Projection The Concurrent Circles meeting in the Poles A and B are Meridians Those Meridians are 180 in number and divide the Equator C D into 360. degrees because every one of them cutteth it twice that is once in each Hemisphear By these are numbred the Right Ascensions of the Stars and Planets and the hours and minutes of Day and Night for every 15 of these Meridians numbred from the Limb is an hour Circle as hath been shewed Book 1.6 they are numbred from D to C that is from Septentrio to Meridies 1.2.3 c. for the Morning hours and back again from C to D in like manner for the Afternoon the Axeltree line A B falling out to be the six a clock line both ways By those Meridians also are numbred the Longitudes of Towns and Countries in Geography The Circles or Semicircles crossing these Meridians are the Parallels of Declination they are lesser Circles whose propertie it is to divide the Sphear into unequal parts In the midst of them lies the Equator C D being here a straight line and cutting the Axtree-line A B at Right Angles in the Center E the Parallels are greatest near the Equator and from thence they lessen toward the Poles they are 180 in number i. e. 90 on each side the Equator save that the two extream Parallels are reduced to two points in the Poles By these Parallels are numbred the Declinations of the Stars in Astronomie and the Latitudes of Towns and Countries in Geography And this name and use have the Circles of the Mater always in the Meridional Projection The Ecliptick always standeth for it self when it is used which is onely in the first Mode of this Projection But the Circles of the Reet have divers names and uses in the divers Modes of this Projection which here follow 1 The first mode of the Meridional Projection The point A of the Reet in which the Concurrent Arches meet is called the Vertex of the Reet Set the Vertex of the Reet to the Latitude of your place so shall the Vertex be Zenith and the Concurrent Arches there meeting shall be Azimuths called also Vertical Circles and Circles of Position passing from Zenith to Nadir and dividing the Horizon into 360 degr as the Meridians on the Mater pass from Pole to Pole and divide the Equinoctial The Semicircles crossing these Azimuths shall be Almicanters or Circles of Altitude The Diameter crossing the Axeltree of the Reet at Right Angles shall be the Horizon or Finiter whose Graduations are set to him in a border below the Center and from him are the Almicanters reckoned upward to the Zenith The Azimuths may be reckoned from the North or South Semicircles of the Meridian or from the Axtree line of the Reet which is the East or West Azimuth commonly called the Prime Vertical When I bid you set the Vertex of the Reet to the Latitude of your place you must first know what your Latitude is It is the nearest distance of your place from the Terrestrial Equinoctial numbred in degrees and minutes of a great Circle The Latitude of London is 31 degr 32 min. North. The Latitude of Ecton or Northampton is 52 degr 15 minutes or very near And how to get the Latitude of those or any other place shall be shewed Book 4.11 The Latitude had number the degrees thereof upon the Ring from C or Meridies where the Equator cutteth the Meridian toward A or Oriens which in this Projection is the North Pole because we in England have North Latitude At the end of this number see for London 51. degrees 32. minutes from the Equator Northward set the Vertex of the Reet so this Vertex representeth the Zenith or point in the Heaven which is just over your head in which point all the Azimuths meet and through which also passeth the Meridian of your place which here is represented by the outmost Circle of the Mater or the innermost Circle of the Ring Now is the upper Semicircle of your Meridian divided into four notable parts From the Zenith Southward to the Equator is the Latitude 51. degrees 32 minutes from thence to the Horizon is the complement of the Latitude 38. degrees 28. minutes making up a Quadrant againe from the Zenith Northerly to the Pole is the complement of Latitude 38. degr 28. minutes as before and from thence to the North of the Horizon is the Elevation of the Pole above your Horizon which is always equall to the Latitude of your place for where in a right Sphear the Polesly in the Horizon and have on Elevation there the Equator passeth through the Zenith and if you go from such a Country Northward till the Pole be Elevated one degree the Equator shall there decline from your Zenith one degree Southward because the Equator keeps always the distance of 90 degrees from the Poles And this distance of the Zenith of your place from the Equator is called by Geographers Latitude and is always equal to the Elevation of your Pole So that it is all one whether you set the Vertex 51. degrees 32. min. above the Equator or set the North point of the Horizon 51. degrees 32. minutes below the North Pole Now the Vertex of the Reet set to the Latitude and consequently the Pole mounted to his due Elevation your Planisphear is in a right mode and posture speedily to resolve all questions concerning the Diurnall motion as the Suns longitude Declination Right Ascension the Ascensionall differences with the Semidiurnall Arch or length of the day the Suns Altitude Azimuth and Amplitude the hour and minute of the day the beginnings endings and duration of twilight and such like and that with so great facility that having onely the Longitude of the Sun with the Ephemeris on the Ring shall give you for asking and therewith either the Altitude Azimuth or Houre one of them you may see all the rest at the first view without changing the posture of your Instrument as shall appear in the fourth book 2 The second Mode of the Meridional Projection Set the Zenith or Vertex of the Reet to the North Pole of the Ecliptick or which is all one set the Horizon line of the Reet in the Ecliptick line of the Mater so the Azimuth shall in this posture become Circles of Longitude and the Almicanters Circles of Latitude And in this Mode your Planisphear is fitted to resolve all Questions of the Longitude Latitude Right Ascension and Declination of the Stars 3 The third Mode of the Meridional Projection Number the Altitude of Culmen Caeli that is the Southing point of the Ecliptick in the Ring from the North Pole toward Meridies if the Ascendant be a North Signe or toward Septentrio if the Ascendant be a South Signe To the end of this numeration palce the Finiter Reckon also upon the Finiter from the Center toward Septentrie the Amplitude of the Ascendant the Meridian cutting there gives you
Reclining Declining Dyal another way HAving found the arches and angles requisite by Chapter 16. and platted down your Horizontal and Vertical lines and placed the Noon line above oâ— below the Horizontal line according as the arch of his Oblique Ascension or Descension requireth and having placed also the Sub-style in his due situation as is above taught you may easily find the distances of the several Hours from the Sub-style as you found them in the former Chapter for the Declining Horizontal Dyal For when you have set the Finitor to the Latitude of your plain as there you did the Limb is Sub-stylar and if you number thence in the Finitor the Declination of the Gnomon there shall meet you the Meridian of the Place Here you shall begin and take every 15th Meridian forwards and backwards for an Hour line and observing how many degrees are in the Finitor between the Limb and every one of these Hour lines so many degrees shall you place that Hour line from the Sub-style in the plain If you understand the former Chapter this will need no Example CHAP. XXIII To draw the proper Hours of any Declining Dyal EVery Declining plain whether it Recline or not hath two great Meridians much spoken of 1. The Meridian of the plain which is the proper Meridian of that Country to whose Horizon the plain heth Parallel 2. The Meridian of the Place which is the Meridian of your Country in which you set up this Declining plain to shew the Hours and so either of these Meridians Dyals may be conformed How to draw the Hours of our Country on such a plain is the harder work because the plain is Irregular to our Horiz on yet I suppose I have made the way very easy in the former Chapters But to draw the Hours of the Country to which the plain belongs is most easy For if you take the Sub-stylar for the Noon-line and the Elevation of the Pole above the plain for the Latitude you may make this Dyal in all points like the Vertical Dyal after the precept of the 9th Chapter CHAP. XXIV To know in what Country any Declining Dyal shall serve for a Vertical Dyal IF the Dyal Decline East add the difference of Longitude found as above Chapter 21. to the Longitude of your Place and the sum or the excess above 360 is the number of the Longitude sought If the Dyal Decline West subtract the said difference of Longitude out of the Longitude of your Place and the difference is the Longitude inquired but when the Longitude of your Place happens to be less then the difference of Longitude you must add to it 360. before you subtract the difference of Longitude The Elevation of the Pole above the plain is the Latitude of the Place inquired Example The Declining plain of Chapter 12. will be a Vertical plain in the Longitude 61. degrees and North Latitude 32. degrees that is in the Mediterranean Sea between Alexandria and the Isle of Creet And the Declining Reclining plain of Chapter 16 17 18. is Parallel to the Horizon of those that sail in Longitude 359. degrees and North Latitude 29. degrees that is as Terrestrial Globes and Mapps shew me between the Azores and Hesperides CHAP. XXV To set a Plain Parallel to the Horizon of any Country proposed IF you can get the Declination and Reclination of such a plain you have enough to place him in his true Situation And those may be found by the difference of Longitude and the Latitude of the strange Country which are in this Probleme supposed to be given even as in Chapter 16. you found both those by the Declination and Reclination given Example I would set a plain Parallel to the Horizon of Jerusalem to shew me what time the Sun Rises and Sets there any day of the Year and what Hour passeth at Jerusalem at any time of our day First I seek by Geographical Tables or Mapps the Longitude and Latitude of Jerusalem and I find that Jerusalem is removed Eastward from London in Longitude 47 degrees and that the Latitude there is 32 degrees or thereabouts Therefore in the Rectangled Triangle P R O of Chapter 16. I have the angle P 47 degrees difference of Longitude also the side P R the Latitude of Jerusalem 32 degrees and hence by the 4th Probleme of Rectangled Triangles Book 3.6 I get P O 42.30 minutes and by consequence O N 9.45 minutes because P N is our Latitude and I get also the angle O 51.40 minutes And these had I get by the same Probleme in the adjoyning Triangle O N D both D N 12.05 degrees the Complement of the Declination inquired and the angle D 39.23 Complement of the Reclination inquired Wherefore I conclude that a plain which shall represent here the Horizonof Jerusalem must Decline Eastward 77.55 minutes and Recline Northward 50.37 minutes Draw upon this plain the proper Hours of Jerusalem by Chapter 23. and know that when the Sun leaveth this plain ceasing to inlighten the upper part of it then he setteth at Jerusalem and look how many Hours and minutes the Sun setteth after noon in any Country so many Hours and minutes he rose before noon CHAP. XXVI How other Circles of the Sphear besides the Meridians may be Projected upon Dyals THe Projection of some other Circles of the Sphear beside the Meridians though it be not necessary for finding the Hours yet may be both an ornament to Dyals and usefull also for finding the Meridian and placing the Dyal in his due Situation if it be made upon a moveable Body as shall be shewed Chapter 33. The Circles fittest to be projected in all Dyals for those purposes are the Equator with the Tropiques and other his Parallels which may be accounted Parallels of Declination as they pass through equal degrees as every 5th or 10th of Declination or Parallels of the Signes as they pass through such degrees of Declination as the Sun Declineth when he entreth into any Signe or any notable degree thereof or Parallels of the length of the day as they pass through such degrees of Declination wherein the Sun increaseth or decreaseth the length of the day by Hours or half-Hours Also the Horizon with his Azimuths and Almicantars are an ornament to Horizontal and Vertical Dyals and are likewise use full for projecting the Equator and his Parallels in all Dyals My purpose is to be breif in this Treatise of the Tumiture here following because I hasten to an end I shall therefore think it sufficient if I shew you one way to furnish any Dyal with the Circles of the Sphear Leaving you to devise others which I could have shewn CHAP. XXVII How to describe on any Dyal the proper Azimuths and Almicantars of the Plain FRom any point of the Gnomon taken at pleasure let fall a Perpendicular upon the Sub-style that Perpendicular shall be part of the Axis of the plain and shall be reputed Radius to the Horizon of your
and Mars in twain Sets forward and comes round again Then in one Year the Sun displaies Three hundred sixty and five dayes And near a quarter which in four Encompassings makes one day more Between the Sun and us there fly Fair Venus and swift Mercury These alwayes near the Sun we find Not far before nor far behind The Moon 's the lowest who in seven And twenty dayes goes round the Heaven And above two dayes more do run Before she overtakes the Sun So twenty nine and an half in all Do make a Moneth Synodical These Planets make their course to th' East Though they be faster hurled West And six degrees the rest may stray Beside the Suns Ecliptique way The Circles of the Sphear SIx greater Circles mark you shall Which equally divide this Ball. Just in the midst between the Poles From East to West th' Equator rolles Th' Ecliptique cuts him and doth slide Scarce twenty four degrees aside Horizon even with the ground From Stars below our sight doth bound Meridian upright doth rise Parting the East and Western Skies Two Colures through the Poles do run Quarrring the Circle of the Sun One where the Spring and Fall begin Th' other where longest dayes come in Four lesser Circles mark them well Are to th' Equator Parallel Two Tropiques bound the Suns high way Shewing the Long'st and Shortest day The Arctique Circle curs the Beares Th' Antarctique opposite appeares Meridians half twenty four For Hours and for Degrees ninescore Through both the Poles o th World do pass And th' Equinoctial down right cross And ninescore Parallels hath that line By which Stars North and South decline Th' Ecliptique hath his Longitudes And Parallels of Latitudes For Stars but in Geography The Towns beside th' Equator lie Over our Head and under Feet The ninescore Azimuths do meet And here as many Parallels Of Altitude Horizon tells Longitudes and Meridians all And Azimuths great Circles call But all their Parallels in Heaven Being lesser cut the Globe uneven Degrees three hundred and threescore Hath every Circle and no more When I consider thy Heavens the work of thy Fingers the Moon and the Stars which thou hast ordained What is Man that thou art mindfull of him Or the Son of Man that thou visitest him Ps 8. Errata Some Faults have been committed between the Writer and the Printer the cheif whereof the Reader is desired to amend as followeth pag. and line Faults Amendments 2 3 4. c. to pag. 30. in the Title The first Book of the Fabrique of the Planisphere The first Book Of the Fabrique of the Planisphear 31 and 32. in the Title The second Book of the Projections of the Sphear The second Book Of the Projections of the Sphere 1. 13. mossie massie 2. 7. Declination Delineation 3. ant Declination Delineation 4. 16. look up look upon 4. 36. eye beam eye-beame 5. 13. Euclid 4 5. Euclid 4.5 22. required of your Compass over reach required If your Compass reach short 5. 23. if it reach short if it over-reach 6. 39. structures structure 8. secant 67. 25693. 25593.  The 5. last Tangents want a place You must add a Cypher to each of them 9. 16. two so 12. 18. all but all But 13. 07. working it working It 16. 19. foure fewer 17. 18. Alamath Alamach 21. Henerichus Heniochus 17. antop little rain little Waine 18. 8. brow Crowne 18. 30. Praecepe Praesepe 19. 16. Bedalgieure Bedalgieuze 23. Alhaber Alhabor 20. 6. round the inner circle or edge of this Ring it must round The inner circle or edge of this Ring must 20. 14. naile screwes male screwes 17. small screwes female screwes 19. bare beare 22. 30. is made and gon for that year your scale is made And so for that year your scale 24. 9. but one degree but for one degree 25. 7.  put out the marks of Parenthesis 26. 8 year Henr. 3. year of Henr 3. 23. Periodus Periodus 28. alwayes upon alwayes upon 35. thus set thus set 28. 1. and 5. Grostons Grastons 30. 3 second Meridional second or the Meridional 33 6. set for London namely for London 33. â—1 on Elevation no Elevation 34. â—◠〈◊〉 the which the 9. Azimuth Azimuthes 37. 6. the eyes place the eye is placed 41. 3. Center B A Center B A 48. 4. either way either way 22. A C C A 50. 16. Zenith of Zenith of 32. Zenith and B Zenith A and B 53. 12. 12 and 13 number 12th and 13th numbred 56. 8. these sides the sides 20. subâ—endeth A which subâ—endeth A 62. 17. fall falls 63. 7 9. wayes rayes ult of deleatur 64. 10. min. at 70 min. and at 70 11. between 8 degr 34. min. between 18 and 24 min. 12. Here Refraction is as the Sun Her Refraction is as the Sun 's 65 1. your Meridians your Meridian 66. 30. require enquire 67. 3. Michals Michaels 68. 39. Long long 73. 6 CHAP. II CHAP XI 74. 20. Alrucabe Alrucaba 75. 8. Alrucabe Alrucaba 75. 12. first made first mode 76. 29. prick here prick here 8â— 16 17. by Declin by their Declin 82. 12. her Declin his Declin antep sta Star 86. 16 17 18 19. Pleiades Riseth setteth Pleiades Rise set 86. 30. to be least to be lost 87. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 88. 4. could happen could not happen â— 14. note know 17. Asera Asera 91. â—1 Duet Deut. 99. 21. 23 degrees 23d degree 102. 6 and 30. Eniph Alph. Eniph Alph. 23. 35 â…“ 56 â…“ 105. 8. Stars I Stars I â— Caeti Ceti 19. 120 deg 125 degr 110. pen. by Oblique Problemes by Probl 2 Obliqu 111. 25. in 39 ½ in all 39 ½ 114. 17. grees setting grees Setting 11. Houses also Houses also 31. 49 30 50 51. 118. 6 7. 49 50 50 51. 24. and so and to 119. 1 Astrologers Astrologie 17. futurus futurus 122. 29. no man no men 123. 3. princeps Nero princeps Nero 4. citherae citharae 10. dereliquit Nero dereliquit Nero 12. persuesum persuasum 27. se nore temerè 128. 26. as by and by 29. setting go setting therefore 130. 34. Jupiter in that Meridian Iupiter In that Meridian 139. 6. Christ time Christs time 17. Ticius Tacitus 141. 6. 4 5. 11. 4. 5 11. 145. 13. Suns Dyals Sun Dials 147. 5. or Equinoctial deleatur 19. so the hour lines to the hour-lines 154. in the scheam the letter I is wanting at the lower end of the hour-line of 11.  157. 17. with an extension with any extension 174. 32. precrucem per crucem 176. 11. by the arch by R T the arch 180. 9. Declination plain declining plain 181. 20. pre per 184. 27. the Vertical of my Dial and also deleatur 185. 28. and so and to 188. 9. Tumiture furniture 190. 7. you use you may use 192. in the scheme the prickt line last save one should be put out  193. an t a Vertical plain a Vertical or a South Horizontal
both the Schemes of the former Chapt. Now I told you Book 3.2 that if any two parts of a Rectangled Triangle be given with the Right angle the rest may be easily found observe then your Triangle A B C in the first Scheme of the former Chapter and likewise in the Meridional Projection of your Planisphere you shall see the very same For the Finitor being set to the Latitude C shall be where the Tropick of Cancer cuts the Finiter the arch of the Meridian between C and the Equator is C A and the Declination thence in the Equator to the center is A B the Base and the Ascensional Difference B C in the Horizon is the Amplitude B is the complement of Latitude A is 90 degr C is unknown and we need it not else if you have read the third Book I hope you can find him Here are six Cases 1. Admit now that the Declination and Amplitude be given put the term of the Amplitude I mean the point where it ends counting from the Center upon the Parallel of the Declination and your Triangle is formed and thereby the Ascensional difference and the complement of Latitude are discovered 2. Or if the Declination and Ascensional difference be given number the Ascensional difference from the Center downwards in the Equator Then go up in a Meridian as many degrees as the Declination comes to and to the point where you end which is C set the Finiter so he is placed to your Latitude and the Amplitude also is shewn 3. Or if the Declination and Latitude be given the Finiter being set to the Latitude follow the Parallel of Declination to the Finiter there is C thence go down by a Meridian to A in the Equator thence in the Equator to Bat the Center thence turn by the Finiter to C and you have compassed your Triangle and therefore have all known but C. 4. If the Latitude and Ascensional difference be given the Finiter being set to the Latitude count from the Center in the Equator to the end of the Ascensional difference there is A Go up thence in a Meridian to the Finiter there is C Go thence in the Finiter to the Center there is B. 5. If the Latitude and Amplitude be given the Finiter being set to the Latitude count from the Center B in the Finiter to the end of the Amplitude where shall be C go down thence in a Meridian to the Equator where is A thence in the Equator return to the Center B. 6. If the Amplitude and Ascensional difference be given prick the end of the Amplitude numbred in the Finiter from the Center and prick the end of the Ascensional difference numbred in the Equator from the Center then turn about the Reet till some one of the Meridians cut both these pricks and that shall make up the Triangle Note that for South Stars or the Sun in South Signes this Triangle lies on the South-side the center and above the Finiter but for North Signes it lies North of the center and below the Finiter CHAP. XVI To do the same in the Equinoctial Projection HEre serves the second figure of the Horizontal Triangle in Chap. 14. where B A is the Ascensional difference C A the Declination B C the Amplitude B complement of the Latitude If the Latitude and Declination be given number the Declination on the Label inwards and at the end make a prick turn this prick to the Horizon of the Mater and so shall the outward arch of the Label be C A the shorter arch of that Horizon B C and an arch of the Limb B A of your Triangle If the Latitude and Amplitude be given do as in this Example I observed Sirius to rise 27 ¼ from the East South-ward my Latitude is 52 degr ¼ I go to the 52 ¼ Meridian on the Mater reckoned from the Center on the South-side because the Star is Southern as his rising shewes This 52 ¼ Meridian being my Horizon as Book 2.2 I number in him the Amplitude of Sirius from Oriens toward Meridies 27 ¼ and thereto I lay the Label and I see my Horizon cuts the Label in 16¼ that is C A the South Decimation of Sirius and between the Label and Oriens in the Limb I have B A 22 ¼ his Ascensional difference If you can do these two you may resolve the four other Cases of this Chapter with like facility View but the Scheam in the Book and in your Planisphear and that alone will instruct you CHAP. XVII To find the Semi-diurnal and Semi-nocturnal Arches of the Sun or Stars the time of their Rising and Setting and the length of their Day and Night by Declination and the Latitude of the Place SEt the Finiter to the Latitude as-in the first Mode of the Meridional Projection Then seek the Parallel of the Declination of the Sun or Star North or South as it hapneth to be That Parallel shall be divided by the Finiter into two arches the arch above the Finiter is the Semi-diurnal arch in which you may count the time of Rising and Setting and the Length of the Day that below is the Semi-nocturnal arch in which you may reckon the length of the Night or if your Question be of a Star the time he spends under the Horizon Example In the first Scheme of the 14th Chapter D E is the Tropick of Cancer that is the 23 ½ Parallel of North Declination C E is the Semi-diurnal arch C D the Semi-nocturnal And you shall find in the Meridional Projection of your Planisphear those arches are divided by the Meridians and the arch C E containeth 124 degr 10 min. which turned into houres and minutes accounting every degree 4 minutes of Time and every 15 degrees an houre is 8 houres 16 min. 40 sec half the length of our longest Day and the arch C D containeth 55. deg 50 min. that is three houres 43 min. 20 sec half the length of our shortest Night therefore at three hours 43 min. after midnight the Sun Riseth in the Tropick and sets so much before midnight that is at eight hours 16 min. 40 sec and so may you find your desire in any other Parallel Example 2. I observe that Fomahant his Meridian Altitude is but 6.30 min. therefore by Chap. 13 he declineth Southward 31¼ I would know how long he shines with us and I presently see in the Meridional Projection of my Planisphear that his Parallel hath but 38 degr above the Horizon that is he will set two hours 32 min. after he is South and the whole time he shines in our Horizon is five hours four minutes Example 3. Lyra her Declination is 38.30 min. North and I see his Parallel comes within 45 min. of the Horizon in the North part of the Meridian but never toucheth it therefore I conclude that Lyra never sets with us at all CHAP. XVIII To find the same in the Equinoctial Projection TUrn about the
Pleiades in our Lat Cosmically Set ☉ in ♠29 ½ Nov. 11. At Athens Cosmically Rise ☉ in ♉ 19 ½ April 30. At Athens Cosmically Set ☉ in ♠27 ½ Novem. 9. Arcturus in our Lat. Cosmically Ri. ☉ in ♎ 0 Sep. 13. Arcturus in our Lat. Cosmically Set. ☉ in ♋ 4 June 15. At Athens Cosmically Rise ☉ in ♎ 10 ½ Sept. 23. At Athens Cosmically Set ☉ in ♊ 6. May 17. CHAP. XXI To find the time when any Star riseth or setteth Acronycally by his Declination and Right Ascension and the Latitude of the Place WHen a Star Riseth just at Sun-setting he is said to rise Acronically To find the time turn the Star to the East part of the Horizon in the Equinoctial Projection and mark what degree of the Ecliptique descendeth in the West for when the Sun comes to that degree the Star shall rise Acronically Example When Sirius toucheth the South East Quarter of our Horizon I see ♒ 18. setting Therefore when the Sun is in ♒ 18. Sirius riseth Acronically A Star setteth Acronically when he setteth with the Sun To find the time place the Star setting in the West-part of the Horizon and see what degree of the Ecliptique setteth with him for when the Sun is in that degree the Star shall set Acronically Thus in our Latitude Sirius Acronically Riseth ☉ in ♒ 18. Jan. 27. Sirius Acronically Seteth ☉ in ♉ 23. May 3. At Athens Sirius Acronically Ri. ☉ in ♒ 4. Janu. 13. At Athens Sirius Acronically Set. ☉ in ♊ 9. May 20. Pleiades Acronically Riseth ☉ in ♠13. Octo. 26. Pleiades Acronically Seteth ☉ in ♉ 29 ½ May 10. At Athens Pleiades Acroni Riseth ☉ in ♠19 ½ Nov. 1. At Athens Pleiades Acroni Seteth ☉ in ♉ 27 ½ May 8. Arcturus Acronically Riseth ☉ in ♈ 0. March 10. Arcturus Acronically Seteth ☉ in ♑ 4 Dec. 15. At Athens Arcturus Acroni Riseth ☉ in ♈ 10. ½ Mar. 20. At Athens Arcturus Acroni Seteth ☉ in ♠6. Nove. 18. CHAP. XXII To find when a Star riseth or setteth Heliacally AStar riseth Heliacally when he geteth out of the beames of the Sun and beginneth to be seen in the East a little before Sun rise And a Star is said to set Heliacally when he getteth into the beams of the Sun and beginneth to be least in the evening by reason of the Suns opproach to him Those Stars which you see nearest the East Horizon in the Morning Twilight are Heliacall Risers and those which you see nearest the Westpart of the Horizon in the evening Twilight are Heliacall Setters For this no exact rule can be given for all men have not like quickness of sight nor all Stars like brightness nor all Climates Countries and Dayes of the Year the same clearness of Air. And the Moon oft times augmenteth the Twilight when she is within a few dayes of the Change and keepeth the Stars longer Combust Commonly about twenty dayes before their Acronicall setting they come within the Sun beames and so set Heliacally and they appear again that is rise Heliacally about twenty dayes after their Cosmicall rising But if they be great Stars the Air clear your sight good the angle made between the Ecliptique and the Horizon great they may appear sooner and later in the contrary Cases According to this rule the Pleiades set Heliacally now at Athens ☉ in ♉ 7. and rise Heliacally ☉ in ♊ 9. so they should be Combust there 32 dayes but because they be Stars of less Magnitude we may perhaps allow them 40 dayes as Hesiod did in his time in the beginning of his Second book of Weeks and Dayes 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 CHAP. XXIII To find the Age when any Astrologer lived and what time of the Solar year the Seasons hapned in his Country by knowing his Latitude and the Rising of any Star in his time THe old Grecians and after them the Latines before Julius Caesar especially designed the Seasons of the Year by the rising and setting of some notable Stars Hesiod begins his second book of Weeks and Dayes with this Georgical Canon 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 That is when the Pleiades rise begin to Mow and to Plow when they set And in the same Book Vers 182. he saith 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 That is 60 dayes after the Winter Tropique Arcturus riseth Acronically and then appears the Swallow the Spring being then new begun These and the like rules were the Husband-mans Almanack by which they measured the Solar Year and the return of the Seasons For in their Civill Year consisting of Lunar Moneths by reason of an intercalary Moneth which was added every third Year and somewhat ofter the Seasons could happen upon the same day of the moneth yearly but sometimes 2 or 3 weeks sooner or later as our moveable Feasts do The rising and setting of the fixed Stars keep the same distance Yearly from the Equinoctial and Solstitiall points for a mans age near enough but longer those rules cannot last without some perceivable error for in 100. years the Stars go forward in Longitude according to Tycho 1 degree 25 minutes by reason whereof the risings and settings of the Stars happen later in the Year about a day and half every 100 years in the same Latitude Now if you would note in what Age a Star had such a rising or setting in such a Latitude as for Example In what age Arcturus rose 60 dayes after mid-winter in the Latitude of Asera in Boeotia near Athens whose Latitude is 37 ¼ and consequently how long since Hesiod lived in whose dayes Arcturus had such rising you shall reason thus 60. dayes after the Winter Tropick the Sun is in ♓ 1 degree by the Ephemeris for in those 60 dayes near his Perigium he goeth about 61 degrees I am therefore to seek when Arcturus did rise at Athens with the opposite degree of the Ecliptique ♠1 degree the Sun is in ♓ 1 degree then setting over against it I seek the Longitude and Latitude of Arcturus and find in Tycho'es Tables that Anno Domi. 1600. Arcturus had Longitude ♎ 18. 39 minutes Latitude B. 31.02 minutes then I will suppose that Hesiod lived 830. years before Christ for there some Chronologers place him but without any good proof that I find that is 2430 years before Anno Domi. 1600. in which space of time Arcturus must have increased his Longitude by Tycho ' Hypothesis 34 degrees 25 minutes which being subducted out of the Longitude which Arcturus had Anno Domi. 1600. leaves his Longitude for the year before Christ 830. ♠14. degree 14. minutes his Latitude was then and ever 31.02 minutes Now from this Longitude and Latitude I get his Right Ascension and Declination by Chap. 34. of this Book where I find Ascension 180. degrees Declination North 34. degrees 15 minutes those had I
the Moons age Example January 20. 1656. According to the accompt of the Church of England who begin the Year with March 25. which was the Equinoctial day about Christ time the Epact is 14. January is the 11th Moneth and the 20th day is proposed now add 14 11 and 20. together they make 45. out of which I take 30. and there remains 15. the Moons age This Rule is of good use not onely to find the age of the Moon and so her changes to a day but also for examining of Chronologie where the time is most certainly reckoned by Eclipses But you must note that if you apply this Rule to the Years past before Anno Dom 1600. then for every 312. Years that the Year proposed precedes Anno Dom. 1600. you must subtract one day out of the age of the Moon found by this Rule Example â—icius lib. 1. Reports That in the beginning of Tiberius Caesar's reigne there was an Eclipse of the Moon and Temporarius saith that whereas Augustus died Aug. 29. I think he should say 19. this Eclipse hapned Sep. 27. I would know whether it were possible for an Eclipse to happen that day supposing the beginning of Tiberius to be in August Anno Dom. 14. and Anno Periodi Julianae 4727. The Prime for that Year is 15 and the Epact 15. by Book 1. 11. add now to the Epact for September 7. and for the day of the Moneth 27. and the sum is 49. out of which subducting 30. I leave the Moons age 19. but because Anno Dom. 14. precedes Anno Dom. 1600. 5. times 312. Years therefore out of 19 I subduct 5. and there remaines 14. the age of the Moon corrected for September 27. Anno Dom. 14. Therefore it was about the full Moon and it is possible the Moon might be Eclipsed then as Temporarius saith But it could not be Eclipsed September 27. Anno Dom. 13. for then the Epact being 4. the age of the Moon by the same Rule was 3. neither could it happen Sep. 27. Anno Dom. 15. for then by the same Rule the age of the Moon was 25. at what age the Moon was far from her opposition to the Sun and therefore could not be Eclipsed CHAP. LXVIII To find in what Parallel and Climate a Place is by the Latitude given PArallels in Geography are lesser Circles Parallel to the Equator and passing through the Zenith of a Place and succeeding one another at such distance that at every Parallel the length of the day is varyed a quarter of an hour A Climate is such a Parallel as altereth the length of the day half an hour The Parallels and Climates begin from the Equator under which the day is alwayes equal to the Night and each 12 hours long hence they count the Parallels and Climates Northward and Southward but because the Earth was not so far known to Ptolomy and the Ancient Geographers as it hath been to those of later Times therefore there is great difference between the Ancient and later Geographers about the number and quantity of the spaces contained by them as among others Kerkerman Syst Geography lib. 1. hath shewed Yet may they easily be found to every Mans mind by the Planisphear in the Meridional Projection thus Find by 4. 17. what is the Semi-diurnal arch of the Sun in ♋ out of which take 6 hours and look how many quarters of an hour the double of the residue containeth so many Geographical Parallels is the place removed from the Equator and half so many Climates Example I find the Semi-diurnal arch in our Latitude to be 8 hours 16 minutes in the Tropique of Cancer out of which taking 6. and doubling the residue I have 4. 33. which is more then 9 half hours or more then 18. quarters so much our longest day exceeds 12 hours therefore we should be past the 18th Parallel and 9th Climate viz. in the beginning of the 10th Climate and 19th Parallel CHAP. LXIX The Longitude and Latitude of two Places given to find their Distance WHat Longitude and Latitude in Geography are and how they differ from Longitude and Latitude in Astronomy hath been shewed Book 4 5.11 If the places differ only in Latitude and have one Longitude bearing full North or South one from another then take their difference of Latitude by subducting the less out of the greater if the places have both North Latitude or both South Latitude or take the sum of their Latitude if one be North and the other South Then for every degree of this difference or aggregate number you may reckon 69 ½ English miles of the Statute which ordaineth 1760. Yards to be a Mile but of English Miles measured by common estimation there go not above 60. to a degree so that every such Mile that you Travel North or South shall alter your Latitude about one minute If they differ in Longitude onely and have no Latitude but be both under the Equator you shall reckon in like manner for every degree they differ in Longitude 69 ½ Miles of distance In all other Cases you have a Triangle soluble by the second Probleme of Obliquangled Triangles of which Triangle the Complements of Latitude make the two comprehending sides and the difference of the Longitudes of the places is the angle comprehended between them and the third side is the arch of the distance of the places which when you have found in degrees and minutes of a great Circle you may turn into Miles as before mark how the distance of two Stars is found by their Longitude and Latitude given Chapter 37. in the same manner may you find the distance of two Cities or Towns Example I would know the distance of London from Jerusalem The Complement of the Latitude of London is 38. 28 minutes the Complement of the Latitude of Jerusalem is 58. 05 minutes the difference of their Longitudes 46. 0 minutes I set the Zenith to the Latitude of London in the Limb that is 38. 28 minutes from the Pole so the Limb is the Circle of Longitude in which London standeth then I seek the 46 Meridian from that side of the Limb where Zenith is set for London for that 46 Méridian is the Circle of Jerusalems Longitude because the difference of Longitude is 46. Now because Jerusalems Latitude is 31. 55. and the Complement thereof or distance from the Pole 58. 5 minutes I walk on in the 46 Meridian till I come where the 58th Parallel from the Pole crosseth him and there is the place of Jerusalem the Azimuth that goes hence to the Zenith is the nearest way from Jerusalem to London what Azimuth this is I regard not for I enquire not the angle at London but I observe by the Parallels how many degrees there be in him between the places of Jerusalem and the Zenith and I find 38 degrees 20 minutes which being resolved into Miles is 2300. Miles of common estimation but Miles of the Statute 2664. the distance of
the arch of the Ecliptick from the Ascendant to the Midheaven and his match taken so many degrees on the other side the Center gives the other arch of the Ecliptick from the Midheaven to the Descendant The rest of the Meridians and the Parallels are in this Mode of no use The Almicanters and Azimuth of the Reet here shew you the Altitude and Azimuth of every degree of the Ecliptick at one view CHAP. II Of the Equinoctial Projection shewing the Northern or Southern Hemisphears THe Equinoctial Projection representeth the Northern or Southern Hemisphear projected upon the plain of the Equator Here the Limb or outmost Circles of the Mater and Reet are Equator The eye-point is the North or South Pole which you will by turns Which Poles are here expressed on the Center of the Equator because the Sphear is pictured on a plain or flat The Axtree line of the Mater A B is Colurus Equinoctiorum the Diameter C D crossing him is Colurus Solstitiorum But contrary on the Reet the Axletree is Colurus Solstitiorum and the Finiter Colurus Equinoctiorum The Colurus Solstitiorum on the Mater is also the Meridian of your place and therefore is marked with Septentrio and Meridies and the ends of the Axtree with Oriens and Occidens The rest of the Meridians being all straight lines meeting in the Poles or Center are casily supplyed by the Label and so may the Parallels also being Concentrick with the Equator For if you lay the Label on the 15. degree in the Limb from Meridies toward Occidens the fiduciall edge of the Label there designeth the 15 Meridian or the One a clock line the North Quadrant of the said Meridian proceeding from the Center now the North Pole outward to the Limb or Equinoctial and the South Quadrant returning in the same line from the Equinoctial to the Center now the South Pole and if you remove the Label 180 degrees from One a clock of the day there it shall designe One a clock at night made by the other Semicircle of the same Meridian which joyneth with his match in the Center without any angle that is into the same straight line and so of the rest And for the Parallels if you set the point of your Compass or a needles point in the 23. degree ½ of the Label and turn about the Label with the point it shall describe a Circle which will serve for both the Tropicks and so may you make any other of the parallels I do not advise you to draw the Meridians and Parallels in this form least you cumber your Instrument but I shew you how you may represent any of them in a moment when ocasion requireth The Meridians of the Mater that were so called in the Meridional Projection are here turned into the severall Horizons of the World And the Parallels here serve only to graduate those Horizons Out of these Horizons choose your own Horizon and distinguish him if you will that you may readily find him when you shall looke for him Your Horizon is thus inquired Because the Elevation of the Pole at Northampton is 52. degrees 15. minutes therefore from the Center now North Pole number in the Meridian line Northward 52. degrees 15. minutes and there cutteth the the North Semicircle of our Horizon or there you may Imagine him between the 52 and 53 Horizons and the Southern Semicircle thereof lies 52 degrees 15 minutes on the other side the Center towards Meridies This may seeme strange that the North and South points of the Horizon which in the Sphear are unequally distant from the North Pole viz. the one but 51. degrees 15. minutes and the other 127. degrees 45. minutes the supplement thereof should be equally distant in this Projection But the reason is because the Center is both North and South Pole here at pleasure and the Northern and Southern Hemisphears are both here represented by turns Carry this in your head and then lay the Eabel upon the South part of the Meridian and number thereon from the Center now North Pole outward to the Equator at the Limb 90. degrees thence number backward toward the Center now the South Pole the Elevation of the Equator which is always complement of the Elevation of the Pole and is here 37. degrees 45 minutes there is the Southern point of the Horizon and is distant from the Center now South Pole onely 52 degrees 15 minutes but from the Center being North Pole 127. degrees 45. minutes and from the Northern point of the Horizon before found just 180. degrees as it is in the Sphear Having found the North arch of your Horizon 52. degr 15. min. behind the Center count as many degrees and minutes forward in the Meridian before the Center toward Meridies and the arch crossing there shall be his match to make up the whole Circle and so may you find your whole Horizon upon the Mater whatsoever your Latitude be Here you must remember that Stars which have Northern Declination rise and set upon the Northern arch of the Horizon and those which have Southern declination upon the Southern arch Remember also that many Stars between the Tropicks which have Northern Latitude have nevertheless Southern Declination and contrary many which have Southern Latitude have Northern Declination The lineaments of the Reet serving you in this Projection are onely the Ecliptick and the fixed Stars the Almicanters and Azimuths here are of no use The Meridians and Parallels are supplyed by the Label for the Reet as well as for the Mater And whereas the Ecliptick here seemes to be irregular seeing the Solstitial points of Cancer and Caprcorn are not distant 180 degrees as they should be you must imagine that the Southern arch of the Ecliptick is Projected by the eye placed in the North Pole and for the Northern arch the eyes place in the South Pole and the Center serveth for both the Poles alike as hath been shewed number therefore as you were taught for the Horizon in this Projection For the reason of the draught of the Horizon and of the Ecliptick in this Projection is the same CHAP. III. Of the Nonagesimal Projection shewing the Eastern and Western parts of the Sphear being divided by the Azimuth of the Nonagesimus gradus NUmber in the Limb from the Equinoctial line toward the Pole the Altitude of the Nonagesimus gradus which is the highest degree of the Ecliptick and thereto set the Finitor turning the Almicanters either to the North or to the South as your work proposed shall require Now is the Finiter Ecliptick his point at the Limb-is Nonagesimus gradus The Center of the Planisphear is Ascendant and Descendant the East and west points of the Horizon are here distant from the Center as much as the Amplitude of the Ascendant cometh to to be counted from the Center upon the Eqinoctial line of the Mater which here stands for Horizon the Meridians and Parallels of the Mater are here
Meridian 3. A third way When the great Wain is seen under Cynosura the Pole Star observe with your eye the distance of the Thill-horse called Alioth from the next wheel of the Wain and setting that distance by aime in 5 parts observe by a plumb-line when Alioth drawes neer to be in the same Perpendicular with the Pole Star For when he wanteth but one of those 5 parts to come into the Perpendicular then is the Pole-star in the Meridian over the Pole in our age at other times of the night the Pole-star may be 4 degrees wide and in one hour neer the Meridian he changeth his Azimuth above one degree 4. A fourth way Because the distance of the Pole-star from the Pole is now 2 degrees 30 minutes and the Pole is in the circle or line which passeth from the Pole-star neer Alioth as before you may by guess cut off from that line 2 degrees 30 min. and in that Section you have the Pole at any time This way may be used abroad in the fields where you cannot stand upon exactness and herein you shall miss very little if you accustome your self to observe the distances of the Stars about the Pole CHAP. IIII. To Observe the Azimuth of the Sun or Stars LAy your Planisphear upon an Horizontal plain or Level and his Meridian on the Meridian line of your Place found by the last Chapter Then turn your Label that the Sun may cast the shadow of one Sight upon the other or directly towards it or till the shadow of a plumb line cut both the Sights alike then doth the Label shew the Azimuth in the Limb. For the Stars you must so direct the Sights by your eye that their edges may touch the Visuall line that comes from the Star to your eye and if your long Sight prove too short turn him toward your eye and inlightning the shorter Sight by a candle held behind you mark where the edge of the long Sight cuts both the edge of the short Sight and the Star for there is your Label in the Azimuth of the Star which you may count on the Limb. Note that if you seek the Azimuth to get the hour you shall find it most easily when the Sun or Stars are neer the Horizon and then you shall not be troubled with their Refraction But there is most use of observing Azimuths neer the Meridian because there the Azimuth changeth apace the Altitude very slowly Yet if you may choose choose to take Altitudes rather then Azimuths so you come not within 2 or 3 hours of the Meridian because the Sights serve all Altitudes with like facility and you may sooner have a true plumb line any where then a true Horizontall plain and a true Meridian line CAAP. V. To find the Suns Longitude THe Longitude of the Sun is the arch of his distance from ♈ 0 in the Ecliptick or it is the angle made at the Pole of the Ecliptick comprehended between the circle of Longitude passing through ♈ 0 and another Circle of Longitude passing through the center of the Sun for the said arch of the Ecliptick is always the proper measure of this Angle And because the Suns center never hath Latitude therefore for the Sun you shall enquire the arch but contrarily for the Stars which have Latitude you shall require the Angle and they be both as was said of one measure The Suns Longitude Arch or Angle is presently found by the Ephemeris upon the Limb of your Planisphear for if you lay the Label upon the day of the Moneth it shall cut the degree of the Signe also in which the Sun is and that is his Longitude in doing whereof you shall observe the cautions given Lib. 1.8 to which I refer you Note here that the Longitude of a place in Geographie is the Angle at the Pole of the World comprehended between the first Meridian passing by the hither side of S. Michals Island which is the neerest of the Azores and the Meridian of the Place and this Angle hath his measure in the Equator CHAP. VI. The Suns Longitude Declination Right Ascension any one of them given to find the rest in the first Projection WHat the Suns Longitude is hath been shewed chap. 5. His Declination is his diâ—â—ance from the neerest point of the Equator and therefore is alwaies measured in an Arch of that Meridian which hapneth to pass through the center of the Sun and always cuts the Equator at right Angles as do all the Meridians The Right Ascension of the Sun is the angle at the Pole of the World comprehended between that Side of the Colurus Equinoctiorum which cuts the intersection of the Ecliptick with the Equator in ♈ 0 and the arch of another Meridian which passeth through the center of the Sun And note that this angle may increase above 180 degrees even to 360 degrees though every angle properly so called be less then 180 degrees and never more then 90 degrees comes into the Triangle for if you number backwards or forwards from either of the Equinoctiall points you shall have like arches of Right Ascension answering to like arhces of Longitude and Declination so that having found the Right Ascension in any one Quadrant or the complement therof you shall find the whole Right Ascension from ♈ 0 by adding one two or three whole Quadrants to the Right Ascension found or to the complement therof as by the view of your Planisphear you shall presently know how to do better then by more words Otherwise thus The Right Ascension of the Sun is an arch of the Equator comprehended between the Vernal Equinox and that point of the Equator which riseth with the Sun in a right Horizon A right Horizon is where the Equator passeth through the Zenith and maketh right angles with the Horizon and consequently where the Poles have no Elevation For from that posture of the Sphear in which the Equator riseth upright is the term of Right Ascension borrowed I would if I might call it rather Equation because it is numbred on the Equator and serves for the Equation of naturall days and may as easily be found in any Sphear as in a right Sphear since the Horizon of a right Sphear limits the Right Ascension only because that Horizon falls in with a Meridian and the Meridians do limit it in all parts and postures of the Equator without any respect to the Horizon at all But the old term hath so long inured that I beleeve it will not be changed without better Authority These definitions premised you shall know that these three arches viz. of Longitude in the Ecliptick of Right Ascension in the Equator and of Declination in a Meridian do make up a notable Rectangled-Triangle in the Sphear The Ecliptical Triangle like unto that which was made the common Example in all the five Problemes of Rectangled-Triangles Book 3 3. c. But to see your Triangle and resolve
place Arcturus in my Reet according to that Right Ascension and Declination as was taught Book 1 7. and Book 4.18 and by Chapter 21. I find â™ 4 rising with him and at the same time ♓ 4. setting in the same Herizon of Athens But I ought to find ♓ 1 degree setting in Hesieds time Therefore I will suppose again that Hesiod lived 1130 years before Christ and proceeding as upon the former supposition I find that then â™’ 29. degrees did set at his Acronical rising but I ought to find ♓ 1 degree rising And seeing it is hereby found that in 300 years his Acronicall setting varies 5. degrees or dayes I take the proportional part of that time and lay that in the year 1010. before Christ Arcturus did set Acronically 60. dayes after the Winter Trepique and then lived Hosiod or soon after For being an Astrologer himself as Pliny tells us Lib. 18.25 saying Huâ—us quaque nomine extat Astrologia it is likely he would not use an antiquated rule Arcturus therefore rose Acronically at Athens in Hesiods time ☉ in ♓ 1 degree that is about Febr. 9. of our Julian year as it now goeth then the Swallow used to come to Athens but in our Age he riseth Acronically at Athens ☉ in ♈ 10 ½ that is Mar. 20. and at Ecton or Northampton ☉ ♈ 0. that is Mar. 10. By this you may see that the old Astrological Rules concerning the rising and setting of the Stars left us by Hesiod Cato Aratus Varro Palladius Virgil Ovid Pliny Columella Ptolomy and other Ancient Authors cannot serve for our Age nor for every Latitude and the best use we can make of them is to find the Age when they lived Pliny Lib. 18.26 saith that in Caesurs Calender octavo Calend Martij was Hirundinis adventus jostero die Arcturi exor us Vespertimus Which agrees not to Caesars time Also Lib. 2.47 he saith Ardentissimo aestatis tempore exoritur Caniculae fidus Sole primem partem Leonis ingrediente qui dies est 15. ante Caelend Augusti that is July 18. Rome is in Latitude 42 degrees Pliny lived about 70. years after Christ then was Canicula that is Sarius in ♊ 17. degrees Latitude 39 ½ Right Ascension 79 ½ Declination South 16 â…” and did rise at Rome Cosmically decimo quinto Calend. Augusti or July 18. as thus far he reports truly but the Sun was not then in ♌ 1 deg as Pliny saith but in ♋ 23 degrees for the Sun entred ♌ in his time not decimo quinto Calend Augusti but octavo Calend. Augusti The Sun in those dayes entring the several Signes mostly on the 5 day of the several moneths as in our Age about the 11th day as Astronomers well know Pliny seemes to have taken his Astrologie upon trust And I cannot devise what should lead him to suppose that howsoever the Equinoxes and Solstices in his time hapned octavo Calend. as he denyeth not yet the Sun entred into a new Signe about the Ides of every Moneth and that the Equinoctial and Soistitial points were in Octavis partibus signorum as if the Sun came not to the Equinoctial till he came to the 8th degree of Aries See Pliny Book 18. Chapter 25 26 27 28. He seemeth to distruct the Julian Calender and to adhear more to the account used by Varro de Rerusticâ Lib. 1.27 but either he understood neither of them well or I do not well understand him Now Sirius riseth in our Horizon with ♌ 18½ about August 1 in the Declination of the heat who in Plinyes time rose ardentissimo astatis tempore And our Dog-dayes if we follow the Dogs rising will be every age colder and colder and at length fall in Winter It were better to reduce them to the Suns entrance into Leo or to Cancer 23 rather as they were in Plinyes time and to count the ardentissimum tempus a fortnight before and a fortnight after for Sirius was not by the Ancients supposed the cause of the sultry heat of Summer but a concomitant signe of that Season whereof the Suns continuance in the North-Signes was the cause Would you know also when they began to Plow and to Mow in Greece in Hesiods Time He saith when the Pleiades rise begin to Mow and to Plow when they set The Pleiades I mean the brightest of them 1010 years before Christ were in ♈ 17.25 minutes Latitude 4 degrees North. Declination therefore by Chapter 34 11 degrees Right Ascension 14½ degrees therefore they rose Cosmically at Athens or Ascra Hesiods birth Place ☉ in ♈ 10 â…“ that is as our Julian year now goeth about March 20. The Heliacall rising is about 20. dayes after the Cosmicall Chapter 22. that is about April 9. Therefore either March 20. at the Cosmical rising or April 9. at the Heliacall rising they began to Mow and I think he means the Cosmicall the Acronicall rising was there in his Age ☉ in ♎ 10. â…“ about Sep. 23. which is too late beyond reason Now that they should begin Mowing in Greece within 10 dayes after the Equinoctial is not strange seeing the first fruits of ripe Corn were offered at Jerusalem yearly at Easter which fell ordinarily 15. dayes after the Equinoctial or thereabout Duet 16. And in Egypt cum falce arva visunt Paulo ante Calendas Apriles mossis autem peragitur Maio saith Pliny 18.18 viz. Harvest began in Egypt a little before April and April then began 8 dayes after the Equinoctial onely The Cosmicall setting of the Plaiades at Athens in Hesiods time 1010. years before Christ was ☉ in ♎ 18. degrees Octob. 1. then began they to Plow and Sow the Egyptians began Novembri mense incipiente Pliny 18.18 But if Hesiod were now alive at Ascra he would find the Plaiades rise Cosmically with ♉ 19 ½ Alpril 30. and set Cosmically ☉ in â™ 27 ½ Nov. 9. so much are his Georgique rules now antiquated and serve for little else but to shew how many Ages ago he lived and how the Seasons hapned in his Age. CHAP. XXIV The Latitude of your Place the Declination Altitude Azimuth and Hour of the Sun or Stars any three of these being given so find the other two SEt your Planisphear in the first Mode of the Meridional Projection The Complemental Triangle and you shall find all these five in one Oblique-angled Triangle which I use to call the Complemental Triangle because it consists of three Sides which are all Complements Others may call it as they please A B in the Limb between the Pole and Zenith Complement of Latitude A C in a Meridian Complement of the Declination or the Supplement of that Complement B C in an Azimuth Complement of the Altitude A at the Pole is the Angle of Horary distance from the Meridian whose full measure is in the Equinoctial line but because every Parallel is divided by the Meridians into 180. degrees as the Equator is and every 5th and 15th Meridian
The Parallactical Triangle which may be called the Parallactical Triangle and the leg which hath the Parallax of Longitude is a segment of the Ecliptique or of a Parallel near it and the leg which hath the Parallax of Latitude is a segment of a Circle of Longitude passing through the apparent place of the Planet and through the Poles of the Ecliptique and cutting the Ecliptique or his said Parallel at Right angles as in the Figure C is the apparent place of the Planet B is his true place in which he must be seen from the Center A B C is the Parallactique angle B C is the Parallax of Altitude B A the Parallax of Longitude C A the Parallax of Latitude Wherefore by the third Probleme of Rectangled Triangles Book 3. 5. you may presently get both the legs Example The Parallactical angle B was found Chapter 62. to be 86. 41 minutes and the Parallax of the Moons Altitude Chapter 63. to be 46 ½ minutes for the same time Here therefore having laid the Label to 86. 41 minutes from the Equinoctial I number in the Label from the Center 46 degrees and an half in stead of 46 minutes and an half the Parallax of Altitude and I find that the 46 ⅓ Parallel cutteth the said 46 ½ degree of the Label by which I know that the Leg C A for the Parallax of Latitude is 46 ⅓ very near for the ☽ here being near the Nonagesimus gradus all her Parallax almost goes into Longitude but B A of my Triangle is covered by the head of my Label Nevertheless I may see his measure in any of the Parallels to be 3 ½ minutes for the Parallax of Longitude for it is the 3 ½ Meridian from the Axis which cutteth 46 ½ of the Label and if I had not this shift I might have my choice of other shifts shewed Book 3. the 8 9 10 11 12 and 13th Chapters The Suns Parallax of Altitude Chapter 63 for the same time was found 1 minute ½ therefore laying the Label to the Parallactique angle as before I number on the Label for the side B C the Suns Parallax of Altitude being 1 minute ½ 9 degrees so every degree here signifieth 10 seconds and I find there cutting almost the 9th Parallel shewing me that C A the Parallax of the Suns Latitude is 1 ½ minute almost that is almost as much as his Parallax of Altitude and there cutteth also the Meridian 0 ⅔ shewing me that the side B A Parallax of Longitude is almost 7 seconds The Sun therefore though he never have Latitude by reason of his Parallax appeared in the middle of this Eclipse to have South Latitude 1 ½ minute the Moons true Latitude was then by Lantsbergius his Tables 45 minutes 24 seconds North so that by this accompt the Sun and Moons Centers were distant in Latitude 46 minutes 54 seconds but when out of this distance you have subtracted 46 ⅓ for the Moons Parallax of Latitude there remains 34 seconds for the apparent distance of the Centers of the Sun and Moon But by Observation I found them distant 1 minute 48 seconds for the digits Eclipsed at Ecton were 11. 22 ½ minutes and so perhaps might I have found by my Planisphear or some what near had it been large enough and had I regarded every minute and second precisely in setting down this Example which were more then needed for my purpose in this place CHAP. LXV To find the Moons Latitude by her distance from either of the Nodi called Caput and Caudi Draconis AS the Ecliptique crosseth the Equator with an angle of 23. 30 minutes for our Age so the Orbite or Circle in which the Moon moveth crosseth the Ecliptique but the angle of Inclination is not alwaies nor long the same for in the Conjunctions of the Sun and Moon the angle is ever 5 00 minutes and increaseth to the time of the Quadrature when it is found 5 degrees 16 minutes thence it decreaseth to the Opposition where it is again but 5 degrees as in the Conjunction thence it increaseth again to 5 degrees 16 minutes in the latter □ and again thence decreaseth to 5 degrees in the ☌ Get by the Astronomical Tables the quantity of the angle made between the Ecliptique and the Orbite of the Moon which in all Conjunctions and Oppositions and therefore in all Eclipses is 5 degrees as was now said and get also by the like Tables the Moons distance from the nearest of the Nodes then may you find the Moons Latitude by the Probleme 3. Rectangled Triangles Book 3. 5. just as you use to find the Suns Declination by his Longitude and greatest Declination Example The ☽ in the former Case was distant from Caput Draconis by Lantsbergius Tables 8 degrees 43 minutes I lay the Label from the Equinoctial line to 5 degrees in the Limb and counting in the Label from the Center 8. 43. I see there the Parallel of 0 ¾ that is 45 minutes or 46 minutes crossing for the Moons Latitude CHAP. LXVI To find the Dominical Letter the Prime Epact Easter day and the rest of the moveable Feasts for ever by the Calender discribed Book 1. 11. AN Example shall serve here instead of a Rule For the Year 1657. I would know all these wherefore I seek the Year 1657. in the Table of the Suns Cycle and over against it I find 14. for the Year of the Cycle of the Sun and D for the Dominical Letter And note here that every Leap-year hath 2 Dominical Letters as 1660. hath A G and the first viz. A serveth that Year till February 25 and the second G for the rest of the Year And note that these letters go alwayes backwards when you count forwards as B A then G F c. not F G and then A B as you may see by the Table Then in the Table of the Cycle of the Moon I have for the Year 1657. the Prime 5. the Epact 25. Those had I go to the Table for Easter and seek there in the first rank the Prime 5. and under it in the middle rank stands E that is not my Dominical Letter therefore I seek not backward but alwayes forward in the middle rank till I come to my Dominical Letter D. and under it I find in the third rank March 29. upon which Easter day falls this Year 1657. The rest of the moveable Feasts may be had by their distances from Easter which are alwayes the same Onely for Advent Sunday remember that the next Sunday after November 26 is Advent Sunday Read Book 1. 11. and that will sufficiently instruct you with this Example CHAP. LXVII To find the age of the Moon by the Epact REmember first that the Epact begins with March which must be here accounted the first Moneth Then if you add to the Epact the number of the Moneth current and the number of the day of the Moneth current the sum or the excess above 30 is
12. 52. N. 3. Lyra 276. 27. 38. 30. N. 1. In Ariadnes brow Mumir 230. 12. 27. 51. N. 2. The Swans bill 289. 23. 27. 18. N. 3. The Eagles Heart 293. 41. 08. 03. N 2. Tail 282. 36. 13. 25. N 3. The Dolphins tail 304. 24. 10. 14. N 3. Pegasus his mouth Eniph 322. 03. 8. 24. N 3. Head 328. 24. 4 38. N. 4. Neck 336. 21. 9. 08. N. 3. Right shoulder Sheat 341. 59. 26. 18. N. 2. First in the wing Marcab 342. 07. 13. 28. N. 2 Last in the wing 359. 08. 13. 22. N. 2. The Rams head 27. 12. 21. 54. N. 3. Horn 23. 54. 17. 40. N 4. Horn 24. 08. 19. 12. N. 4. The Bulls North eye 62. 23. 18. 26. N. 3. South eye Aldebaran 64. 17. 15. 48. N 1. Brightest of the Pleiades 52. 00. 23. 03. N 3. Gemini Head of Apollo 108. 24 32. 33. N. 2. Head of Hercules 111. 19. 28. 46. N. 2. The first foot 88. 48. 22. 33. N 4. The first foot 90. 48 22. 38. N. 3. The third foot 94. 41 16 38. N. 2. Cancer Praecepe 125. 22. 20. 48. N ne Leo the Lions neck 150. 26. 21. 29. N. 2. Heart Regulus 147. 43. 13. 33. N 1. Back 164. 08. 22. 20. N 2. Tail 173. 04. 16. 25. N. 1. Virgo Spica ♠Azimech 196. 56. 9. 31. S. 1. Libra South ballance 218. 13. 14. 37. S. 2. North ballance 224. 52. 8. 07. S.  Scorpio in his forehead the lowest 234. 50. 25. 06. S. 3. Midst 235. 15. 21. 38. S. 3. Highest 236. 36. 18. 51. S. 3. Heart Antares 242. 23. 25. 37. S. 1. Sagittaries head the midst 281. 18. 22. 07. S. 4 Capricoms horn the highest 299. 58. 13. 29. S. 3. Tayl 320. 29. 18. 02. S. 3. Tayl 322. 15. 17. 32. S. 3. Aquarius right shoulder 327. 16. 1. 52. S. 3. left shoulder 318. 07. 6. 56½ S 3. Right leg Scheat 339. 22. 17. 31. S. 3. End of the flood Fomahant 339. 46. 31. 17. S. 1. The Whale Mandibula 41. 21. 2. 48. N 2. Mouth the midst 36. 36. 1. 50. N 3. Check 35. 44. 1. 07. S. 3. Belly Baten Kaitos 23. 52. 11. 54. S. 3. Tayl Northern 0. 43. 10. 37. S. 3. Tayl Southern 6. 45. 19. 48. S. 2. Orion Right shoulder Bedalgieure 84. 23. 07. 18. N 1. Left shoulder Bellatrix 76. 54. 06. 01. N 2. Girdle the first 78. 52. 0. 35. S. 2. Second 79. 55. 1. 26. S. 2. Third 81. 04. 2. 09. S. 2. Left foot Rigel 74. 44. 8. 37. S. 1. Right foot 83. 03. 9. 49. S. 3. Thegreat Dogs mouth Alhaber Sirius 97. 42. 16. 14½ S. 1. Formost foot 92. 08. 17. 49. S. 2. The litle dogs neck 107. 22. 8. 54. N 3. Thigh Procyon 110. 34. 6. 03. N 2. Hydra the heart Alphard 137. 54. 7. 15. S. 2. Corvus in his beak the first of the □ 177. 50. 22. 54 S. 4. Second of the □ 179. 49. 15. 39. S. 3. Third of the □ 183. 16. 14. 39. S. 3. Fourth □ 184. 20. 21. 33. S. 3. CHAP. VIII Of the Ring or Limb of the Mater THe third part of this Instrument is the Ring or Limb which is nothing else but the skirt of a Circular plate equal with the Mater whose middle is cut out by a lesser concentrique Circle It is bounded with two Parallel Circles the outmost must touch the edge of the Mater round the inner Circle or edge of this Ring it must be a little less then the Limb of the Reet that it may take hold of the Reet to keep it flat and safe from harms This Ring had need be thicker then the Reet but not so thick as the Mater and for breadth about 1 10 part of the Diameter It must be pinned or screwed on to the Mater with 6 or 8 pinnes or screws that so you may take your plates asunder when need is to cleanse them from any stain or dust that may get between Let the pins that carry the naile-screws be riverted in the Ring and chair heads so filed down and polished that they be not seen to check the Label and holes being made in the Mater for the pins to pass through you shall have smal screws of what fashion you like best to turn upon them on the backside these screws would be made all of a length and may serve as feet to bare up the Instrument about a third part of an inch from the ground that it be not scratched and be readier to take up And that the Reet may turn more pleasantly under the Ring and lie as near as may be in the same plain with the Ring you shall abate half the thickness of the upper edge of the Reet about a barly-corn's breadth round about so far as he shall run under the Ring and likewise aba e half the thickness of the inner edge of the Ring on the lower side where he clasps down the Reet which a good Turner knowes now to do or you may make a shift to do it with a beam-compass if you make your running point like a narrow chesill Your Ring thus fitted to the Mater you shall set one foot of your Compasses in the Center of the Mater and with the other draw near the inner edge of the Limb a Circle about 8 100 of an inch distant from the edge Also opening your Compasses about ⅙ of an inch more you shall draw another Parallel Circle and laying your Ruler or Label from the Center to the several degrees of the fundamental Circle of the Mater you shall draw short lines for every degree from the inner edge of the Ring to the first Circle and every tenth degree you shall prolong to the second Circle and let every fifth be drawn half way Between these two Circles also you shall set figures to every tenth degree numbring from the Equinoctial line C D to the Poles on both sides both wayes Also without the second Circle you shall set great figures for the several Hours setting XII at C and thence proceeding in order to the right hand toward B at 15 degrees set I at 30 degr set II at 45 degr set III and so on till you come to D where you must set XII Thence you shall proceed in the other Semicircle D A C setting I II III and so on in order till you be come round And remember that you write on the Ring at A Oriens at C Meridies at B Occidens and at D Septentrio CHAP. IX Of the Ephemeris or Calender on the Ring IF there be space enough left upon the Ring without the Circles of the degrees and Hours you may fill it up with the Ephemeris of the Sun in this manner The former Scale on the inner edge of the Ring shall serve you to this purpose for an Ecliptique and you may set to him the Characters of the Signes if you will at every thirtieth degree beginning at Oriens and there setting ♈ and
♋ at Meridies and the rest in like order Then draw another Scale without this upon the Ring consisting of two spaces In the inner space shall be the Dayes of the Year in the outer space which must be a little larger shall be the Names of the moneths in their order And to divide this Scale rightly you shall do thus Go to some Eshemeris for the Leap Year that next comes viz. 1660 or rather for some Leap Year about 20 Years hence that your Scale may serve without any Prosthapheresis for 40 Years to come without sensible error and beginning your year with March look where the Sun was on the 29 of February at Noon which you shall find to be ♓ 20 degr 47 min for the Year 1660. Therefore laying the Label or a Ruler from the center to ♓ 20 degr 47 min. in the inner Scale strike a long stroke through your outward Scale and from thence begin your Year writing from thence toward the right hand March 1660. Then lay the Label to ♓ 21 degr 47 min which is the Suns place on the first day of March at noon the same year and where it cuts the outer Scale mark the first day of March and so the rest in order And to the first day of every moneth you shall set his proper Letter which belongs to him in the Calender as to the first of March you shall set D and to the first of April G c. and when you have done December you must take the Suns place for January and February out of the next years Ephemeris viz. 1661 and note that the space for the last day of the year Febr. 28 will fall out to be less by a fourth part then the rest by reason that the Sun wants almost 6 hours to finish his Circle which he finishes in dayes 365 5 hours 48 minutes And for this cause these Scales will serve you to find the Suns place at noon for any day in a like year that is every fourth year accounted hence either backwards or forwards which year shall evermore be accounted to begin from Febr. 29. and may be accounted the first year after Leap year because the Intercalation was February 25 next before Then for the year next following viz 1661. beginning March 1 and being second from the Bissextile or Leap year these Scales shall give you the place of the Sun at six hours after noon and the third year from Bissextile 1662 beginning as before March 1 these Scales shall give you the Suns place 12 hours after noon or the midnight following And the fourth year 1663 being Bissextile these Scales shew the place of the Sun at 18 hours after noon the next year 1664 being the first after Bissextile and beginning as aforesaid March 1 is the very same year for which your Scale is made and gon for that year your Scale shewes the Suns place at noon again But because the Julian years are bigger then the true Solar years by almost 12 mi. of time that is near a quarter of an hour in which time the Sun moves 27 sec 13 thirds 37 fourths therefore when you have found the Suns place by the former Scale any year after 1660 look how many years are passed since 1660 and so many times you must add 27 sec 13 thirds 37 fourths that is almost half a minute to the Suns place found and for years past â—ou must subtract as much that you may find the Suns place exactly This Prosthapheresis in 2 or 3 years is scarce considerable in an Instrument but in 10 years there will be 4 minutes 32. seconds and in 20 years 9. minutes 5. seconds to be added after 1660. and as much to be subtracted in like number of years preceding the year 1660. to which this Scale is supposed to be framed This Ephemeris or Calender M. Blagrave would have on the back-side where hee would also have a Ruler with Sights to take the Altitude of the Sun or Stars But this will be found incommodious in many respects both in the framing and in the using and therefore I advise that nothing be set on the back-side but the Tables of the Prime Epact and Cycle of the Sun thereby to find the age of the Moon her Conjunctions and Oppositions and the moveable Feasts for ever Of which see Chap. 11. CHAP. X. Of the Label and Sights THe Label is a Ruler slit in the midest and the half of it cut away to the Head where it is pinned to turn upon the Center and reaching to the outside of the Limb. The Fiducial edge thereof which pointeth upon the Center must be graduated like to the semidiameters of the Mater and Reet into 90 degrees to be numbred either inward or outward The fashion of it may be understood by the figure without more words To this Label you may fit Sights either fixed or moveable as you like best for observing Altitudes and Azimuths but for taking Azimuths you had need have one tall Sight at least half as long as the Label and then it had need be moveable to take off at pleasure For taking the Altitude of the Sun I have made a pair of moveable Sights to slip up and down upon the edge of the Planisphear having on the backside springing plates of brass to pintch them close and make them stick where you set them These are commonly to be set at C and D the ends of the Equinoctial line At A in the Limb and in the Circle next unto the inner edge which boundeth the strokes of the severall degrees you shall drill a small hole through which you may put a thred to hang a plummet on The Sun then shining through the Sights placed at C and D the plumb-line shall shew his Altitude in the semicircle B C A you beginning to number from B and observing where the plumb-line crosseth the Circle in which the hole for hanging the plumb-line was made And here you must remember that because the plumb-line falleth not from the Center of the Planisphear but from a point in the circumference about A therefore the space of two degrees must be taken but one degree so that if the Plumb-line fall 20 degr below B toward C the Suns Altitude is 10 degrees as you may see demonstrated Euclid 3.20 and Pitisc Trigonem 1.53 And thus you may observe the Suns Altitude neer the Horizon as exactly as by a Quadrant whose semediameter were equal to the diameter of your Planisphear But if the Altitude exceed 30 or 40. degrees then will the Plumb-line cut the limb too slope and have too much play to your trouble For remedy whereof you shall remove the Sight at D towards A some degrees as for example 60 degrees by which means you shall abate the Suns Altitude 30 degrees which 30 degrees must be added to the Altitude observed as for example the Sights are placed one at C the other 60 degrees above D toward A and the