the Instrument being a part of the Horizon the Parallels Meridians Verticall Circles that are contained or may be described in our Latitude sufficiently necessary induceth any one in the understanding of the uses of it that is but indifferently versed in the linaments and principles of the Globe what to speake and what to answere in a Proposition without farther direction And having had this Horizontall Quadrant for many yeares past as a Pocket Instrument diverse about this Kingdome being importunate with me for to have it or to publish the use of it seeing its great facilitie and expedition in comparison of such Pocket Instruments as are now used here or in forraigne parts I was willing at last after I had given order for the making of fower of these Instruments in Silver for severall Noble Personages to disburthen my selfe of Transcribing the uses of the Instrument and Tables for the making of it to satisfie those which were importunate and to let others that are studious in Mathematicall Practices also participate of it Now what I have delivered vpon the accommodating of the Instrument thus the making thereof with the uses that I have delivered in this Tractat upon it following I acknowledge due to none Inferiour assistant but to mine owne Industry search and labour and that 64. 65. and 66. Pages of the Booke of the Sector before specified in which is onely shewne the 2. 3. 19. 22. 25. and 30. Propositions of the Index or Table following as uses of the said Projection But I have extended them to many more and abundantly and plentifully supplied the obscuritie of that Scheme or Diagramme there drawne as for a generall good in the use of this Horizantal Quadrant I deliver therfore first the making of it first by the Sector somewhat different from that of Master Gunters secondly by Geometrie and lastly I shew a third way how it may be Proiected and made by my Mathematicall Ring and by Numbers which I have Calculated and accommodated to that end in Tables for more exactnesse Part of the generall scope and use of which Instrument I deliuer in the Index or Table following An Index or Table of the vses of the Horizontall Quadrant Viz of the Horizon Line of Shadowes Kalender Parallels Aequator Eclipticke Houre-lines Index 1 By the Horizon to shew 1. The Sunne or Starres Altitude at any time Pag. 53. 2. At any Day of the yeare how farre the Sun riseth or setteth from the true East or West Pag. 28. 3. The Suns Azimuth and Altitude at any houre for any day Pag. 62. 4. The Meridian line upon any appearance of the Sunne Pag. 55. 5. The vncertaintie of time by noting the Shadow of things Pag. 63. 6. The Site of a Building or Costing of a Place Pag. 57. 7. The Variation of the Needle Pag. 59. 8. The Declination of a Wall or Plaine the Sunne shining thereon Pag. 71. 9. The Inclination of a Plaine and to place a Plaine Horizontall Pag. 89. 2. By the line of shadowes is had 10. At what houre in any Day of the yeare the shadow of an Altitude is equall double triple c. unto it Pag. 35. 11. Instantly the houre of the day the Azimuth and Altitude of the Sun with the Meridian line without observation or sight of the Sun by knowing the Proportion betweene the length of a shadow upon a Horizontall Plaine that which casts the shadow Pag. 67. 12. At any houre an Altitude of the Sun or Azimuth what Proportion shadowes have to their Bodies Pag. 37. 13. Whether and Altitude be above or below the Iewell of the eye how much 14. The hight of an Altitude accessible or in accessible Pag. 100. 101. 15. The measure of any Part of Altitude not approchable Pag. 102. 3. By the Kalender is knowne 16. The inequality of Time in equall Months or equall number of Dayes Pag. 44. 17. What number of dayes wil make the day and houre longer or shorter at any time Pag. 43. 18. The houre of the Sun rising setting with the length of the day at any time Pag. 23. 19. What dayes are alike in length what day the Sun rising in the one shall be the Sun setting in the other Pag. 24. 20. The inequality of Time between day breake and Sun rising Pag. 41. 4. By the Parallels to search out 21. At any day the Suns declination Pag. 24 22. The Latitude of a Place or hight of the Pole above the Horizon Pag. 60. 23. At what houre in any day the Suns Azimuth and Altitude will be equall and how much the Altitude Azimuth wil be Pag. 42. 5. By the Aequator is seene 24. The Suns equall motion right Ascention and oblique Ascention Pag. 26. 6. By the Eclipticke to give 25. The Sunnes Place at any time of the yeare Pag. 25. 26. The Degree of the Aequator in the Horizon by supposing the degree of the Ecliptick in the Horizon Pag 46. 27. The Degree of the Eclipticke in the Horizon by supposing the degree of the Aequator in the Horizon Pag. 47. 28. The degree of Medium Coeli or the degree of the Eclipticke in the Meridian by supposing the degree of the Eclipticke in the Horizon Vel contra Pag. 47. 29. The Horoscope or the degree ascendant ' or descendant and the Nonagessima degree at any houre Pag. 49. 30. What Angle the Eclipticke makes with the Horizon or the Altitude of the Nonagessima degree and what Azimuth it is in at any houre Pag. 50. 7. By the hour lines to find 31. The houre of the Day and Azimuth of the Sunne Pag. 54. 32. The houre of the day agreeable to any Altitude or Azimuth Pag. 39. 33. The Sunnes Difference of Ascention for any day Pag. 23. 34. The Quarter of the yeare and day of the moneth houre of the day Meridian-line and Azimuth of the Sunne if it were forgotten Pag. 64. 8. By the Index adioyned with other lines you have 35. At what houre Altitude the Sun wil be due East at any day of the yeare Pag. 27. 36. The Suns Azimuth houre without observation Pag. 58. 37. The time of day-breake or end of Twi-light for any day in the yeare Pag. 30. 38. The hight or Depression of the Sun in the Meridian for any day in the yeare here or for any Latitude Pag. 29. 39. The Suns depression Azimuth at any houre of the Night assigned Pag. 40. 40. The houre of the day to our Antipodes by supposing the suns depression under the Horizon Pag. 42. 41. What houre Altitude the sunne commeth upon a declining wall any day in the yeare how long the sun shineth thereon Pag. 32. 42. At what houre and Altitude the Sun must have to be opposite or Perpendicular to a Declination Plaine Pag. 33. 43 The declinatiō of a wall by seing the sun beginning to shine thereon or going from it Pag. 69. 44. The houre Altitude of a stars coming to the Meridian at
the South Pole under the Horizon which is alwayes equall to the elevation of the North Pole above the Horizon So if upon the tenth of Aprill Exam. the Meridian Altitude should be found to be 50. gr the Declination belonging to that day by the 3. Pro. is 11. gr and a halfe North which being subtracted according to the former directions leaves 38. gr 30. m the height of the Aequinoctiall above the Horizon that taken from 90. leaves 51. gr 30. m the depression of the South Pole under the Horizon or the elevation of the North Pole above the Horizon for the height of the Aequinoctiall knowne the Complement thereof is alwayes the Latitude of the place or height of the Pole and here note generally that the height of the Pole and Aequinoctiall together doe alwayes make a Quadrant or 90. gr therefore the height of one of them being knowne the height of the other is also knowne and further here note that if the sun have North Declination the sun is so much higher then the Aequinoctiall at none that day by so much as his Declination cometh to but if the Sun have South Declination then the Sun is lower then the Aequinoctiall that day at noone by so much as his Declination cometh to by which you may easily gether when to adde or subtract the suns Declination to or from the suns Meridianall Altitude to get the height of Aequator which knowne the Poles height cannot be unknowne Pro. 34 Eightly to finde the suns Azimuth and Altitude for any houre Constru ¦ ctio 44 Marke where the parallel for the day of the Month meeteth with the given houre and bring the edge of the Index thereto so the degree that the edge of the Index cutteth in the Limbe of the Instrument that shal be the Suns Azimuth and the degree that the houre cutteth in the Index that shall be the Suns Altitude required So if upon the tenth of December at nine of the Clocke in the Morning Exam. the Suns Azimuth and Altitude were required marke first where the Tropick of Capricorne which is the parallel for that day given meeteth with the given houre of nine and bring the Index thereto so the edge of it in the Limbe pointeth out neere 40. gr and a halfe so much is the Suns Azimuth from the South at nine of the Clocke in the forenoone the said tenth of December and the houre line meeting with the Index sheweth neere 5. gr 25. m. so much is the suns Altitude at that time now if you move the Index softly along as the edge of it passeth by any houre for any day of the yeare so the edge of the Index in the Limbe of the Instrument sheweth the suns Azimuth and the intersection of the parallel with the Index shall shew the Suns Altitude belonging to that houre Ninthly to shew the uncertaintie Pro. 35 of time by noting the shadow of things It is usually noted by some that when the shadow of the edge of a Window Dore Wall or such like shall touch such or such markes that it shall be then such or such an houre of the day and so constantly to hould for all the yeare this obseruation is farre from truth and the principalls of Astronomie and may be easily contradicted by such which have but indifferent judgement in the Nature of shadowes and the Suns passages by the Meridians and verticall Circles of the Heavens for by how much greater the propinquitie of the Suns approchment is unto the Zenith or verticall point by so much the more shall the houre or time be various in one and the same Azimuth So in the last Pro. the Azimuth of the Sun the tenth of December at nine of the Clocke in the forenoone was found to be 40. gr and a halfe Exam and the Suns distance from the Zenith at that time was neere 84. gr 35. m Now admitte the Suns distance from the Zenith the tenth of Iune were but 32. gr 35. m the Sunne being in the same Azimuth the houre would be halfe an houre past 10. For the Index being layed to the houre of 9. in the Tropicke of ♑ which is the Suns parallel for the said tenth of December and it cutteth the Constru ¦ ctio 45 parallels of the Suns Motion in the inequalitie of time and so the complement of the former 32. gr 35. m in the Index meeteth with the Tropicke of ♋ which is the Suns parallel for the tenth of Iune in halfe an houre past 10. so that it evidently appeares that the shadow of a perpendicular thing on the tenth of December denoting the houre of the day to be 9. of the Clocke the same shadow the tenth of Iune shall represent halfe an houre past 10. so the error shall be an houre and a halfe but if you move the Index unto the houre of 9. belonging to the tenth of Iune the Index shall point you out in the Limbe neere 68. gr of Azimuth for that houre which at 9. of the Clocke the tenth of December was but 40. gr an halfe so the difference of Azimuth in one and the same houre shall be 27. gr and a halfe the time as before an houre and a halfe which differences are sufficient to confirme the point Tenthly to finde the Quarter of Pro. 36 the yeare and day of the month if it were forgotten Constru ¦ ctio 46 At any appearance of the Sun by the 27. Pro. take the Suns Altitude then place the North and South edge of the Instrument unto the Meridian line formerly drawne if in the forenoone otherwise place the East and West edge of Instrument to the Meridian-line and erect the prependicular at the end of the Index then moove the Index to and fro untill the shadow of the prependicular fall by the side of the Index so the parallel that meeteth with the degree of the Suns obserued Altitude in the edge of the Index parallel in the Kalender that shall shew the day of the Month required So if Exam. upon a certaine day in the yeare the suns Altitude were observed and found to be 36. gr having placed the edge of the Instrument to the Meridian line and rectified the Index then move the Index untill the shadow of the prependicular fall by the edge of the Instrument let the Instrument rest at this position and account the former 36. gr upon the Index which degree meeteth with the houre in the Aequator and also that intersecteth the Kalender in the tenth of March the thirteenth of September but which of these dayes is the day of the Month the next dayes obseruation of the Sun upon the same houre will helpe you for if the suns Altitude besound to be greater then the day of the month inquired after it was the tenth of March because the sun from the tenth of December unto the eleventh of Iune doth every day at one the same houre ascend but if the Suns Altitude be found to be
21. 19. 25. 24. 35. 2. 38. 37. 20. 41. and 42. as followeth The day of the Month knowne to finde 1. The houre of Sunne rising setting and length of the day 2. The Sunnes difference of Ascention 3. The Sunnes Declination 4. What dayes are alike in length and what day the Sunne rising in the one shall be the Sunne setting in the other 5. The Sunnes place or degree in the Eclipticke 6. The Sunnes right Ascention and oblique Ascention 7. The houre and Altitude of the Sunnes comming East or West 8. The distance of the Sunnes rising or setting from the East or West 9. The height or depression of the Sunne in the Meridian here or for any Latitude 10. The time of day breake and end of twylight 11. The inequality of time betweene day breake and Sunne rising 12. The houre and Altitude of the Sunnes comming upon any declining wall 13. At what houre and Altitude the Sun must have to be opposite or perpendicular to a declining wall First to finde the time of Sunne Pro. 1 rising or setting and length of the day for any day of the yeere Seeke the day of the Month in the Kalender Constru ¦ ctio 1 and the houre line that meeteth therewith sheweth the time of Sunne rising or setting So if the day of the Month were the 13. Exam. of October the parallell that meeteth therewith is the houre viz. 7. of the clocke at which time the Sun riseth the same houre is noted also with 5. which is the time of Sun setting that day this doubled makes 10. the length of the day required Secondly to finde the difference Pro. 2 of Ascention for any day of the yeere Marke what Meridian meeteth with the day Constru ¦ ctio 2 of the Month in the Kalender as suppose the day to be the former 13. of October which is the houre line of 7. and 5. as before and account the Numbers of Meridians to the houre of 6. so have you 15. gr or an houre which is the difference of Ascention for the 13. day of October required Pro. 3 Thirdly to finde the Sunnes declination for any day Constru ¦ ctio 3 Marke what parallell of Declination meeteth with the day of the Month in the Kalender and account how many degrees it is from the Equinoctiall so have you the Sunnes Declination for that day Exam. So if the day were the last of August the parallell that meeteth therewith is the 5th from the Equator and somuch is the Sunnes declination that day viz. 5. gr North declination Pro. 4 Fourthly to finde what dayes in the yeare are alike in length and what day the Sunne rising in the one shall be the Sunne setting in the other Constru ¦ ctio 4 For the first note that the dayes betweene the 10th of December and the 11th of Iune are dayes of Increase and the rest are dayes of Decrease Now right against any day of decrease in the Kalender is the day of increase which dayes are equall one to the other Exam. So the 19. day of May is against the 4. of Iuly at which time the Sunne riseth and setteth alike without sensible error viz. 4. of the clocke and therefore those dayes are of equall length and so of others For the second to finde what day the sunne rising in the one shall be the sunne setting in the other Admit the day to be the 18th of February and according to the first pro. finde the time of Sunne rising which is at 40. m. after 6. Exam. of the clocke Constru ¦ ctio 5 for that day and the setting 20. m after 5. then marke what day of the Month the houre line of 20 m after 5. in the forenoone meeteth with the Kalender which will be the 23. of August so the 18th day of February the Sun did set at the same houre that it did rise the 23. day of August Fiftly to finde the sunnes place or Pro. 5 degree for any day of the yeere Note where the parallel of the day of the Month crosseth the Eclipticke that is the Sunnes Constru ¦ ctio 6 place So the former parallell of the 13th of October meeteth with the Eclipticke in the beginning of ♠and ♓ but which of these is the Sunnes place the quarter of the yeare may easily tell you viz. ♠which is the Sunnes place or the degree in the Eclipticke for that day Pro. 6 Sixtly to finde the Sunnes right ascention and oblique ascention at any time Constru ¦ ctio 7 Consider what Meridean meeteth with the Sunnes place in the Eclipticke for the day given and marke the number of Meridians in the Equator for the Meridians are numbred in the Equator as is sayd before in the description so have you the Sunnes right Ascention but here note that the degrees in the Eclipticke are numbred forward and backeward in the Eclipticke unto 360. gr upon this Instrument so are the right Ascentions of those degrees also numbred forward and backward in the Aequator for the right ascention of any degree in the Eclipticke is that degree of the Aequator which is opposite unto it the succession of the signes considered so if the Sun were in the beginning of ♠the right Ascention is neere 208. degrees for the Meridian that passeth by the beginning of ♠is accounted in the Equator from ♈ and is within 6. m of 28. gr Now the right Ascention of ♋ is 90. gr and the beginning the of ♎ is 180. gr and from the beginning of ♎ to the beginning ♠is within 6. m of 28. gr as before all is which put together makes neere 208. gr the right Ascention of the Sun the 13th day of October To find the Sunnes Oblique Ascention at any time Note that the difference of Ascention is the Constru ¦ ctio 8 difference alwayes betweene the right Ascention of the Sun and the oblique Ascention thereof therfore the right Ascention known by the last directiō the difference of Ascention by the second direction the oblique Ascention is easily had by Addition or substraction thus If the Sun be in a Southerne signe then the oblique Ascention is greater then the right Ascention by so much as the difference of Ascention comes to but if the Sun be in a Northerne signe the oblique Ascention is so much lesse which difference of Ascention as before by the 2 Pro for the said 13th of October was 15. gr this ad unto the right Ascention of the beginning of ♠viz. 208. gr makes 223. gr the Suns oblique Ascention for the beginning of ♠on the 13th day of October but if the Sun had beene in the beginning of ♉ the oblique ascention would have beene onely neere 13. gr viz. 12. gr 54. m. Seventhly to find the suns Altitude Pro. 7 and houre of the suns comming East or West any day of the yeare above the Horizon Here note that this Proposition holds in use Constru ¦ ctio 9 onely for that time of the Suns being
in the Northerne signes that is from the 10th of March to the 13th of September therefore lay the Index to the East or Aequinoctiall point noted with E. or 40. 50. in the Limbe so have you instantly at once without farther rectification both the Altitude and houre of the Suns comming East or West above the Horizon for all or any of the dayes above specified so the parallel of any day of the Moneth meeting with the edge of the Index gives the Suns Altitude in the Index and the Meridian meeting therewith shewes the houre Exam. So if it were the second of May or the 22. of Iuly the parallel belonging to those daies meetes with the Index neere about 23. gr 17. m and there also meetes with that point the houre line of 7 and 5. which sheweth that when the Sun is 23. gr 17. m high either upon the second of May or the 22. of Iuly then the Sun will be due East or West and that will happen to be at 7 of the clocke in the forenoone and 5. of the clocke in the afternoone Pro. 8 Eightly to find the distance of the suns rising or setting any day of the yeare from the East or West called the suns Amplitude Constru ¦ ctio 12 Lay the Index to the day of the Moneth for the time given the edge of it in the Limbe of the Instrument shall shew the Amplitude required So if the day were the 13th Exam. of October the number of degrees from the points of East noted with 40. 50. unto the Index is 18. gr 40. m. which is the Suns Amplitude for the given day viz. the 13th day of October Ninthly to know the suns Meridionall Pro. 9 Altitude or the suns depression under the Horizon at Midnight here or in any Latitude for any day in the yeare Lay the Index unto the houre of 12 and where Constru ¦ ctio 11 the parallel of the day of the Moneth meeteth that therewith shal be the Suns Meridionall Altitude So if it were the 13th day of October as before Exam. the parallell for that day is 11. gr and a halfe from the Equator South this crosseth the Index in 27. gr which is the Sunnes Meridionall Altitude that day Now for the Sunnes depression at midnight here is to be noted that any degree of the Eclipticke is at any time so much below the Horizon as his opposite degree in the Eclipticke is above the Horizon at the same time Constru ¦ ctio 12 Therefore where the contrary parallell of the Sunne viz. 11. gr and a halfe North meeteth with the Index in the houre of 12. that shall bee the Sunnes Meridionall depression at midnight the said 13th day of October Pro. 10 Tenthly to finde the time of day-breake and end of twy-light with the Position of the sunne under the Horizon for any time This proposition hath reference to the Sunnes depression under the Horizon for it is said to bee day breake or twi-light to end when the Sun is 18. gr under the Horizon therefore the Construction in this will be thus Constru ¦ ctio 13 Account 18. gr on the Index then move the Index untill that degree meete with the Contrarie parallel of Declination for the day given so the Meridian or Houre-line that meeteth therewith shall bee the houre of day breake required Exam. So if the day were the 10. of Aprill the parallel of Declination for that day is North II. gr and a halfe which I seeke out one the other side of the Aequator viz. II. gr and a halfe South Declination and Marke where the 18th gr of the Index meeteth therewith for there also is the houre of day breake viz. with in 20. m. of 3. in the Morning and 20. m. past 9. for the end of twi-light the sayd 10th of Aprill also the Index in the Horizon at that Instant sheweth the position of the Sun under the Horizon viz. neere 48 gr 10. m. to the North of the East but if the day had beene the 13th of October the houre of daybreake had beene 2 minuts before 5. and twi-light would have ended 2. m. after 7. Eleventhly to finde the inequallitie Pro. 11 of time betweene day breake and Sun rising for any day of the yeare assigned By the first Construction for the dayes given Constructio 14 finde the time of Sun rising and by the former 13th Construction the houre and time of day breake belonging to those dayes then compare the time betweene the Sun rising and day breake of the one with that of the other so the difference of those two shall bee the difference of time required Example    H. M.  H. M.  So on the tenth of March the Sun rising is at 6. 00 The time betweene day breake and Sun rising is 2. 0 the difference is 12. m. day breake is at 4. 00 Docemb the Sun rising it at 8. 12 2. 12 day breake is at 6. 00 the difference is 1. ho. 22. m. May the Sun rising is at 4. 11 3. 34 day breake at 12 37 So the difference of time betweene day breake and Sunne rising the 10th of December is neere a quarter of an houre longer then that of the 10th of March but more then an houre and halfe longer betweene day breake and Sun rising the 10th of May then the 10th of March Pro. 12 Twelfely to finde the houre and Altitude of the sunnes comming upon a Declining wall any day of the yeare ☞ Seeing the declinations of Plaines or Walls are accounted from the points of East or West in the Horizon as the sunnes Amplitude is the numbering of them therefore shall bee alike in the Limbe of the Instrument Now admit the Declination of a Plaine or Wall to be 22. gr the opperation Constru ¦ ctio 15 would be thus The Index being set thereto you may instantly see at what houre the Sunne will come upon the Plaine for any day in the yeare for where the parallell of the day of the Moneth crosseth the Index amongst the houre-lines which Index represents the Plaine that is the houre of the Suns comming upon the Plaine and the degrees in the Index gives the Sunnes Altitude Examp. So if the Sunne were in the Tropicke of ♋ the Tropicke meeteth with the Index almost within 5 m. of 9 in the Morning and at that time the Sunne commeth upon the Plaine and there the Tropicke cuts also the Index in 45. gr 40. m. which is the suns Altitude at that time that the Sun wil glance or begin to shine upō the Plaine As for the time of the suns continuance on the Plaine as is specified in the Index or Table account the Declination on the other side of the East point and lay the Index thereto so the edge of it in the Tropicke of ♋ will point out at what houre the Sun goes of the Plaine viz. at 6. of the clock 38. m neere if the declination were West as here it
is supposed which added to the time of the suns coÌ„ming on the Plaine makes 9. houres 33. m so long the sun shines on the Plaine Thirteenthly to finde at what Pro. 13 houre and Altitude the sun must have to be opposite or perpendicular to a declining Plaine any day in the yeere Let a Plaine decline from the East point towards the South 22. Example gr account this in the Limbe Constru ¦ ctio 16 from the houre of 12. and lay the Index thereto so the parallell that crosseth the Index doth shew the Sunnes Altitude and the Meridian meeting therewith gives the houre at which time the Sun will be opposite to the Plaine so have you at one instant for every day in the yeare at what houre and Altitude the Sunne will bee opposite to the Plaine  gr m. As admit the dayes were these Decem. the tenth the Suns place at which time is in ♑ and the houre of the Suns being opposite to the plaine that day would be at 40-m past 1 and the Suns Altitude at that time would be 12.12 March ♈ 14 m. past 1. 36.25 Iune ♋ 48 m. past 12 60.45 Thus touching the resolution of the former 13 uses of the aforesaid Table or Index which had reference only to the knowledge of the day of the Month there are 13. other uses of the foresaid Index or Table viz. the 10. 12. 32. 39. 40. 23. 17. 16. 26. 27. 28. 29. 30. Which have no dependance upon the sight of the Sun of which the 6 first are resolued only by knowing the day of the Month and the other 7. are as followeth viz by knowing the day of the Month to finde 1. At what houre the shadow of an Altitude is equall double triple c. unto it 2. At any houre and Altitude of the Sun or Azimuth what proportion shadowes have to their bodies 3. The houre of the day agreeable to any Altitude or Azimuth 4. The Suns depression and Azimuth at any houre of the night Assigned 5. The houre of the day to our Antipodes by suposing the Suns Depression under the Horizon 6. At what houre in any day the Suns Azimuth and Altitude will be equall and how much the Altitude and Azimuth will be To finde 7. What number of dayes will make the day an houre longer or shorter at any time 8. Thâ— inequallitie of time in equall moneths or equall number of dayes 9. The degree of the Aequator in the Horizon by supposing any degree of the Eclipticke in the Horizon 10. The degree of the Eclipticke in the Horizon by supposing the degree of the Equator in the Horizon 11. The degree of Medium Coeli or the degree of the Eclipticke in the Meridian by supposing the degree of the Eclipticke in the Horizon vel contra 12. The Horoscope or the degree ascendant or descendâ—nt and the Nonagessima degree at any houre 13. What Angle the Eclipticke makes with the Horizon or the Altitude of the Nonagessima degree what Azimuth it is in at any houre First to finde the Proportion of Pro. 14 shadowes to their Altitudes at any time As if it were required the 20 of Aprill Declara ∣ tio at what houre of the day and how high the Sun must be either in the forenoone or afternoone that the shadow of a man or any Altitude shall be equall unto his height double triple quadruple Quintuple c. Constru ¦ ctio 17 Lay the Index unto the numbers in the line of shadowes viz. to 1. 2. 3. 4. 5. c. and wheresoever any of those divisions in the line of shadowes meete with the Index amongst the degrees there it sheweth what height the Sun must have to make the shadowes equall double triple c. to the Altitude Exam. So laying the Index upon 1 in the line of shadowes it meeteth with 45. gr in the Index so high the Sun must be to make the shadow of a man or any thing equall to his height upon an Horizontall plaine then move the Index to and fro untill the said 45. gr in the Index meete with the parallel of the day Month viz the 20. of April so the houre line that meeteth therewith is the houre of the day that the shadow of a Man or other Altitudes will be equall to his heigth or Altitude viz neere 10. of the Clocke in the forenoone or 2. of the Clocke in the afternoone      forenoone afternoone    gr m.  ho. m. ho. m. And according to the same directions when shadows are Double The Altitude would be 26. 33 and the houre the said 20. of Aprill would be 7. 37 4. 23 Triple 18. 26 6. 43 5. 17 Quadruple 14. 2 6. 16 5. 44 Quintuple 11. 19 5. 58 6. 02 Sextuple 9. 27 5. 46 6. 14 Septuple 8. 7 5. 37 6. 23 Octuple 7. 7 5. 31 6. 29 Nâ—nocuple 6. 20 5. 25 6. 35 Decuple 5. 43 5. 21 6. 39 Vigecuple 2. 51 5. 2 6. 58 Secondly to finde what proportion Pro. 15 shadowes have to their bodies at any houre in the day Azimuth or Altitude of the Sun asigned If the houre be knowne or supposed move the Constru ¦ ctio 18 Index until it meete with the houre in the parallel of the day of the Month so the intersection of that parallel with the Index is the suns Altitude and the edge of the Index in the Limbe wil shew the Suns Azimuth then move the Index until the degree of Altitude intersect the line of shadowes so shall you have the proportion of shadowes to their bodies required So if on the 11th of Aprill at 7. Exam. of the Clocke in the forenoone if the Sun shine it were required what proportion the shadow of a man shall beare to his height or the shadow of an Altitude to the Altitude the parallel that belongeth to the given day is neere 12. gr Marke where this parallel meeteth with the given houre of 7. and bring the Index to it so have you the Suns height at that houre viz 18. gr 26. m and the edge of the Index in the Limbe of the Instrument shall give the Azimuth viz 4. gr from the East then move the Index untill the degree of the Suns Altitude viz 18. gr 26. m meete with the line of shadowes which will be in 3 which sheweth that at 7. of the Clock in the forenone the said 11th of Aprill the shadow of a man or the shadow of an Altitude shall be Triple to his height the like will be at 5. of the Clocke in the afternoone for equall distances of the Sun from the Meridian the same day without sensible error will give equall Altitudes of the sun and equall Altitude of the sun doth produce equall shadowes upon Horizontall Plaines Constru ¦ ctio 19 Secondly if the Position or Azimuth of the Sun be knowne or supposed which admit 4 gr from the East towards the South Lay the Index unto it in the limbe
marke what degree in the Index the parallel meeteth with which is with 18. gr 26. m so have you the suns Altitude in the Index then move the Index until the degree meete with the Line of shadowes so have you the proportion of shadowes required at that instant viz Triple as before Constru ¦ ctio 20 Thirdly if the Suns height be knowne or supposed which admit 18. gr 26. m account it in the Index and moove the Index until that degree meete with the line of shadowes so where it intersecteth the line of the shadowes there you have the proportion of shadowes to their bodies at that instant of time required which will be triple as before so the 10th of Aprill if the houre be 7. or the Altitude 18. g. 26. m or the Azimuth 4. gr from the East toward the South the proportion of shadowes to their bodies will be Triple Thirdly to finde the houre of the Pro. 16 day agreeable to any Altitude or Azimuth for any day of the yeare Proposed For the first account the Suns Altitude in the Constru ¦ ctio 21 Index and move it to and fro untill that degree meete with the parallel of the day of the Month so the Meridian that passeth by that point shal be the houre required Thus if the day were the tenth of March Exam. the Sun being that day in the Aequinoctial the Altitude supposed to be 32. gr 37. m this I seeke out upon the Index and move the Index till that degree meete with the Aequator so the Meridian or houre Circle that passeth thereby is the houre viz. 10. of the Clocke in the forenoone or 2. of the Clocke in the afternoone and if you move the Index softly along as the degrees of the Suns Altitude in the Index intersect the Aequator and so of any parallel so the Meridian that meeteth therewith is the houre of the day agreeable to that Altitude For the second to finde the houre Constru ¦ ctio 22 of the day agreeable to any Azimuth As suppose it were 36. gr 35. m Exam. from the South Move the Index in the Limbe unto this Azimuth known or supposed so where the Index crosseth the parallel for the day given there the Meridian that meeteth therewith shewes the houre of the day viz 10. of the Clocke in the forenoone or 2 in the afternoone as before And if you move the Index softly along as the Index passeth by any Azimuth in the Limbe so the edge of the Index shall intersect the parallel of declination for the day of the Month in the houre of the day agreeable to that Azimuth by which proposition and the last Glasses may be easily placed to burne according to the Suns Azimuth or houre assigned Pro. 17 Fourthly to finde the suns depression position under the Horizon at any houre of the night with the houre of the day to our Antipodes by supposing the sun any number of degrees under the Horizon Constru ¦ ctio 23 By the 11th Construction it is said that any degree of the Eclipticke is asmuch belowe the Horizon at any time as his opposite degree is above the Horizon at the same time therefore if the Index be layed to the like parallel on the contrary side of the Aequator that meeteth with the given houre the intersection in the Index shall shew you the degree of the Suns depression under the Horizon at that houre So if at 10 of the Clocke at night the said 13th of October it were required to finde the Suns depression under the Horizon Exam. consider the declination or the suns parallel for that day which is 11. gr and a halfe South which declination I seeke in the other side of the Aequator and marke where it meeteth with the houre of 10. unto which I lay the Index so the edge thereof in the Limbe sheweth the suns Azimuth to be nere 42 gr 30. m from the South and the parallels intersection that meeteth with the Index gives the Suns depression viz. neere 43. gr and so much is the Sun below the Horizon and in that position the 13th of October at 10. of the Clocke at night But if it were required at what houre of the Night the Sun would touch the verticall Circle of East and West under the Horizon Lay the Index to the point of East and marke Constru ¦ ctio 24 where about the Contrary palleâ— meeteth with the Index for there you have both the houre and the degree of the suns depression So the day being as before the 13th of October Exam. the declination south 11. gr and a halfe this account amongâ—â— the North declinations it meeteth with the Index in 38 m past 6. the houre of the Suns being West and with all the suns depression at the same time is neere 14. gr and 50. m. Pro. 18 Fiftly to finde the houre of the day to our Antipodes by supposing the suns depression under the Horizon Constru ¦ ctio 25 Consider the declination for the day and move the Index to and fro untill the degree of the suns depression in the Index meeteth with the like parallel or the other side of the Aequator so the houre that meeteth therwith is the houre of the day to our Antipodes Exam. So if on the 20th of Aprill we should suppose the sun to be 13. gr under the Horizon desire to know the houre to our Antipodes the parallel of declention for that day is 15. gr North Now in the Index account 13. degrees and move it to and fro untill the said thirteenth degree in the Index meete with the 15th parallel of South declination so the Meridian that meeteth therewith is the houre of the day to our Antipodes within 2 m of 9. at night Pro. 19 Sixtly to finde at what houre in any day the suns Azimuch and Altitude will be equall and how much the Altitude and Azimuth will be Constru ∣ ction Move the Index to fro untill the edge of the Index meete with the parallel belonging to that day in the same Number of degrees that the end of the Index in the Limbe from the point of East doth so have you the degree of the Suns Azimuth and Altitude equall the one to the other and the Meridian meeting with the Index in the parallel of the given day sheweth at what houre that Azimuth and Altitude will be equall So admit the sun to be in the Tropicke of ♋ Exam the Index being moved to and fro untill there be like degrees in the Index and in the Limbe which will be neere 16. gr 45. m and there the houre that meeteth therewith is 12. m after 6. in the forenoon at which houre the eleventh of Iune the Suns Azimuth and Altitude will be equall viz. neere 16. gr 45. m as before Seventhly to finde what number Pro. 20 of dayes any time of the yeare will make the day an houre longer or shorter Account 7. gr and a halfe amongst
the Meridians Construc ¦ tio 27 from the given day in the Kallender and note the day of the Month against it then number the dayes betweene that day and the given day and you haue the answer So if the day were the last of February Exam. or the first of March consider the Suns setting that day by the Instrument which is 40. m past 5. this doubled makes the length of the day 11. houres 20. m then from the last of February account 7. gr and a halfe and it will point out the fifteenth of March at which time the Sun seteth at 10. m past 6 which doubled makes 12 houres 20. m so the fifteenth of March the length of the day is an houre longer then it was the first of March and the difference of time only but 15. dayes but if the number of daies were accounted to or from the Suns entring into the Tropicall points it will be more then 35. dayes before the day will be an houre longer or shorter Exam. So if from the tenth of Iune we should account 7. gr and a halfe amongst the Meridians from that Meridian that meeteth with the tenth of Iune it would fall out at the 16th day of Iuly at which time the day will be an houre shorter then it was the tenth of Iune and the intervall of time more then twise as much as the former viz. 39. dayes Pro. 21 Eightly to finde the inequalitie of time in equall Mounthes or equall number of dayes This proposition at the first seemes as a Paradox yet by this Instrument may easily be resolued and so consequently from Mathematicall principles demonstrated not onely the inequalitie of equall Months but also the inequalitie of Naturall dayes Now a day naturall according to the generall definition is one revolution of the Aequator or primum mobile that is from sun rising to sun rising or it is the time wherein the sun passeth by the Meridian and commeth to the Meridian againe commonly taken for 24. houres but be cause that in that intervale of time the sun passing from the Meridian and commeth to the Meridian againe the Sun moves according to his Naturall motion secundum antiquiorum traditionem neere a degree more or lesse therefore the Naturall day shall be some what longer or shorter then 24. houres viz. by so much as the difference of right ascention of that degree of the Eclipticke comes to that the sun is in and seeing the degrees of the Eclipticke amongst themselues have not the same difference of right Ascention that the other degrees have notwithstanding the degrees of the Eclipticke amongst themselves being equall the one to the other the suns motion ender those degrees being sometimes quicker and sometimes slower it will necessarily follow that the sun will move more or lesse untill the sun can touch the Meridian which is the limit or tearme of the suns diurnall revolution as before this difference and inequalitie of time in naturall dayes may by calculation be given from day to day but because it is so insensible little in a day hardly by an Instrument of this nature can be seene but by a number of dayes compared with another number of dayes it will evidently appeare So Exam. if it were required how much the Month of December is longer then the Month of March in the first of which months the suns motion is quicker being about the Perigeum then at other Constru ¦ ctio 28 times now both of which months have equal number of dayes viz. 31. Finde the right ascention for the beginning and ending of Mar. viz. 350.0 the difer of right ascention for the Month of Mar. is 29.30 the difference betweene these is 5. gr 19. 30. beginning and ending of Dece viz. 257. ¾ the difer of right ascention for the Month of Dece is 34. 30. 292. ¼ which 5. gr being conuerted into time by allowing 4 minits to a degree makes about 20. m and so much is the Month of December longer then the Month of March notwithstanding both of these Months containing equall number of dayes Pro. 22 Ninthly to finde the degree of the Aequator in the Horizon by suppossing the degree of the Eclipticke in the Horizon Notatio If the degree given be in the Northerne part of the Ecliptike the oblique Ascention is lesse then the Constru ¦ ctio 29 right Ascention vel contra Get therefore first the right Ascention of the point given by the sixt Pro. and the difference of Ascention by the 2. Pro. for that taken from the right Ascention gives the degree of the Aequinoctiall in the Horizon but if the given degree had beene in a Southren signe the difference of Ascention must be added to the right Ascention so have you the degree of the Aequator in the Horizon Tenthly to finde the degree of Pro. 23 the Eclipticke in the Horizon by supposing the degree of the Aequator in the Horizon This is but the Conuerse of the former onely Constru ¦ ctio 30 consider the correspondent quarters of the Aequinoctiall to these of the Eclipticke Eleventhly to finde the degree of Pro. 24 Medium Coeli or the degree of the Eclipticke in the Meridian by supp sing any degree of the Eclipticke in the Horizon Seeke the degree of the Aequator in the Horizon Constru ¦ ctio 31 by the 22. Pro. subtract 90. from it if the Number be too little adde a whole Circle to it then the degree of the Eclipticke opposite to the remainder is the Answer but note that if the remainder be betweene 270. and 360. the opposite point belongs to the last Quarter of the Ecliptike if the remainder be betweene 180. and 270. then it respects the 3 quarter of the Eclipticke if the remainder be betweene 90. and 180. it hath reference to the second Quarter c. But if the degree of the Eclipticke in the Horizon were required by knowing the degree of the in Eclipticke the Meridian This is onely but the converse of the former Constru ¦ ctio 23 is thus performed first seek the right Ascentiō of the given degree of Medium Coeli adde thereto 90. gr by accounting it from the former right Ascention note the suns place opposit therto for the difference of Ascention of this last degree being subtracted from the former degree of the Aequator in the Horizon if it be a degree of the Southren signes otherwise Adde gives the degree of the Eclipticke in the Horizon demanded Twelfthly to finde the Horoscope Pro. 25 or the degree Ascendant or descendant and the Nonagessima degree at any houre First note the right Ascention for the day given Constru ¦ ctio 33 according to the 6. Pro. which is the degree of the Aequator in the Meridian at 12. of the Clocke unto which degree adde 90. so have you the degree of the Aequator in the Horizon at 12. of the Clocke Then consider how many houres the given houres wants of 12. or is past 12.
which conuerted into measure and accounted Eastward or Westward according to the houre given from the former points of the Aequator in the Horizon at 12. will give the degree of the Aequator in the Horizon at the houre proposed then by the 23. Pro. I seeke out the degree of the Eclipticke in the Horizō answerable to the degree of the Aequator so have you the degree Ascendant from which account 90. gr or 3 signes so have you the degree of the Nonagessima point in the Horizon but if you reckon 6. signes from the Ascendant you have the desendant degree of the Eclipticke in the West of the Horizon Pro. 26 Thirteenthly to finde what Angle the Eclipticke makes with the Horizon or the Altitude of the Nonagessima degree of the Eclipticke above the Horizon and what Azimuth it is in at any houre According to the last Pro. sinde the degree Constru ¦ ctio 34 Ascendant and the Nonagessima degree then by the 24. Pro. finde what degree of the Eclipticke is in the Meridian Answerable to the degree of the Eclipticke in the Horizon so shall you know on which side of the Meridian the Nonagessima degree is how far from the Meridian then if that Index be layed upon the houre of 12 where the parallel of the Nonagessima degree crosseth it that should be the height of it if it were in the Meridian account therfore from the Meridian or houre of 12. in the Aequator the number of degrees betweene the Nonagessima degree and the degree of the Eclipticke in the Meridian marke where that Meridian meeteth with the parallel of the of the Nonagessima degree lay the Index thereto so have you the Altitude of the Nonagessima degree in the Index and the Azimuth in the Horizon or Limbe of the Instrument There are yet the 48. 49. 50. 9. 13. 14. and 15th uses of the said Index or Table which haue no relation to the suns sight or observation in there operation and resolutions and should have followed these 26. uses that have beene delivered but I referre them to the end of this Tractat as for these uses of the Instrument which depend upon the Suns sight or observation they are these 13. following viz. the 1. 31. 4. 6. 36. 7. 22. 3. 5. 34. 11. 43. and 8th viz. to shew 1. The Sun or starres Altitude above the Horizon at any time 2. The houre of the day and Azimuth of the sun 3. The Meridian Line upon any appearance of the Sun 4. The sit of a building or costing of a place 5. The Suns Azimuth and houre without Observation 6. The variation of the Needle 7. The Latitude of a place or height of the Pole above the Horizon 8. The Suns Azimuth and Altitude at any houre 9. The vncertainetie of time by noting the shadow of things 10. The Quarter of the yeare and day of the Month with the houre Azimuth and the Meridian line 11. Instantly the houre of the day the Azimuth and Altitude of the Sun with the Meridionall line without observation or sight of the Sun by knowing the Proportion betweene the length of a shadow upon a Horizontal Plaine and that which did cast the shadow 12. The Declination of a Wall by seeing the Sun beginning to shine thereon or going from it 13. The Declination of a Wall the Sun shining thereon First how to obserue the Sun or Pro. 27 starres Altitude above the Horizon at any time Lift up the edge of the Instrument to the eye Constru ¦ ctio 35 so that the sight which is at the Limbe or Circumference of the Quadrant be next the eye and the Index to hang perpendicular and to play easily by the side therof then move the Quadrant up and downe untill you may through both sights see the Center or midle of the Sun or starre so the Index in the Limbe shall fall upon the degrees of the Sun or starres Altitude above the Horizon at that time Or without looking at the sun the Altitude thereof may be thus found hould the Quadrant Constru ¦ ctio 36 that the Index may hang perpēdicular or be verticall as before then move about the Instrument untill the edge of it be opposite to the body of the Sun Now supposing the Instrument to hang thus upon his Center softly lift up the edge thereof which is towards the Sun untill you see the beames of the sun passe through both sights then the Index in the Limbe shall give the suns Altitude as before Pro. 28 Secondly how to finde the houre of the day and Azimuth of the Sun upon any appearance of the Sunne Constru ¦ ctio 37 By the last Pro. obserue or take the suns Altitude and account it on the Index then seeke for the parallel of the day of the Month for the day present move the Index untill that degree of Altitude in the edge of the Index meete with the parallel of the day so the Meridian that meeteth with that degree of Altitude in the Index shall be the houre of the day required the edge of the Index in the Limbe of the Instrument shall likewise shew the Suns Azimuth belonging to that houre So if upon the last of August the Suns Altitude in the forenoone should be obserued and found to be 30. Exam. gr a halfe seeke this Altitude out upon the Index move the Index untill the degree of Altitude meete with the parallel for the day of the Month given viz. the fift parallel from the Aequator Northward so the houreline that meeteth also with the 30. gr a halfe in the Index is the houre viz. neere 9. that shall be the houre of the day at that instant the edge of the Index in the Limbe cutteth neere 35. gr and 30. m from the point of East towards the South and so much is the Suns Azimuth at that time Thirdly how to finde the Meridian Pro. 29 line and the true points of North South East and West upon any appearance of the Sunne According to the 27. Pro. first obserue the Constru ¦ ctio 38 Suns Altitude above the Horizon and by the last Construction finde the Suns Azimuth agreeable to that Altitude let the Index and rest at that degree and erect the prependicular at the end of the Index then houlding the plaine or face of the Quadrant parallel to the Horizon move the Instrument Circular untill the shadow of the said perpendicular fall by the side of the Index and so the houerline of 12 or the edge of the Instrument which is parallel unto it which is the North and south edge of the Instrument shall represent the Meridian line and pointeth out the North and South in the Horizon of the world by the termes thereof and the other straight edge of the Instrument which is perpendicular unto that edge is the East and West edge of the Instrument and denoteth or sheweth the line of East and West in the
Horizon of the world But this may be more accurately done if you place the backe of the Instrument downe upon an Horizontall plaine and the edge of the Index being at the degree of the suns Azimuth observed and the perpendicular erected at the end of the Index as before then moving the Instrument as it so lyeth untill the shadow of the perpendicular fall by the side of the Index so the Meridian of the Instrument shall be in the Meridian of the World and every point and degree in the Limbe of the Instrument shall point out and be opposite and represent his like degree in the Horizon of the world Constru ¦ ctio 39 But here note that this Construction serves only but for the forenoone observation for if the practice be in the afternone the way to finde the Meridian line may be thus Having found the suns Azimuth as before lay the Index upon the houre line of 12. and erect the perpendicular at the end thereof and move the Instrument about Circular untill the shadow of the said perpendicular fall by the side of the Index for then if the edge of the Index be moved unto the suns Azimuth before known the edge of the Index shall represent the Meridian line 90. gr farther shall be the point of East and the Center of the Instrument the point of West therefore if upon the plaine that the Instrument lies upon you make a marke at the edge of the Index which is in the Meridian as before and another marke right under the Center and so place the North and South edge of the Instrument unto these two points then every degree in the Horizon or Limbe of the Instrument shall point out as before his opposite or â—ike degree in the Horizon of the world Fourthly how to finde the sit Pro. 30 of a Building or Costing of a place By the last Pro. finde out or draw the Meridian Constru ¦ ctio 40 line and place the North and South edge of the Instrument unto it if the Building or Place ly in the Easterne semicircle of the world but if it ly in the Westerne semicircle then let the East West edge of the Instrument be placed upon the Meridian line so the eye being over the Center of the Instrument and behoulding the place let the Index be moved untill it be also with the visual line observed by the eye that is opposite to the place so the edge of the Index from the Cardinall points of the Instrument in the Limbe viz. from the East or West North or South shall shew the bearing of that place from you in respect of the Cardinall points of the world in the Horizon but if two sights be placed at the Index which is according to the description thereof then may you observe the place through the sights of the Index by leting the Instrument rest and moving the Index to and fro untill you see the obiect so the edge of the Index in the limbe shall point out the bearing or Position of the place from you in degrees from the East West North or South accounting 11. gr and ¼ as often as you can in those degrees observed you have the point of the Compasse which the place or obiect beares from you Pro. 31 Fiftly to finde the suns Azimuth and houre without observation The Meridian line being drawne first upon a Constru ¦ ctio 41 plaine according to the former directions consider if it be in the forenoone or afternoone if in the forenoone then let the North and South edge of the Instrument be placed unto the Meridian line but if it be in the afternoone then set the edge of East West of the Instrument unto the Meridian line and let the Instrument rest there then erect the perpendicular at the end of the Index move the Index about untill the shadow of the perpendicular fall by the side of the Index so the edge of the Index will amongst the degrees in the Limbe shew the Suns Azimuth at that time and where the edge of the Index meeteth with the parallel of the day of the Month that is the houre of the day at that time But if the Axis be rectified then there is no neede of a Meridian line to be drawne for this Instrument will with great facilitie finde out his owne Meridian by moving it to and fro untill the shadow of the perpendicular which is ouer the Center of the Instrument intersect the same houre in the Parallel of the day of the Moneth that the Axis doth amongst the Common houres so that houre shall be the houre of the day for that instant and the shadow of the said perpendicular cutting the Limbe or extended unto it doth there shew the Suns Azimuth and so the Meridian of the Instrument at that position shal be in the Meridian of the world required Sixtly to finde the variation Pro. 32 of the needle By the twentie nineth Pro. vpon an even Plaine parallel to the Horizon draw the Meridian line Constru ¦ ctio 42 place the North South line of the Card directly over the said Meridian line so the Number of degrees that the Needle cutteth in the Card from the North and South line of the Card that shall be the variation of the Needle required otherwise it may be found thus Neere unto the Center of the Index upon the Index may a small Brosse pinne be so placed that it may be erected perpendicular to the Center of the Instrument and halfe an inch above it Let a Needle by placed upon this pinne then lay the East and West edge of the Instrument to the Meridian line when the Needle resteth move the Index untill the edge of it be directly under the Needle so the edge of the Index in the Limbe of the Instrument shall point out or shew the Needles variation required Pro. 33 Seventhly to finde the Latitude of a place or the Poles hight above the Horizon Constru ¦ ctio 43 First draw the Meridian line upon some plaine by helpe of the 38. Construction then erect the prependicular at the end of the Index and place the North and South edge of the Instrument to the Meridian line so drawne upon the plaine and move also the Index untill the edge thereof touch the houre of 12. let the Instrument rest at this position then marke diligently about noone or 12. of the Clocke when the shadow of the perpendicular doth fall by the edge of the Index for then the sun is in the Meridian at which time according to the 27. Pro. obserue or take the suns height which is his Meridian Altitude for that day and by the 3. Pro. finde the Suns declination agreeable to that day and adde it to the Suns Meridionall Altitude observe if it be South declination otherwise subtract it from the former Meridionall Altitude so have you the height of the Aequinoctial above the Horizon that taken from 90. gives the depression of
lesse then the former dayes observation specified was then the day required was the thirteenth of September because that from the eleventh of Iune unto the tenth of December the suns Altitude every day doth sensibly diminish at one and the same houre ☞ But here is to be noted that if there be no Meridionall line then the prependicular over the Constru ¦ ctio 47 Center and the Axis of the Index being erected place downe the backe of the Instrument upon an Horizontall plaine and move the Instrument to and fro untill the shadow of the Axis meete with the same houre below the Tropicke amongst the common houres that the shadow of the prependicular over the Center of the Instrument meeteth with on the face of the Instrument for then the parallel that crosseth or meeteth with the shadow of the prependicular and the houre will in the Kalender shew the day of the Month required and so then the Meridian of the Instrument shall be in the Meridian of the world and every point or degree in the Horizon of the Instrument it shall point out his like or opposite degree in the Horizon of the world Constru ¦ ctio 48 Or otherwise it may be done thus take the Suns Altitude then immediatly by some Watch clock or Sun-dyall learne the houre of the day and move the Index to and fro untill the Suns Altitude in the Index meete with the former houre so the parallel that meeteth therewith shall shew the day of the Month in the Kalender required then having the day of the Month you have the Quarter of the yeare for from the tenth of March unto the eleventh of Iune is the Spring quarter from the eleventh of Iune to the thirteenth of September is the Summer quarter from the thirteenth of September to the tenth of December is the Autummuall quarter and from the tenth of December unto the tenth of March is the Winter Quarter Eleuenthly to finde the houre of Pro. 37 the day the Azimuth and Altitude of the Sun with the Meridionall line without obseruation or sight of the sun by knowing the proportion betweene the length of a shadow upon a Horizontal Plaine and that which cast the shadow First let the thing that casteth the shadow or Constru ¦ ctio 59 something equall in length unto it be divided into ten equall parts and each of those parts subdived into ten other equall parts which thing so divided shal represent a common scale then measure the shadow with the scale and marke how often the shadow is longer then the scale and the Decimall part if there be any so have you the proportion betweene the shadow and that which did cast the shadow and then is it resolved accor to the conuerse of the fifteenth Pro. Exam. Admit some one upon the 12. of February or on the ninth of October houlding a staffe prependicular as A B or supposing it to be part of the Coyne of a House or edge of a Window or such like should cast a shadow as B C which being noted or drawne and having divided the staffe or thing as before and should then measure the shadow as B C by the said staffe or scale and finde it to be contained therein three times and 6 parts or 6 decimals the porportion of the Gnomon or scale A B to the shadow B C would be as 1 to 3. and 6 10. Construc ¦ tio 50 Move therefore the Index to and fro untill the edge of it meere with 3. and 6 10 in the line of shadowes so have you the degree of the Suns Altitude at that instant in the Index viz. 15. gr and ½ then seeke out the parallel for the 12. of February or the ninth of October the day given which is neere the tenth degree from the Aequator South move the Index until the former 15. gr and ½ in the Index meeteth with the said parallel for the day so have you the houre belonging to that time which will be neere 42 m past 8. in the Morning or 18. m past 3 in the after noone and the edge of the Index in the Limbe of the Instrument sheweth the suns Azimuth also at that instant viz neere 39. gr 12. m from the East toward the South Now for the Meridionall line this may be done Constru ¦ ctio 51 at any time after if the Azimuth be not forgotten for if the Center of the Instrument be layed downe upon any part of the shadow B C and so the Instrument to be mooved upon his Center untill the said shadow B C formerly drawne cut the edge of the Limbe in the aforesaid Azimuth of 39. gr 30. m then the Meridian of the Instrument shall be in the Meridian of the world and if that shadow were from a Window or Building the position of the Instrument shall denote the position of the Window or Building Twelfthly to finde the Declination Pro. 38 of a Wall by seeing the sun beginning to shine thereon or going from it By the 27. Pro. take the height of the Sun and Constru ¦ ctio 52 by the 28. Pro. finde the Suns Azimuth for the Altitude so the Azimuth thus found shall be the declination of the Plaine required for the declination of any perpendicular Plaine is accounted from the points of East West North or South in the Horizon as the Suns Azimuth is therefore whatsoever Plaine is in the plaine of any virticall Circle that Plaine is as far from any of the Cardinal points of the Horizon as the sun is at that time so the Sun being in that virticall Circle shall necessarily glance upon the Plaine and therefore looke what the Suns Azimuth is at that instant such shall be the Declination of the Plaine required Thirteenthly to finde the Declination Pro. 39 of a Plaine upon any appearance of the Sunne Thus for the Construction of the aforesaid 13. uses which did depend upon the suns observation the 48. 49. 50. 9. 13. 14. and 15th uses of the Index or Table against Page the first should have followed but before I speake of them it will not be inconvenient that I apply the Instrument unto the resolution of the 44. 45. 46. 47. uses of the aforesaid Index or Table which have reference to night observation upon such Starres which are or may be placed on the face of the Instrument betweene the two Tropickes or under the Tropicke of Cancer according to there Declinations and right Ascentions which are these following The names of the Stars Decli Rec The names of the stars Decli Rec. G. M. H. M. G.M. G.M. H. M G. M. Ex. Alae Pegasi 13.9 N. 23.54 1. 30. Coâ— Hydrae 7.5 A 9. 10. 42.45 pri ♈ â—1 40 N. 1.46 26. 30. Cor Leonis 13.45 B. 9. 48. 33.00 Oculus ♉ 15.42 N. 4.15 63.45 Cauda ♌ 16.38 B 11.30 7.26 pri singuli Ori. 0. 17. S. 5. 13. 78.15 Spica â™ 9. â—0 M. 13. 5. 16.15 Canis maior 16 1â— S. 6. 30. 82.15
But if from the said 7 houres and 24. m the said 6 houres 15. m be taken there will rest 1. houre 9. m and so much before 12. of the clocke at noone doth Oculus ♉ rise that is 51. m after 10 of the Clocke and so consequently if the said 7. houres and 24. m be added unto the houre of the starres being in the Meridian viz. 6. of the Clocke and 15. m as before the said starre will set at 39. m past 1 in the Morning Lastly if at any houre betweene the rising of the starre and the setting thereof it be required at what Position and Altitude the starre is in It is thus done Account to the given houre from the houre of the starre rising setting or being in the Meridian Constru ¦ ctio 56 in the parallel of the starres declination and lay the Index thereto so the edge of it in the Limbe of the Instrument shall shew the starres Azimuth or Position and where the parallel of the starres Declination crosseth the edge of the Index that shall be the starres Altitude at that houre So if on the said 6th of February at 11. Exam. of the Clocke at night it were required in what Position or Azimuth Oculus ♉ was in and also how high above the Horizon I make or suppose the houre of 12. to be the aforesaid 6. of the Clocke and 15. m for at that houre as before Oculus ♉ was in the Mridian and from thence in the stars parallel of Declination I account untill I come unto 11. of the Clocke viz. that is 4. houres and 45. m from 12. and lay the Index thereto so the edge of the Index in the Limbe pointeth out 4. gr 24. m and so farre Oculus ♉ is distant from the West at 11. of the Clocke at night and the parallel of the starres Declination meeteth with the Index in 24. gr neere which is the starres Altitude at that houre required Pro. 42 Thirdly to find in any night of the yeare in what part of the Horizon any of the starres on the instrument riseth or setteth and at what houre and Altitude a starre will be due East or West Constru ¦ ctio 57 For the first Marke where the parallel of the starres declination crosseth the Horizon or Kalender Lay the edge of the Index hereto so the number of degrees betweene the edge of the Index and the point of East or West upon the limbe of the Instrument sheweth the distance of the starres rising from the East or West So if it were required in what part of the Horizon Oculus ♉ riseth Exam. marke where the parallel of the stars Declination crosseth the Horizon and lay the edge of the Index thereto so it cutteth the Limbe of the Instrument from the East neere 26. gr and so farre Oculus ♉ riseth from the East towards the North. For the second to finde the time of a starres coming East or west By the 40th Pro. consider at what houre the star Constru ¦ ctio 58 is in the Meridian then lay the edge of the Index to the point of East and West and account in the parallel of the stars Declination the number of houres betweene the edge of the Index and the houre of 12. which being taken from the houre of the stars being in the Meridian gives the houre of the stars coming East but added unto the houre of the stars being in the Meridian shewes the houre of the stars being West So if it were demaunded at what houre Exam. upon the 6th of February Cor ♌ would be due East or West and what Altitude the starre should then have First lay the edge of the Index to the point of East and West wheresoever the parallel of the starres declination crosseth the edge of the Index that shall be the starres Altitude viz. neere 17. gr 45. m then account the number of houres in the parallel of the starres Declination betweene the edge of the Index and the houre of 12. which is neere 5. houres and 12. m which taken from the houre of the starres being in the Meridian which by the 40th Pro. was at 11. of the clocke 48. m at night rests 6 houres and 36. m but if the said 5. houres and 12. m be added unto the said 11. houres and 48. m it makes 17. houres from which 12. being taken leaves 5 houres So upon the 6th of February Cor ♌ shall be due East at 36. m past 6 at night and due West at 5 of the Clocke in the Morning and the Stars Altitude being either East or West is neere 17. gr 45. m as was required Pro. 43 Fourthly upon the sight or appearance of any of the aforesaid stars to finde the Azimuth thereof and the houre of the night By the 40th Pro. for the day given finde the Constru ¦ ctio 59 houre of the starres coming to the Meridâ—â— then by the 27. Pro. take the starres heigh◠〈◊〉 account that height in the Index the◠〈…〉 Index untill the degree of the starre◠〈…〉 the Index meete with the parall◠〈…〉 Declination so the edge of the 〈…〉 sheweth the starres Azimuth and the Meridian that meeteth with the degree of the Altitude in the Index shall shew you the houre that the starre wants to be in the Meridian or is past the Meridian which added or subtracted from the houre of the starres being in the Meridian gives the houre of the night required So if the day were the 26th of Iuly Exam. and if Aquila should be observed to be on the West of the Meridian 29. gr 20. m high above the Horizon this I seeke out upon the Index and move the Index to and fro untill the said 29. gr 20. m meete with the parallel of Declination of Aquila so the edge of the Index in the Limbe doth point out the starres Azimuth from the South viz. 63. gr 12. m and the Meridian that meeteth with the aforesaid degree of Altitude is the time of the starres distance from the Meridian viz. neere 3. houres and 28. m this added unto the houre of Aquilas being in the Meridian which by the 40th Pro. was at 10. of the Clocke 32. m at night makes 14. houres or 2 of the Clocke in the Morning so if Aquila were observed the 26th of Iuly to be 29. gr 20. m high to the West of the Meridian then the Position or Azimuth of that starre from the Meridian was 63. gr 12. m and the houre at that instant was at 2. of the Clocke in the Morning Thus touching the resolution of the aforesaid 44. 45. 46. and 47th Pro. of the aforesaid Index or Table which did belong to Astronomicall obseruations the last uses now follow viz. 48. 49. 50. 9. 13. 14. and 15th uses of the Index or Table which are onely proper to Geometricall Practices viz. to shew 1. How to measure the Quantitie of an Angle or to take the distance of two Starres 2. How to measure distances and