the Meridian circle the common section of it and the Horizon being a right line is the Meridian line or the line of North and South the right line which crosseth this Meridian line at right angles in the center of the Horizon is called the line of true East and true West or simply the line of East and West which poynts the ends thereof extended directly fall vpon The Arimute standing vpon this line Ioannes de Roias others specially such as write of Dyalling as it were for dignitie and preheminence doe call the Verticall circle which name being common to all Azimutes because they passe by the Zenith in Latin called Vertex or punctum eregione verticis for a distinction Gemma Frosius hath named it the Circle of the East The other Azimutes haue no proper names but are measured or determined in the Horizons circumference That and so likewise all other Circles Astronomers doe imagine to be diuided into 360. equall parts which they name degrées that is to say euerie quarter or quadrant into 90. degrees euery degrée they further diuide into 60. minutes euery minute into 60. seconds euery second into 60. thirds and so continue sometimes vnto tenths and may goe further if they will By these degrees minutes c. which are betwéene that point where any Azimute cutteth the Horizon and the Meridian line or the line of East and West the Azimute is determined assigned or said to be giuen Vpon the points where the Verticall circle cutteth the Horizon which poynts are the true poles of the Meridian and the precise East and West if by often and diligent viewing you shall see two Starres the one in the East and the other at the same time right against it in the West in winter time euen in one night you may behold that which is in the East first ascending and then againe descending at length to come into the West and that which was in the West being till that time hidden from your sight then to appeare againe rising in the East all this while continually the like shape of an Hemisphere being still represented to your eye without any chaunge or alteration whereby you may gather the heauen to bee a perfect Globe or Sphere hauing that part vnder the Horizon equall and like to that which you sée aboue it and that the place where you stand is the very center thereof A line drawne from the pole Starre or rather from the poynt immoueable before mentioned called the Articke or North pole a line I say drawne or imagined to be drawne from that poynt to the place of your standing is called the Aris of the world and extended to the other side of the celestiall Sphere which is vnder vs falleth there vpon the South or Antarcticke pole which in these our countries neuer appeareth These things being but a little héedily considered be so manifest and apparant that neither example nor figure is greatly requisite for the perfect vnderstanding of them yet in this beginning to remoue all difficultie and to make euery thing as plaine as may be doe thus much In some plaine ground or rather vpon a poste or stone or some such like thing made
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
making his section with the quadrant in the line G F and also perpendicular vnto the plaine of the quadrant you may by a plumbe line hanged vpon this plate or standard and the other plumbe line holde the quadrant G F H both at Sea and Land preciselie leuell with the Horizon Besides this you must make a round boxe hauing the circle in the bottome diuided into 360 degrées or euery quadrant into 90 as you like best which boxe must be fastened vnto the quadrant in such manner as the two Diameters crossing one another at right angles haue the one one end directly answering the poynt L the other another end likewise precisely answering the point M in the center of this bore you must set a pinne to beare a néedle touched with a very good Loadstone making the néedle of such length as it may fréely play in the boxe this bore must be couered with a glasse to kéepe it from dust and other hurt as in dials and compasses is vsed The standards and the triangle may be so shouldered to the quadrant that you may take them off and put them on when you will the manner how I néed not to stand vpon euery workeman can easily deuise how and also supplie euery particular circumstance in the making of this instrument required which I very willinglie referre to their handines and skill onely I must warne them very carefullie to place the triangle precisely perpendicular to the quadrant with the poynt of the acute angle agréeing with the center and that the endes of the Diameters in the bottome of the boxe doe very exactly respect the poynts L and M in the sides of the quadrant you shall vse this instrument thus Holde the quadrant by the plumbe lines leuell with the Horizon and turne the triangle towards the Sunne till the shadowe of the plate or Standard that is next G doe fall precisely vpon the line G F or if you will place it so vpon some line parallell vnto it the shadowe in the lymbe of the quadrant will cut off accounting from F vnto it a circumference equall to the height of the Sunne At the same time if you marke the poynt M and the circumference that is betwéene it and the South ende of the néedle that is the distance of the Sunne from the South of the Magnet or the Magneticall Azimute of the Sunne reckoned from the South By the instrument now described at noone tyde in any Countrey to finde the Meridian line the variation of the Compasse and hauing the Sunnes declination giuen the height of the Pole ALthough it be a matter not very easie to finde precisely when it is noone or the Sunne at the hyest yet may you gesse when it commeth somwhat néere it as it is commonly practised by Sea-men which vse at that time with their Astrolabe or crosse staffe to make foure or fiue sundry obseruations and amongst them take the hiest for the Meridian height in like manner when it draweth to be about nooue make sundrie obseruations with this instrument marking the height of the Sunne and his Magneticall Azimute as was euen now shewed in the vse of the instrument the greatest height is the Meridian height and the Diameter A M doth precisely answere the Meridian line the circumference intercepted betwéene it and the south poynt of the néedle is the variation of the compasse whether East of West is easilie determined by the side of A M on which the néedle resteth Now the Meridian height being giuen with the declination you haue been taught in the tenth Conclusion of the second Section how to finde the Latitude or height of the Pole The common manner of finding it by adding or subtracting of the declination is more artificiallie handled by Nonnius lib. 2. cap. 9. de Reg. Nauig then hath to my knowledge béen hitherto published in English and therfore I thinke it not amisse to translate his words which be thus We must obserue the sunne when he is highest aboue the Horizon which is at noone then if the shadowes of bodies perpendicular to the Horizon be cast that away that the Sunne declineth in the day of your obseruation you must adde the complement of his greatest height to the declination so haue you the degrées and minutes of the latitude North if the Sunnes declination be North South if it be South But if the shadowes be cast to the contrarie part then you must compare the Sunnes declination with the complement of his height which if you finde equall the Zenith is in the Equinoctiall but if they be vnequall subtract the lesse from the greater the remainder is the latitude named of the declination if the declination be greater but if lesse of the contrarie part or side When the sunne hath no declination the complement of his greatest height is the latitude and toward that part or pole towards which the shadowes are cast you may know by the Mariners Compasse whether the shadowes be cast North or South When the Sunne is in the Zenith the declination if it haue any is the latitude thus much Nonnius By the same instrument two obseruations being taken when the Sun hath equall altitudes to finde the Meridian line the variation of the compasse and the Sunnes declination beeing giuen the height of the Pole THe Sunne doth not alwaies shine at noone therefore at other times you may helpe your selfe thus Make an obseruation with your instrument marking the height of the Sunne and the circumference intercepted by the point of the néedle and that diameter which is perpendicular to that side of the quadrant on which the triangle standeth and doe this if you will foure or fiue times before noone in the after noone marke when the Sun commeth againe to the same height which it had anie time when you made your obseruations in the forenoone and againe how many degrées are betwéene the Diameter that is perpendicular to the side of the Triangle and the North point of the néedle then compare that found in the fore noone with that you found in the afternoone if they be both on the same side of the néedle subtract the lesse frō the greater and the halfe of the residue pointeth forth the right North to which if you adde the excesse of the greater magneticall Azimute aboue the lesse you haue the variation of the Compasse Eastward if the first obseruation were lest Westward if the second But if the one be on the one side and the other on the other then adde both the circumferences together of them both take the half that point determineth the precise north with this halfe compare the last obseruation and if it be greater the variation is Eastward but Westward if it be lesse Now the Meridian line being found you know the Azimute wherein the Sunne was at the time of your obseruation and you also tooke his height which two being giuen with his declination you may finde the latitude as was