0.05401 Place required in the year 1674 compl 7.95678 CHAP. XV. Of the Theory of the Moon and the finding the place of her Apogaeon quantity of excentricity and middle motion THe Moon is a secondary Planet moving about the Earth as the Earth and other Planets do about the Sun and so not only the Earth but the whole System of the Moon is also carried about the Sun in a year And hence according to Hipparchus there arises a twofold but according to Tycho a three-fold Inequality in the Moons Motion The first is Periodical and is to be obtained after the same manner as was the excentrick AEquation of the Sun or Earth in order whereunto we will first shew how the place of her Apogaeon and excentricity may be found At Bononia in Italy whose Longitude is 13 degrees Eastward from the Meridian of London Ricciolus and others observed the apparent times of the middle of three lunar Eclipses to be as followeth The first 1642. April the 4. at 14 hours and 4 Minutes The second 1642 September 27 at 16 hours and 46 minutes The third 1643. September 17 at 7 hours and 31 Minutes The equal times reduced to the Meridian of London with the places of the Sun in these three observations according to Mr. Street in the 25 Page of his Astronomia Carolina are thus Anno Mens D. h. d. 1642. April 4. 13. 37. ♈ 25. 6. 54 1642. Septemb. 27. 15. 57 ♎ 14. 50. 09 1643. Sehtemb 17. 6. 46 ♎ 4. 20. 20 Hence the place of the Moon in the first observation is in ♎ 25. 6′ 54. in the second ♈ 14. 50. 9. in the third ♓ 4. 20. 20. Now then in Fig. 10. let the Circle BHDGFE denote the Moons AEquant T the Center of the Earth the Semidiameters TD TE and TF the apparent places of the Moon in the first second and third observations C the Center of the Excentrick CD CE and CF the Lines of middle motion From the first observation to the second there are 176 d. 2 h. 20′ The true motion of the Moon is deg 169. 43. 15″ The motion of the Apogaeon subtract 19. 37. 07 The motion of the true Anomaly is the arch DE 150. 06. 08 The motion of the mean Anomaly DCE 140. 42. 28 From the first observation to the third there are 530 d. 17 h. 9. The true motion of the Moon is degrees 159. 13. 26 The motion of the Apogaeon subtract 159. 07. 32 The motion of the true Anomaly is the Arch DF 100. 05. 54 The motion of the mean Anomaly DCF 93. 46. 45 And deducting the Arch DGF from the Arch DFE the remainer is the Arch FE 50. 00. 14 And deducting the Angle DCF from the Angle DCE the remainer is the Angle FCE 46. 55. 43 Suppose 10.00000000 the Logarithm of DC continue FC to H and with the other right Lines compleat the Diagram 1. In the Triangle DCH we have given the Angle DCH 86. 13. 15. the complement of DCF 93. 46. 45 to a Semicircle The Angle DHC 50. 02. 57. The half of the Arch DF and the side CD 1000000. To find CH. As the Sine of DHC 50. 02. 57 9.88456640 To the Side DC so the Sine of HDC 43. 43. 48. 19.83964197 To the Side CA 9.95507557 2 In the Triangle HCE we have given CH as before the Angle CHE 25. 00. 07. The half of the Arch FE the Angle HCE 133. 04. 17 the complement of FCE and by consequence the Angle CEH 21. 55. 36 To find the Side CE. As the Sine of CEH 21. 55. 36 9.57219707 To the Side CH 19.95507557 So is the Sine of CHE 25. 00. 07 9.62597986 To the Sine CE 19.58105543 10.00885836 3. In the Triangle DCE we have given DC CE and the Angle DCE 140. 42. 28. whose complement 39. 17. 32 is the Summ of the Angles to find the Angle CED and DE As the greater Side CE 10.00885836 Is to the lesser Side DC 10.00000000 So is the Radius 10.00000000 To the tang of 44. 24. 54 19.99114164 Which subtracted from 45. 2 the remainer is the half Difference of the acute angles 35. 16.  As the Radius To the tang of the com 35. 16 8.01109962 Is to the tang of the frac12 Z. 19. 38. 46 9.55265735 To the tang of frac12 X. 00. 12. 35 7.56375697 Their Sum 19. 51. 21. is the angle CDE  Their difference 19. 26. 11. is the angle CED  As the Sine of CED 19. 26. 11. 9.52216126 Is to the Sine of DCE 140. 42. 28. 9.80159290 So is the Side EC 10.00000000 To the Side DE. 10.27943164 4. In the Isosceles Triangle DTE we have given the Side DE the angle DTE 150. 06. 08 whose complement 29. 53. 52 is the Summ of the other two angles the half whereof is the angle TDE 14. 56. 56 which being subtracted from the angle CDE 19. 51. 21 the remainer is the angle CDT 4. 54. 25. As the Sine of DTE 150. 06. 08 Co. ar 0.30237482 Is to the Sine of DET 14. 56. 56 9.41154778 So is the Side DE 10.27943164 To the Side DT 9.99335424 5. In the Triangle CDT we have given DC DT and the angle CDT to find CTD and CT As the Side DT 9.99335424 Is to the Side DC 10.00000000 So is the Rad. 10.00000000 To the tang of 26. 18 10.00664576 Deduct 45. As the Radius Is to the Sine of the remainer 0. 26. 18. 7.88368672 So is the tang of the frac12 Z angle 87. 32. 57 11.36854996 To the tang frac12 X angle 10. 08. 04 9.25223668 Their Summ 97. 41. 01 is the angle CTD As the Sine of CTD 97. 41. 01. Co. ar 0.00391693 Is to the Side DC 10.00000000 So is the Sine of CDT 4. 54. 25 8.93215746 To the Side CT 8.93607439  s. d. The place of the Moon in the first Observation 6. 25. 06. 54 The true Anomaly CTD sub 3. 07. 41. 01 The place of the Apogaeon 3. 17. 25. 53 ☽ place in the first Observation 6. 25. 06. 54 The AEquation CDT Add. 04. 54. 25 The ☽ mean Longitude 7. 00. 01. 19 From which subtract the place of the Apogeon 3. 27. 25. 53 There rests the mean Anomaly BCD 3. 12. 35. 26 And for the excentricity in such parts as the Radius of the AEquant is 100000 the Proportion is DT 9.99335424 CT 8.93607439 100000 5.00000000 8764 3.94272015 And this is the Method for finding the place of the Moons Apogaeon and excentricity And from these and many other Eclipses as well Solar as Lunar Mr. Street limits the place of the ☽ Apogaeon to be at the time of the first observation 21′ 04″ more and the mean Anomaly 20. 41″ less and the excentricity 8765 such parts as the Radius of the AEquant is 100000. And by comparing sundry observations both antient and modern he collects the middle motion of the Moon from her Apogaeon to be in the space of four Julian years
rectified to the beginning of the Year of Mans Redemption 1601. The Names of the Stars Longit. Latit The first Star of Aries 07.671 ♈ 7. 8. N 4 The bright Star in the top of the head of Aries 00.583 ♉ 9. 57. N 3 The South Eye of Taurus 01.169 â— 5. 31. S 1 The North Eye of Taurus 00.801 â— 5. 31. S 1 The bright Star of the Pleiades 06.620 ♉ 2. 6. S 3 The higher head of Gemini 04.078 â— 4. 11. N 5 The lower head of Gemini 04.921 ♋ 10. 2. N 2 The bright foot of Gemini 01.069 ♋ 6. 38. N 2 In the South Arm of Cancer 02.238 ♌ 6. 48. S 2 The bright Star in the neck of Leo. 06.662 ♌ 5. 8. S 3 The heart of Leo. 06.745 ♌ â— 47 N 2 In the extream of the tail of Leo. 04.458 â™ 0. 26. N 1 In Virgo's Wing Vindemiatrix 01.217 ♎ 12. 18. N 1 Virgins Spike 05.074 ♎ 16. 15. N 3 South Ballance 02.643 â™ 1. 59. S 1 North Ballance 03.833 â™ 0. 26. N 2 The highest in the Forehead of Scorpio 07.388 â™ 8. 35. N 2 The Scorpions heart 01.171 â— 1. 05. N 3 Former of the 3 in the head of Sagittarius 02.203 â— 4. 27. S 1 Northern in the former horn of Capricorn 07.861 â— 1. 24. N 4 The left Shoulder of Aquarius 04.949 â™’ 7. 22. N 3 In the mouth of the South Fish 03.620 ♓ 8. 42. N 3 The Polar Star or last Star in the â—ail of the lesser Bear  9. 4. N 5  06.400 â— 66. 02. N 2 The last Star in the tail of the great Bear 05.888 â™ 54. 25. N 2 The Tonguâ— of the Dragon 05.259 â™ 76. 17. N 4 Arcturus in the skirt of his Garment 05.181 ♎ 31. 2. N 1 The bright Star of the North Crown 01.845 â™ 44. 23. N 2 The Head of Hercules 02.921 â— 37. 23. N â— The bright Sâ—â—r of the Hâ—rp 0â— 699 â— 61. 47. N â— The Head of Medusa 05.727 ♉ 22. 22. N 3 The bright Star in the Goaâ—s left Shoulder 04.518 ♊ 22. 50. N 1 The middle of the Serpâ—nts Neck 04.583 â™ 25. 35. N 2 The bright Star in the â—agles Shoulder 07.264 ♑ 29. 21. N 2 The bright Star in the 〈◊〉 Tail 02.370 â™’ 29. 8. N 3 The mouth of Pegasâ—s 07 3â—4 â™’ 22. 7. N 3 The head of Andâ—omeda 0â— 4â—0 ♈ â—5 42. N 2 In the top of the Triangle 00.366 ♉ 16. 49. N 4 In the Snout of the Whale 02.643 ♉ 7. 50. S The bright Star in the Whales Tail 07.481 ♓ 20. 47. S 2 Bright Shoulder of Orion 06.444 ♊ 16.06 S 2 Middlemost in the belt of Orion 04.972 ♊ 24. 33. S 2 The last in the tail of the Harâ— 0â— 324 ♊ 38. 26. S 4 The great Dogs mouth Sirius 02.386 â— 38. 30. S 1 The lesser Dog Procyon 05.641 â— 1â— 57 S 2 In the top of the Ships Stern 01.636 ♌ 43. 18. S 3 Brightest in Hydra's Heart 06.044 ♌ 22. 24. S 1 FINIS THE CONTENTS OF THE First Part CONTAINING The Practical Geometry or the Art of Surveying CHapter 1. Of the Definition and Division of Geometry Chap. 2. Of Figures in the General more particularly of a Circle and the Affections thereof Chap. 3. Of Triangles Chap. 4. Of Quadrangular and Multangular Figures Chap. 5. Solid Bodies Chap. 6. Of the measuring of Lines both Right and Circular Chap. 7. Of the measuring of a Circle Chap. 8. Of the measuring of plain Triangles Chap. 9. Of the measuring of Heights and Distances Chap. 10. Of the taking of Distances Chap. 11. How to take the Plot of a Field at one Station c. Chap. 12. How to take the Plot of a Wood Park or other Champian Plane c. Chap. 13. The Plot of a Field being taken by an Instrument how to compute the Content thereof in Acres Roods and Perches Chap. 14. How to take the Plot of mountainous and uneven Ground c. Chap. 15. To reduce Statute measure into Customary and the contrary Chap. 16 Of the measuring of solid Bodies Tables A Table of Squares Page 99 A Table for the Gauging of Wine Vessels 114 A Table for the Gauging of Beer and Ale Vessels 120 A Table shewing the third part of the Areas of Circles in Foot measure and Deoimal parts of a Foot 132 A Table shewing the third part of the Area of any Circle in Foot measure not exceeding 10 f. circumf 136 A Table for the speedy finding of the length or Circumference answering to any Arch in Degrees and Decimal parts 151 A Common Divisor for the speedy converting of the Table shewing the Areas of the Segments of a Circle whose Diameter is 2 c. 154 A Table shewing the Ordinates Arches and A reaâ— of the Segments of a Circle whose Diameter is 〈◊〉 c. 156 The Contents of the Second Part of this Treatise of the Doctrine of the PRIMUM MOBILE CHap. 1. Of the General Subject of Astronomy Chap. 2. Of the Distinctions and Affections of Spherical Lines and Arches Chap. 3. Of the kind and parts of Spherical Triangles and how to project the same upon the Plane of the Meridian Chap. 4. Of the solution of Spherical Triangles Chap. 5. Of such Spherical Problems as are of most general Vse in the Doctrine of the Primum Mobile c. The Contents of the Third Part of this Treatise being an Account of the Civil Year with the reason of the difference between the Julian and Gregorian Calendars and the manner of Computing the Places of the Sun and Moon CHap. 1. Of the Year Civil and Astronomical Chap. 2. Of the Cycle of the Moon what it is how placed in the Calendar and to what purpose Chap. 3. Of the use of the Golden Number in finding the Feast of Easter Chap. 4. Of the Reformation of the Calendar by Pope Gregory the Thirteenth c. Chap. 5. Of the Moons mean Motion and how the Anticipation of the New Moons may be discovered by the Epâ—â—â—ts Chap. 6. To find the Dominical Letter and Feast of Easter according to the Gregorian Account Chap. 7. How to reduce Sexagenary Numbers into Decimals and the contrary Chap. 8. Of the difference of Meridians Chap. 9. Of the Theory of the Suns or Earths motion Chap 10. Of the finding of the Suns Apogaeon quantity of Excentricity and middle Motion Chap. 11. Of the quantity of the tropical and sydereal Year Chap. 12. Of the Suns mean Motion otherwise stated Chap. 13. How to calculate the Suns true place by either of the Tables of 〈◊〉 middle Motion I 〈…〉 Chap. 14. To find the place of the fixed Stars Chap. 15. Of the Theory of the Moon and the finding the place of her Apogaeon quantity of Excentricity and middle motion Chap. 16. Of the finding of the place and motion of the Moons Nodes Chap. 17. How to calculate the Moons true place in her Orbs. Chap. 18. To compute the true Latitude of the Moon and
Watry part of this Globe may be also distinguished by diverse Names as Seas Rivers Ponds Lakes and such like 11. And this Terrestrial Globe may be measured either in whole or in any particular part 12. The measure of this Earthly Globe in whole is either in respect of its circumference â—o its bulk and thickness 13. For the measuring of the Earths circumference it is supposed to be compassed with a great Circle and this Circle in imitation of Astronomers is divided into 360 degrees or parts and each degree is supposed to be equal to 15 common German miles or 60 miles with us in England and hence the circumference of the Earth is found by multiplying 360 by 15 to be 5400 German miles or multiplying 360 by 60 the circumference is 21600 English miles 14. The circumference of the Earth being thus obtained the Diameter may be found by the common proportion between the Circumference and the Diameter of a Circle the which according to Archimedes is as 22 to 7 or according to Van Culen as 1 to 3. 14159. and to bring an Unite in the first place As the circumference 3. 14159. is to 1 the Diameter so is 1 the circumference to 318308 the Diameter which being multiplied by 5400 the Earths Diameter will be found to be 1718 German miles and 8632 parts but being multiplied by 21600 the Diameter will be 6875 English miles and parts 4528. 15. The measure of the Earth being thus found in respect of its whole circumference and Diameter that which is next to be considered is the distinction of it into convenient spaces 16. And this is either Primary or Secondary 17. The Primary distinction of the Earthly Globe into convenient spaces is by Circles considered absolutely in themselves dividing the Globe into several parts without any reference to one another Dutch Geographer inclines much to the bringing back the great Meridian to the Fortunate Islands more particularly to the Peak a Mountain so called from the sharpness in the top in the Isle Teneriff which is believed to be the highest Mountain in the World therefore the same Iohnson in his greatest Globe of the year 1616 hath drawn the great Meridian in that place and it were to be wished that this might be made the common and unchangeable practice 25. The Horizon is a great Circle designing so great a Part of the Earth as a quick sight can discern in an open field it is twofold Rational and Sensible 26. The Rational Horizon is that which is supposed to pass through the Center of the Earth and is represented by the wooden Circle in the Frame as well of the Celestial as the Terrestrial Globe this Rational Horizon belongeth more to Astronomy than Geography 27. The Sensible Horizon is that before defined the use of it is to discern the divers risings and settings of the Stars in divers places of the Earth and why the days are sometimes longer and sometimes shorter 28. The great but less principal Circle upon the Terrestrial Globe is the Zodiack in which the Sun doth always move This Circle is described upon Globes and Maps for ornament sake and to discover under what part of the Zodiack the several Nations lie 29. The lesser Circles are those which do not divide the Terrestial Globe into two equal but into two unequal Parts and these by a general name are called Parallels or Circles aequidistant from the Equinoctial of which as many may be drawn as there can Meridians namely 180 if but to each degree but they are usually drawn to every ten Degrees in each Quadrant from the AEquator to the Poles 30. These Parallels are not of the same Magnitude but are less and less as they are nearer and nearer to each Pole and their use is to distinguish the Zones Climates and Latitudes of all Countries with the length of the Day and Night in any Part of the World 31. Again a Parallel is either named or unnamed 32. An unnamed Parallel is that which is drawn with small black Circular Lines 33. A named Parallel is that which is drawn upon the Globe with a more full ruddy and circular Line such as are the Tropicks of Cancer and Capricorn with the Arctick and Antarctick Circles of which having spoken before in the general description of the Globe there is no need of adding more concerning them now CHAP. II. Of the Distinction or Dimension of the Earthly Globe by Zones and Climates HAving shewed the primary distinction of the Globe into convenient spaces by Circles considered absolutely in themselves we come now to consider the secondary Dimension or distinction of convenient spaces in the Globe by the same Circles compared with one another and by the spaces contained between those Circles 2. This secundary Dimension or Distinction of the terrestial Globe into Parts is either a Zone or a Clime 3. A Zone is a space of the Terrestial Globe included either between two of the lesser nominated Circles or between one and either Pole They are in Number five one over hot two over cold and two temperate 4. The over hot or Torrid Zone is between the two Tropicks continually scorched with the presence of the Sun 5. The two over cold or Frigid Zones are scituated between the two polar Circles and the very Poles continually wanting the neighbour hood of the Sun 6. The two temperate Zones are one of them between the Tropick of Cancer and the Arctick Circles and the other between the Tropick of Capricorn and the Antarctick Circle enjoyning an indifferency between Heat and Cold so that the parts next the Torrid Zone are the hotter and the parts next the Frigid Zone are the Colder 7. The Inhabitants of these Zones in respect of the diversity of their noon Shadows are divided into three kinds Amphiscii Heteroscii and Periscii Those that inhabit between the two Tropicks are called Amphiscii because that their noon Shadows are diversly cast sometimes towards the South as when the Sun is more Northward than their vertical point and sometimes towards the North as when the Sun declines Southward from the Zenith Those that live between the Tropick of Cancer and the Arctick Circle or between the Tropick of Capricorn and the Antarctick Circle are â—alled Heteroscii because the Shadows at noon are cast one only way and that either North or South They that inhabit Northward of the Tropick of Cancer have their Shadows always towards the North and they that inhabit Southward of the Tropick of Capricorn have their noon Shadows always towards the South Those that inhabit between the Poles and the Arctick or Antarctick Circles are called Periscii because that their Gnomons do cast their Shadows circulary and the reason hereof is for that the Sun is carried round about above their Horizon in his whole diurnal revolution 8. The next secundary Dimension or distinction of the earthy Globe into convenient parts or spaces is by Climes 9. And a Clime or Climate is a space of
Earth conteined between three Paralells the middlemo◠whereof divideth it into two equal parts serving for the setting out the length and shortness of the days in every Country 10. These Climates and the Parallels by which they are conteined are none of them of equal quantity for the first Clime as also the Parallel beginning at the AEquator is larger than the second and the second is likewise greater than the third 11. The Antients reckoned but seven Climates at the first to which Number there were afterward added two more so that in the first of these Numbers were comprehended fourteen parallels but in the latter eighteen 12. Ptolemy accounted the Paralells 38 each way from the Equator that is 38 towards the North and as many towards the South 24 of which he reckoned by the difference of one quarter of an hour 4 by the difference of half an hour 4 by an whole hours difference and 6 by a Months difference but now the parallels being reckoned by the difference of a quarter of an hour the Climates are 24 in Number till you come to the Latitude of 66 degrees 31 Minutes to which are afterwards added 6 Climates more unto the Pole it self where the Artificial day is 6 Months in length 13. The distances of all both Climates and Parallels together with their Latitudes from the AEquator and difference of the quantity of the longest days are here fully exprest in the Table following A Table of the Climates belonging to the three sorts of Inhabitants Inhabitants belonging to the several Climes Climes Paralells Length of the Day Poles Elevation Bea of the Clime   0 12.0 0.0   0    4.18   1 12.15 4.18    2 12.30 8.34   1    8.25 Amphiscii  3 12.45 12.43    4 13.0 16.43   2    7.50   5 13.15 20.33    6 13.30 23.10   3    7.3   7 13.45 27.36    8 14.0 30.47   4    6.9   9 14.15 33.45    10 14.30 36.30   5    5.17   11 14.45 39.02    12 15.0 41.22   6    4.30   13 15.15 43.32    14 15.30 45.29   7    3.48   15 15.45 47.20    16 16.0 49.21   8    3.13   17 16.15 50.13    18 16.30 51.58   9    2.44   19 15.45 53.17   Climes Paralells Length of the Days Poles Elevation Breadth of the Clime   20 17.00 54.29   10    2.17 Heteroscii  21 17.15 55.34    22 17.30 56.37   11    2.0   23 17.45 57.34    24 18.00 58.26   12    1.40   25 18.15 59.14    26 18.30 59.59   13    1.26   27 18.45 60.40    28 19.00 61.18   14    1.13   29 19.15 61.53    30 19.30 62.25   15    1.0   31 19.45 62.54    32 20.00 63.22   16    0.52   33 20.15 63.46    34 20.30 64.06   17    0.44   35 20.45 64.30    36 21.00 64.49   18    0.36   37 21.15 65.06    38 21.30 65.21   19    0.29   39 21.45 65.35    40 22.00 65.47   20    0.22   41 22.15 65.57    42 22.30 66.00   21    0.17   43 22.45 66.14  Clime Paralells Length of the Day Poles Elevation Breadth of the Clime   44 23.00 66.20   22    0.11   45 23.15 66.25    46 23.30 66.28   23    0.5   47 23.45 66.30   24 48 24.00 66.31 0.0 Periscii Here the Climates begin to be accounted by Months from 66. 31 where the day is 24 hours long unto the Pole it self where it is 6 Months in length 1 67.15 2 69.30 3 73.20 4 78.20 5 84.0 6 90.0 14. Hitherto we have considered the inhabitants of the Earth in respect of the several Zones and Climes into which the whole Globe is divided there is yet another distinction behind into which the inhabitants of the Earth are divided in respect of their site and position in reference to one another and thus the inhabitants of the Earth are divided into the Perioeci Antoec◠and Antipodes 15. The Perioeci are such as dwell in the same Parallel on the same side of the AEquator how far distant soever they be East and West the season of the year and the length of the days being to both alike only the midnight of the one is the moon to the other 16. The Antoeci are such as dwell under the same Meridian and in the same Latitude or Parallel distance from the AEquator the one Northward and the other Southward the days in both places being of the same length but differ in the Seasons of the year for when it is Summer in the one it is Winter in the other 17. The Antipodes are such as dwell Feet to Feet so as a right Line drawn from the one unto the other passeth from North to South through the Center of the World These are distant 180 degrees or half the compass of the Earth they differ in all things as Seasons of the year length of days rising and setting of the Sun and such like A matter reckoned so ridiculous and impossible in former times that Boniface Arch-Bishop of Mentz seeing a Treatise concerning these Antipodes written by Virgilius Bishop of Salisburg and not knowing what damnable Doctrine might be couched under that strange Name made complaint first to the Duke of Bohemia and after to Pope Zachary Anno 745 by whom the poor Bishop unfortunate only in being learned in such a time of Ignorance was condemned of Heresie but God hath blest this latter age of the World with more understanding whereby we clearly see those things which either were unknown or but blindly guessed at by the Antients 18. The second part of the Terrestial Globe is the Water which is commonly divided into these parts or distinguished by these Names Oceanus Mare Fretum Sinus Lacus and Flumen 19. And first Oceanus or the Ocean is that general Collection of all Waters which encompasseth the Earth on every side 20. Mare the Sea is a part of the main Ocean to which we cannot come but through some Fretum or Strait as Mare