must look upon it as it stands divided into Arabia Deserta 2. Arabia Petraea 3. Arabia Felix and 4. The Arabick Islands Chaldea Chaldea is bounded on the East with Susiana a Province of Persia on the West with Arabia deserta on the North with Mesopotamia and on the South with the Persian Bay and the rest of Deserta Assyria Assyria is bounded on the East with Media from which it is parted by the Mountain called Coathras on the West with Mesopotamia from which it is divided by the River Tygris on the South with Susiana and on the North with some part of Turcomania it was antiently divided into six parts 1. Arraphachitis 2. Adiabene 3. Calacine 4. Aobelites 5. Apolloniates Mesopotamia Mesopotamia is bounded on the East with the River Tygris by which it is parted from Assyria on the West with Euphrates which divides it from Comagena a Province of Syria on the North with Mount Taurus by which it is separated from Armenia major and on the South with Chaldea and Arabia deserta from which last it is parted by the bendings of Euphrates also It was antiently divided into 1. Anthemasia 2. Chalcitis 3. Caulanitis 4. Acchabene 5. Ancorabitis and 6. Ingine Turcomania Turcomania is bounded on the East with Media and the Caspian Sea on the West with the Euxine Sea Cappadocia and Armenia minor on the North with Tartary and on the South with Mesopotamia and Assyria A Countrey which consisteth of four Provinces 1. Armenia major or Turcomania properly and specially so called 2. Colchis 3. Iberia 4. Albania Media Media is bounded on the East with Parthia and some part of Otyrcania Provinces of the Persian Empire on the West with Armenia major and some part of Assyria on the North with the Caspian Sea and those parts of Armenia major which now pass in the account of Iberia Georgia and on the South with Persia. It is now divided into two Provinces 1. Atropatia 2. Media major Persia. Persia is bounded on the East with India on the West with Media Assyria and Chaldea on the North with Tartary on the South with the main Ocean It is divided into the particular Provinces of 1. Susiana 2. Persis 3. Ormur 4. Carmania 5. Gedrosia 6. Drangiana 7. Arachosia 8. Paropamisus 9. Aria 10. Parthia 11. Hyrcania 12. Margiana and 13. Bactria Tartaria Tartaria is bounded on the East with China the Oriental Ocean and the Straits of Anian by which it is parted from America on the West with Russia and Podolia a Province of the Realm of Poland on the North with the main Scythick or frozen Ocean and on the South with part of China from which it is separated by a mighty Wall some part of India the River Oxus parting it from Bactria and Margiana two Persian Provinces the Caspian Sea which separates it from Media and Hyrcania the Caucasian Mountains interposing between it and Turcomania and the Euxine Sea which divideth it from Anatolia and Thrace It reacheth from the 50 degree of Longitude to the 195 which is 145 degrees from West to East and from the 40 degree of Northern Latitude unto the 80 which is within 10 degrees of the Pole it self By which accompt it lieth from the beginning of the sixth Clime where the longest day in Summer is 15 hours till they cease measuring the Climates the longest day in the most Northen parts hereof being full six Months and in the winter half of the Year the night as long It is now divided into these five parts 1. Tartaria Precopensis 2. Asiatica 3. Antiqua 4. Zagathay 5. Cathay China China is bounded on the North with Altay and the Eastern Tartars from which it is separated by a continued Chain of Hills part of those of Ararat and where that chain is broken off or interrupted with a great wall extended 400 Leagues in length on the South partly with Cauchin China a Province of India partly with the Ocean on the East with the oriental Ocean and on the West with part of India and Cathay It reacheth from the 130 to the 160 degree of Longitude and from the Tropick of Cancer to the 53 degree of Latitude so that it lieth under all the Climes from the third to the ninth inclusively The longest summers day in the southern parts being 13 hours and 40 Minutes increased in the most northern parts to 16 hours and 3 quarters It containeth no fewer than 15 Provinces 1. Canton 2. Foquien 3. Olam 4. Sisnam 5. Tolenchia 6. Causay 7. Minchian 8. Ochian 9. Honan 10. Pagnia 11. Taitan 12. Quinchen 13. Chagnian 14. Susnan 15. Cunisay Besides the provinces of Suehuen the Island of Chorea and the Island of Cheaxan India India is bounded on the East with the Oriental Ocean and some part of China on the West with the Persian Empire on the North with some Branches of Mount Taurus which divide it from Tartary on the South with the Indian Ocean Extended from 106 to 159 degrees of Longitude and from the AEquator to the 44th degree of Northern Latitude by which account it lieth from the beginning of the first to the end of the sixth Clime the longest Summers day in the southern Parts being 12 hours onely and in the parts most North 15 hours and a half The whole Country is divided into two main parts India intra Gangem and India extra Gangem The Oriental Islands The Oriental Islands are 1. Iapan 2. The Philippine and Isles adjoyning 3. The Islands of Bantam 4. The Moluccoes 5. Those called Sinda or the Celebes 6. Iava 7. Borneo 8. Sumatra 9. Ceilan and 10. others of less note CHAP. V. Of Africk AFrick is bounded on the East by the Red Sea and Bay of Arabia by which it is parted from Asia on the West by the main Atlantick Oceans interposing between it and America on the North by the Mediterranean Sea which divides it from Europe and Anatolia and on the South with the AEthiopick Ocean separating it from Terra Australis incognita or the southern continent parted from all the rest of the World except Asia only to which it is joyned by a narrow Isthmus not above 60 miles in length It is situate for the most part under the Torrid Zones the AEquator crossing it almost in the midst It is now commonly divided into these seven parts 1. AEgypt 2. Barbary or the Roman Africk 3. Numidia 4. Lybia 5. Terra Nigritarum 6. AEthiopia superior and 7. AEthiopia rinferior AEgypt AEgypt is bounded on the East with Idumea and the Bay of Arabia on the West with Barbary Numidia and part of Lybia on the North with the Mediterranean Sea on the South with AEthiopia superior or the Abyssyn Emperor it is situate under the second and fifth Climates so that the longest day in Summer is but thirteen hours and a half Barbary Barbary is bounded on the East with Cyrenaica on the West with the Atlantick Ocean on the North with the Mediterranean Sea the Straits of
to reduce her place from her Orbit to the Ecliptick Chap. 19. To find the mean Conjunctions and Opposition of the Sun and Moon The Fourth Part or an Introduction to Geography CHap. 1. Of the Nature and Division of Geography Chap. 2. Of the Distinction or Dimension of the Earthly Globe by Zones and Climates Chap. 3. Of Europe Chap. 4. Of Asia Chap. 5. Of Africk Chap. 6. Of America Chap. 7. Of the description of the Terrestrial Globe by Maps Vniversal and Particular A Table of the view of the most notable Epochas The Iulian Calendar Page 461 The Gregorian Calendar 466 A Table to convert Sexagenary Degrees and Minutes into Decimals and the contrary 476 A Table converting hours and minutes into degrees and minutes of the AEquator 480 A Table of the Longitudes and Latitudes of some of the most eminent Cities and Towns in England and Ireland 482 A Table of the Suns mean Longitude and Anomaly in both AEgyptian and Iulian Years Months Days Hours and Minutes 484 Tables of the Moons mean motion 493 A Catalogue of some of the most notable fixed Stars according to the observation of Tycho Brahe rectified to the year 1601. 511 Books Printed for and sold by Thomas Passinger at the Three Bibles on the middle of London-Bridge THe Elements of the Mathematical Art commonly called Algebra expounded in four Books by Iohn Kersey in two Vol. fol. A mirror or Looking-glass for Saints and Sinners shewing the Justice of God on the one and his Mercy towards the other set forth in some thousands of Examples by Sam. Clark in two Vol. fol. The Mariners Magazine by Capt. Sam. Sturmy fol. Military and Maritime Discipline in three Books by Capt. Tho. Kent fol. Dr. Cudworth's universal Systeme The Triumphs of Gods Revenge against the Crying and Execrable sin of wilful and premeditated Murther by Iohn Reynolds fol. Royal and Practical Chymistry by Oswaldus Crollius and Iohn Hartman faithfully rendred into English fol. Practical Navigation by Iohn Seller Quarto The History of the Church of Great Britain from the Birth of our Saviour until the Year of our Lord 1667. quarto The Ecclesiastical History of France from the first plantation of Christianity there unto this time quarto The book of Architecture by Andrea Palladio quarto The mirror of Architecture or the ground Rules of the Art of Building by Vincent Scammozi quarto Trigonometry on the Doctrine of Triangles by Rich. Norwood quarto Markham's Master-piece Revived containing all knowledge belonging to the Smith Farrier or Horse-Leach touching the curing of all Diseases in Horses quarto Collins Sector on a Quadrant quarto The famous History of the destruction of Troy in three books quarto Safeguard of Sailers quarto Norwood's Seamans Companion quarto Geometrical Seaman quarto A plain and familiar Exposition of the Ten Commandments by Iohn Dod quarto The Mariners new Calendar quarto The Seamans Calendar quarto The Seamans Practice quarto The honour of Chivalry do the famous and delectable History of Don Belianus of Greece quarto The History of Amadis de Gaul the fifth part quarto The Seamans Dictionary quarto The complete Canonier quarto Seamans Glass quarto Complete Shipwright quarto The History of Valentine and Orson quarto The Complete Modellist quarto The Boat-swains Art quarto Pilots Sea-mirror quarto The famous History of Montelion Knight of the Oracle quarto The History of Palladine of England quarto The History of Cleocretron and Cloriâ—ma quarto The Arralgnment of lower idle froward and unconstant Women quarto The pleasant History of Iack of Newbâ—â—y quarto Philips Mathematical Manual Octavo A prospect of Heaven or a Treatise of the happiness of the Saints in Glory oct Etymologicunt parvum oct Thesaurus Astrologiae or an Astrological Treasury by Iohn Gadbury oct Gellibrand ' s Epitome oct The English Academy or a brief Introduction to the seven Liberal Arts by Iohn Newton D. D. oct The best exercise for Christians in the worst times by I. H. oct A seasonable discourse of the right use and abuse of Reason in matters of Religion oct The Mariners Compass rectified oct Norwood ' s Epitome oct Chymical Essays by Iohn Beguinus oct A spiritual Antidote against sinful Contagions by Tho. Doolittle oct Monastieon Fevershamiense or a description of the Abby of Feversham oct Scarborough ' s Spaw oct French Schoolmaster oct The Poems of Ben. Iohnson junior oct A book of Knowledge in three parts oct The Book of Palmestry oct Farnaby ' s Epigramms oct The Huswifes Companion and the Husbandmans Guide oct Jovial Garland oct Cocker ' s Arithmetick twelves The Path Way to Health twelves Hall ' s Soliloquies twelves The Complete Servant Maid or the young Maidens Tutor twelves Newton's Introduction to the Art of Logick twelves Newton's Introduction to the Art of Rhetorick twelves The Anatomy of Popery or a Catalogue of Popish errors in Doctrine and corruptions in Worship twelves The famous History of the five wise Philosophers containing the Life of Iehosophat the Hermit twelves The exact Constable with his Original and Power in all cases belonging to his Office twelves The Complete Academy or a Nursery of Complements twelves Heart salve for a wounded Soul and Eye salve for a blind World by Tho. Calvert twelves Pilgrims Port or the weary mans rest in the Grave twelves Christian Devotion or a manual of Prayers twelves The Mariners divine Mate twelves At Cherry Garden Stairs on Rotherhith Wall are taught these Mathematical Sciences viz. Arithmetick Algebra Geometry Trigonometry Surveying Navigation Dyalling Astronomy Gauging Gunnery and Fortification The use of the Globes and other Mathematical Instruments the projection of the Sphere on any circle c. He maketh and selleth all sorts of Mathematical Instruments in Wood and Brass for Sea and Land with Books to shew the use of them Where you may have all sorts of Maps Plats Sea-Charts in Plain and Mercator on reasonable Terms By Iames Atkinson FINIS
from one another a full part of time or an hour for seeing that the Sun is carried 15 Degrees of the Equinoctial every hour the Meridians set at that distance must make an hours difference in the rising or setting of the Sun in those places which differ 15 Degrees in Longitude And to this purpose also upon the North end of the Globe without the Brass Meridian there is a small Circle of Brass set and divided into two equal parts and each of them into twelve that is twenty four all to shew the hour of the Day and Night in any place where the Day and Night exceed not 24 hours for which purpose it hath a little Brass Pin turning about upon the Pole and pointing to the several hours which is therefore the Index Horarius or Hour Index 33. Having described the great Circles framed without and drawn upon the Globe we will now describe the lesser Circles also And these lesser Circles are called Parallels that is such as are in all places equally distant from the Equator and these Circles how little soever are supposed to be divided into 360 Degrees but these Degrees are not so large as in the great Circles but do proportionably decrease according to the Radius by which they are drawn 34. These lesser Circles are either the Tropicks or the Polar Circles 35. The Tropicks are two small Circles drawn upon the Globe one beyond the Equator towards the North Pole and the other towards the South Shewing the way which the Sun makes in his Diurnal Motion when he is at his greatest distance from the Equator either North or South These Circles are called Tropicks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 that is from the Suns returning for the Sun coming to these Circles he is at his greatest distance from the Equator and in the same Moment of time sloping as it were his course he returns nearer and nearer to the Equator again 36. These Tropical Circles do shew the point of Heaven in which the Sun doth make either the longest Day or the Shortest Day in the Year according as he is in the Northern or the Southern Tropick And are drawn at 23 Degrees and a half distant from the Equator 37. The Polar Circles are two lesser Circles drawn upon the Globe at the Radius of 23 Degrees and a half distant from the Poles of the World shewing thereby the Poles of the Zodiack which is so many Degrees distant from the Equator on both sides thereof 38. These Polar Circles are 66 Degrees and a half distant from the Equator and 43 Degrees distant from his nearest Tropick They are called the Arctick and Antarctick Circles 39. The Arctick Circle is that which is described about the Arctick Pole and passeth almost through the middle of the Head of the greater Bear It is called the Arctick Circle 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 from the two conspicuous Stars towards the North called the greater and the lesser Bear 40. The Antarctick Circle is that which is described about the Antarctick or South Pole It is so called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 that is from being opposite to the greater and lesser Bear Having thus described the Globe or Astronomical Instrument by which the Frame of the World is represented to our view I will proceed to shew the use for which it is intended CHAP. II. Of the Distinctions and Affections of Spherical Lines or Arches THE uses of the Globe as to practice are either such as concern the Heavens or the Earth in either of which if we should descend unto particulars the uses would be more in number than a short Treatise will contain Seeing therefore that all Problems which concern the Globe may be best and most accurately resolved by the Doctrine of Spherical Triangles we will contract these uses of the Globe which otherwise might prove infinite to such Problems as come within the compass of the 28 Cases of Right and Oblique angled Spherical Triangles 2. And that the nature of Spherical Triangles may be the better understood and by which of the 28 Cases the particular Problems may be best resolved I will set down some General Definitions and Affections which do belong to such Lines or Arches of which the Triangle must be framed with the Parts and Affections of those Triangles and how the things given and required in them may be represented and resolved upon and by the Globe as also how they may be represented and resolved by the Projection of the Sphere and by the Canon of Triangles 3. A Spherical Triangle then is a Figure consisting of three Arches of the greatest Circles upon the Superficies of a Sphere or Globe every one being less than a semicircle 4. A great Circle is that which divideth the Sphere or Globe into two equal parts and thus the Horizon Equator Zodiack and Meridians before described are all of them great Circles And of these Circles or any other there must be three Arches to make a Triangle and every one of these Arches severally must be less than a semicircle To make this plain In Fig. 1. The streight Line HAR doth represent the Horizon PR the height of the Pole above the Horizon PMS a Meridian and these three Arches by their intersecting one another do visibly constitute four Spherical Triangles 1. PMR 2. PMH 3. SHM. 4. SMR And every Arch is less than a semicircle as in the Triangle PMR the Arch PR is less than the Semicircle PRS the Arch MR is less than the Semicircle AMR and the Arch PM is less than the Semicircle PMS the like may be shewed in the other Triangles 5. Spherical or circular Lines are Parallel or Angular 6. Parallel Arches or Circles are such as are drawn upon the same Center within without or equal to another Arch or Circle Thus in Fig. 1. The Arches ♋ M ♋ and ♑ O ♑ are though lesser Circles parallel to the Equinoctial AE A Q and do in that Scheme represent the Tropicks of Cancer and Capricorn The manner of describing them or any other Parallel Circle is thus set off their distance from the great Circle to which you are to draw a parallel with your Compasses by help of your Line of Chords which in this Example is 23 Degrees and a half from AE to ♋ then draw the Line A ♋ and upon the point ♋ erect a Perpendicular where that Perpendicular shall cut the Axis PAS extended is the Center of that Parallel 7. A Spherical Angle is that which is conteined by two Arches of the greatest Circles upon the Superficies of the Globe intersecting one another Angles made by the Intersection of two little Circles or of a little Circle with a great we take no notice of in the Doctrine of Spherical Triangles 8. A Spherical Angle is either Right or Oblique 9. A Spherical Right Angle is that which is conteined by two Arches of the greatest Circles in the Superficies of the Sphere cutting one another at Right Angles that is
towards the North Pole in these Northern Parts of the World the contrary is to be observed in the Southern Parts Then in the Right angled Spherical Triangle ADF in Fig. 1. we have given the Angle FAD the Sun's greatest Declination The Leg DF the Sun's present Declination To find AF the Sun's distance from the next Equinoctial Point Therefore by the Case of Right angled Spherical Triangles As the Sine of FAD 23. 525. Comp. Ar. 0.3988648 Is to the Sine of DF. 23. 5. 9.5945468 So is the Radius 10.0009000 To the Sine of AF. 80. 04. 9.9934116 PROBLEM 6. The Poles Elevation and Sun's Declination being given to find his Amplitude The Amplitude of the Sun 's rising or setting is an Arch of the Horizon intercepted betwixt the AEquator and the place of the Sun 's rising or setting and it is either Northward or Southward the Northward Amplitude is when he riseth or setteth on this Side of the AEquator towards the North Pole and the Southern when he riseth or setteth on that Side of the AEquator which is towards the South Pole That we may then find the Sun's Amplitude or Distance from the East or West Point at the time of his rising or setting In the Right angled Spherical Triangle ATM in Fig. 2. let there be given the Angle TAM 38. 47. the Complement of the Poles Elevation and TM 23. 15. the Sun 's present Declination To find AM the Sun's Amplitude By the eleventh Case of Right angled Spherical Triangles As the Sine of MAT. 38. 47. Comp. Ar. 0.2061365 Is to the Radim 10.0000000 So is the Sine of MT 23. 15. 9.5945468 To the Sine of AM. 39. 19. 9.8006833 PROBLEM 7. To find the Ascensional Difference The Ascensional Difference is nothing else but the Difference between the Ascension of any Point of the Ecliptick in a Right Sphere and the Ascension of the same Point in an Oblique Sphere As in Fig. 1. AT is the Ascensional difference between DA the Sun's Ascension in a Right Sphere and DT the Sun's Ascension in an Oblique Sphere Now then in the Right angled Spherical Triangle AMT we have given The Angle MAT. 38. 47. the Complement of the Poles Elevation And MT 23. 15. To find AT the Ascensional difference As Rad.  To the Cot. of MAT. 38. 47. Com. Ar. 10.0999136 So is Tang. MT 23. 55. 9.6310051 To the Sine of AT 32. 56. 9.7309187 PROBLEM 8. Having the Right Ascension and Ascensional Difference to find the Oblique Ascension and Descension In Fig. 1. DT represents the Right Ascension AT the Ascensional Difference DA the Oblique Ascension which is found by deducting the Ascensional Difference AT from the Right Ascension DT according to the Direction following If the Declination be N. North Subt. Add The Ascentional Difference from the Right and it giveth the Oblique Ascension The Ascensional Difference to the Right and it giveth the Oblique Descension South Add Subt. The Ascensional Difference to the Right and it giveth the Oblique Ascension The Ascensional Difference from the Right and it giveth the Oblique Descension Right Ascension of ♊ 0 deg 57.80 Ascensional Difference 27.62 Oblique Ascension ♊ 0 deg 30.18 Oblique Descension ♊ 0 deg 85.42 PROBLEM 9. To find the time of the Sun 's rising and setting with the length of the Day and Night The Ascensional Difference of the Sun being added to the Semidiurnal Arch in a Right Sphere that is to 90 Degrees in the Northern Signs or substracted from it in the Southern their Sum or Difference will be the Semidiurnal Arch which doubled is the Right Arch which bisected is the time of the Sun rising and the Day Arch bisected is the time of his setting As when the Sun is in 0 deg ♊ his Ascensional Difference is 27. 62. which being added to 90 degrees because the Declination is North the Sum will be 117.62 the Semidiurnal Arch. The double whereof is 235.22 the Diurnal Arch which being converted into time makes 15 hours 41 minutes for the length of the Day whose Complement to 24 is 8 hours 19 minutes the length of the Night the half whereof is 4 hours 9 minutes 30 Seconds the time of the Sun 's rising PROBLEM 10. The Poles Elevation and the Sun's Declination being given to find his Altitude at any time assigned In this Problem there are three Varieties 1. When the Sun is in the AEquator that is in the beginning of ♈ and ♎ in which case supposing the Sun to be at B 60 degrees or four hours distant from the Meridian then in the Right angled Spherical Triangle BZ AE in Fig. 1. we have given AE Z 51. 53. the Poles Elevation and B AE 60 degrees to find BZ Therefore by the 2 Case of Right angled Spherical Triangles As the Radius  To the Cosine of AE Z. 51. 53. 9.7938635 So is the Cosine of B. AE 60. 9.6989700 To the Cosine of B Z. 71. 88. 9.4928335 Whos 's Complement BC. 18. 12. is the ☉ Altitude required The second Variety is when the Sun is in the Northern Signs that is in ♈ ♉ ♊ ♋ ♌ ♠in which Case supposing the Sun to be at F in Fig. II Then in the Oblique angled Spherical Triangle FZP we have given 1. PZ 38. 47 the Complement of the Poles Elevation 2. FP 67. 97 the Complement of Declination 3. ZPF 45 the Distance of the ☉ from the Meridian To find FZ Therefore by the eighth Case of Oblique angled Spherical Triangles As the Cotang of ZP 38. 47. 10.0997059 Is to the Radius 10.0000000 So is the Cosine of ZPF 45. 9.8494850 To the Tang. of SP. 29. 33. 9.7497791 Then from FP 67.97 Deduct SP. 29.33 There rests FS 38.64 As the Cosine of SP. 29. 33. Comp. Ar. 0.0595768 To the Cosine of PZ 38. 47. 9.8937251 So is the Cosine of FS 38. 64. 9.8926982 To the Cosine of FZ 45. 45. 9.8460001 Whos 's Complement FC 44. 55 is the ☉ Altitude required The third Variety is when the Sun is in the Southern Signs as in ♎ ♠♠♑ ♒ ♓ And in this Case supposing the ☉ to be ♠10 degrees and his Declination South Db 22. 03. and his Distance from the Meridian 45 as before then in the Oblique angled Spherical Triangle Z bP in Fig. 1. we have given Z P. 38. 47. The Side bP 112. 03. and the Angle ZPb 45. To find Zb. Therefore by the 8 Case of Oblique angled Spherical Triangles As the Cotang of ZP 38. 47. 10.0997059 Is to the Radius 10.0000000 So is the Cosine of ZPb 45. 9.8494850 To the Tang. of SP. 29. 33. 9.7497791 Then from bP. 112.03 Deduct SP. 29.33 There rests bS. 82.70 As the Cosine of P S. 29. 33. Comp. Ar. 0.0595768 To the Cosine of ZP 38. 47. 9.8937251 So the Cosine of bS. 82. 70 9.1040246 To the Cosine of Zb. 83. 45. 9.0573265 Whos 's Complement 6.55 is the ☉ Altitude required PROBLEM 11. Having the Altitude of the Sun his Distance
least Denomination and so proceed according to the rule given Example Let it be required to convert 125 degrees of the Sexagenary Circle into their correspondent parts in the Decimal I say as 360 is to 100 so is 125 to 34 722222 c. that is 34 degrees and 722222 Parts 2. Example Let the Decimal of 238 degrees 47 Minutes be required In a whole Circle there are 21600 Minutes and in 238 degrees there are 14280 Minutes to which 47 being added the sum is 14327. Now then I say if 21600 give 100 what shall 14327. The Answ. is 66 3287 c. In like manner if it were required to convert the Hours and Minutes of a Day into decimal Parts say thus if 24 Hours give 100 what shall any other number of Hours give Thus if the Decimal of 18 hours were required the answer would be 75 and the Decimal answering to 16 Hours 30 Minutes is 68 75. But if it be required to convert the Decimal Parts of a Circle into its correspondent Parts in Sexagenary The proportion is as 100 is to the Decimal given so is 360 to the Sexagenary degrees and parts required Example Let the Decimal given be 349 722222 if you multiply this Number given by 360 the Product will be 1249999992 that is cutting off 7 Figures 124 degrees and 9999992 parts of a degree If Minutes be required multiply the Decimal parts by 60 and from the product cut off as many Figures as were in the Decimal parts given the rest shall be the Minutes desired But to avoid this trouble I have here exhibited two Tables the one for converting sexagenary degrees and Minutes into Decimals and the contrary The other for converting Hours and Minutes into Decimals and the contrary The use of which Tables I will explain by example Let it be required to convert 258 degrees 34′ 47″ into the parts of a Circle decimally divided The Table for this purpose doth consist of two Leaves the first Leaf is divided into 21 Columns of which the 1. 3. 5. 7. 9. 11. 13. 15. 17. 19 doth contain the degrees in a sexagenary Circle the 2. 4. 6. 8. 10. 12. 14. 16. 18 and 20 doth contain the degrees of a Circle Decimally divided answering to the former and the last Column doth contain the Decimal parts to be annexed to the Decimal degrees Thus the Decimal degrees answering to 26 Sexagenary are 7 and the parts in the last Column are 22222222 and therefore the degrees and parts answering to 26 Sexagenary degrees are 7. 22222222. In like manner the Decimal of 62 degrees 17. 22222222. And the Decimal of 258 degrees 34′ 47″ is thus found The Decimal of 258 degrees is 71.66666666 The Decimal of 34 Minutes is .15747040 The Decimal of 47 seconds is .00362652 Their Sum 71.82776358 is the Decimal of 258 degrees 34′ 47″ as was required In like mauner the Decimal of any Hours and Minutes may be found by the Table for that purpose Example Let the Decimal of 7 Hours 28′ be required The Decimal answering to 7h is 29.16666667 The Decimal of 28 Minutes is 1.94444444 The Sum 31.11111111 is the Decimal Sought To find the degrees and Minutes in a sexagenary Circle answering to the degrees and parts of a Circle Decimally divided is but the contrary work As if it were required to find the Degrees and minutes answering to this decimal 71. 02776359 the Degrees or Integers being sought in the 2. 4. 6 or 8 Columns c. of the first Leaf of that Table right against 71. I find 256 and in the last Column these parts 11111111 which being less than the Decimal given I proceed till I come to 6666667 which being the nearest to my number given I find against these parts under 71. Degrees 258 so then 258 are the degrees answering to the Decimal given and To find the Minutes and Seconds from 71.82776359 I Substract the number in the Table 71.66666667 The remainer is 16109692 which being Sought in the next Leaf under the title Minutes the next leaf is 11747640 And the Minutes 34 and this number being Subtracted the remainer is 00362652 Which is the Decimal of 47 seconds and so the degrees and Minutes answering to the Decimal given are 258 degrees 34′ and 47″ the like may be done for any other CHAP. VIII Of the difference of Meridiens HAving in the first part shewed how the places of the Planets in the Zodiack may be found by observation and how to reduce the time of an observation made in one Country to the correspondent time in another as to the day of the Month by considering the several measures of the year in several Nations there is yet onething wanting which is by an observation made of a Planets place in one Country to find when the Planet is in that place in reference to another as suppose the ☉ by observation was found at Vraniburg to be in ♈ 3d. 13′ 14″ March the fourteenth 1583 at what time was the Sun in the same place at London To resolve this and the like questions the Longitude of places from some certain Meridian must be known to which purpose I have here exhibited a Table shewing the difference of Meridians in Hours and Minutes of most of the eminent places in England from the City of London and of some places beyond the Seas also The use whereof is either to reduce the time given under the Meridian of London to some other Meridian or the time given in some other Meridian to the Meridian of London 1. If it be required to reduce the time given under the Meridian of London to some other Meridian seek the place desired in the Catalogue and the difference of time there found either add to or subtract from the times given at London according as the Titles of Addition or Subtraction shew so will the time be reduced to the Meridian of the other place as was required Example The same place at London was in the first Point of ♉ 6 Hours P. M. and it is required to reduce the same to the Meridian of Vraniburg I therefore seek in Vraniburg in the Catalogue of places against which I find 50′ with the Letter A annexed therefore I conclude that the Sun was that day at Vraniburg in the first point of ♉ 6 Hours 50′ P. M. 2. If the time given be under some other Meridian and it be required to reduce the same to the Meridian of London you must seek the place given in the Catalogue and the difference of time there found contrary to the Title is to be added or subtracted from the time there given Example Suppose the place of the Sun had been at Vraniburg at 6 Hours 50′ P. M. and I would reduce the same to the Meridian of London against Vraniburg as before I find 50′ A. therefore contrary to the Title I Subtract 50′ and the remainder 6 Hours is the time of the Suns place in the Meridian of London CHAP. IX Of the Theory of the
Sun 's or Earth's Motion IN the first part of this Treatise we have spoken of the primary Motion of the Planets and Stars as they are wheeled about in their diurnal motion from East to West but here we are to shew their own proper motions in their several Orbs from West to East which we call their second motions 1. And these Orbs are supposed to be Elliptical as the ingenious Repler by the help of Tycho's accurate observations hath demonstrated in the Motions of Mars and Mercury and may therefore be conceived to be the Figure in which the rest do move 2. Here then we are to consider what an Ellipsis is how it may be drawn and by what Method the motions of the Planets according to that Figure may be computed 3. What an Ellipsis is Apollonius Pergaeus in Conicis Claudius Mydorgius and others have well defined and explained but here I think it sufficient to tell the Reader that it is a long Circle or a circular Line drawn within or without a long Square or a circular Line drawn between two Circles of different Diameters 4. The usual and Mechanical way of drawing this Ellipsis is thus first draw a line to that length which you would have the greatest Diameter to be as the Line AP in Figure 8 and from the middle of this Line at X set off with your compasses the Equal distance XM and XH 5. Then take a piece of thred of the same length with the Diameter AP and fasten one end thereof in the point M and the other in the point H and with your Pen extend the thred thus fastened to the point A and from thence towards P keeping the thread stiff upon your Pen draw a line from A by B to P the line so drawn shall be half an Ellipsis and in like manner you may draw the other half from P by D to A. In which because the whole thred is equal to the Diameter AP. therefore the two Lines made by thred in drawing of the Ellipsis must in every point of the said Ellipsis be also equal to the same Diameter AP. They that desire a demonstration thereof geometrically may consult Apollonius Pergaeus Claudius Mydorgius or others in their treatises of Conical Sections this is sufficient for our present purpose and from the equality of these two Lines with the Diameter a brief Method of calculation of the Planets place in an Ellipsis is thus Demonstrated by Dr. Ward now Bishop of Salisbury 6. In this Ellipsis H denotes the place of the Suns Center to which the true motion of the Planet is referred M the other Focus whereunto the equal or middle motion is numbred A the Aphelion where the Planet is farthest distant from the Sun and slowest in motion P the Perihelion where the Planet is nearest the Sun and slowest in motion In the points A and P the Line of the mean and true motion do convene and therefore in either of these places the Planet is from P in aequality but in all other points the mean and true motion differ and in D and C is the greatest elliptick AEquation 8. Now suppose the Planet in B the line of the middle motion according to this Figure is MB the line of the true motion HB The mean Anomaly AMB. The Eliptick aequation or Prosthaphaeresis MBH which in this Example subtracted from AMB the remainer AHB is the true Anomaly And here note that in the right lined Triangle MBH the side MH is always the same being the distance of the Foci the other two sides MB and HB are together equal to AP. Now then if you continue the side MB till BE be equal to BH and draw the line HE in the right lined Triangle MEH we have given ME = AD and MH with the Angle EMH to find the Angles MEH and MHE which in this case are equal because EB = BH by Contraction and therefore the double of BEH or BHE = MBH which is the Angle required And that which yet remaineth to be done is the finding the place of the Aphelion the true Excentricity or distance of the umbilique points and the stating of the Planets middle motion CHAP. X. Of the finding of the Suns Apogeon quantity of Excentricity aend middle motion THe place of the Suns Apogaeon and quantity of Excentricity may from the observations of our countrey man Mr. Edward Wright be obtained in this manner in the years 1596 and 1497 the Suns entrance into ♈ and ♎ and into the midst of ♉ ♌ ♠and ♒ were as in the Table following expressed  1596 1597   D. H. M. D. H. M.  Ianuary 25. 00.07 24. 05.54 ♒ 15 March 9. 18.43 10. 00.37 ♈ 0 April 24. 21.47 25. 03.54 ♉ 15 Iuly 28. 01.43 28. 09.56 ♌ 15 September 12. 13.48 12. 19.15 ♎ 0 October 27. 15.23 27. 21.50 ♠15 And hence the Suns continuance in the Northern Semicircle from ♈ to ♎ in the year 1596 being Leap year was thus found  d. h. From the 1. of Ianuary to ☉ Entrance ♎ 256. 13. 48. From the 1. of Iun to ☉ Entrance ♈ 69. 18.43 Their difference 186. 19.05 In the year 1597 from the 1 of Ianuary to the time of the ☉ Entrance into ♎ 255. 19.15 To the ☉ entrance into ♈ 69. 09.37 Their difference is 186. 18.38 And the difference of the Suns continuance in these Arks in the year 1596 and 1597 is 27′ and therefore the mean time of his continuance in those Arks is days 186. hours 18. minutes 51. seconds 30. And by consequence his continuance in the Southern Semicircle that is from ♎ to ♈ is 178 days 11 hours 8 minutes and 30 seconds In like manner in the year 1596 between his entrance into ♉ 15. and ♠15 there are days 185. 17.36 And in the year 1597 there are days 185. 17.56 And to find the middle motion answering to days 186. hours 18. Minutes 51. seconds 30 I say As 365 days 6 hours the length of the Julian year is to 360 the degrees in a Circle So is 186 days 18 hours 51′ 30″ to 184 degrees 03′ 56″ In like manner the mean motion answering to 185 days 17 h. 46′ is 183 degrees 02′ 09 Apparent motion from ♈ to ♎ 180. 00.00 Middle motion 184. 03.56 Their Sum 364. 03.56 Half Sum is the Arch. SME 182. 01.58 In 1596 from 15 ♒ to 15 ♌ there are days 185 hours 01 minutes 36. In 1597. days 135. hours 4. 02′ And the mean motion answering thereunto is 182 d. 30′ 36″ Apparent motion from 15 ♉ to 15 ♠180. Middle motion 185. 17. 56. 181. 04.53 Half Sum is 183. 32. 26 From 15 ♒ to 15 ♌ Days 185. 04 h. 02′ Apparent motion 180. Middle motion 182. 30. 36 Half Sum 181. 15. 18 Now then in Fig. from PGC. 181. 32. 26 deduct NKD 180 the Remainer is DC+NP 1. 32. 26. Therefore DC or NP. 46. 13 whose Sine is HA. And from XPG. 181. 15. 18 deduct
Aphelion for one day viz. 0. 00001. 3014917 by 53245 the product is 0. 69297. 9255665 which being deducted from the place of the Aphelion in the beginning of the Christian AEra before found 18. 97946. 9494841. the remainer 18. 28649. 0239176 is the place of the Aphelion at the time of the observation that is in Sexagenary numbers deg 65. 49′ 53″ 5. The place of the Aphelion at the time of the observation being thus found to be deg 65. 49′ 53″ The Suns mean Longitude at that time may be thus computed In Fig. 8. In the Triangle EMH we have given the side ME 200000 the side MH 3576 the double excentricity before found and the Angle EMH 114. 10′ 07″ the complement of the Aphelion to a Semicircle to find the Angle MEH for which the proportion is As the Summ of the sides is to the difference of the sides so is the Tangent of the half Summ of the opposite Angles to the Tangent of half their difference The side ME. 200000.  The side MH 3576.  Z. Of the sides 203576. Co. ar 4.69127343 X. Of the sides 196424. 5.29321855 Tang. ½ Z Angles 32′ 54′ 56. 9.91111512 Tang. ½ X Angles 31. 59. 21.  Angle MEH 0. 55. 35. 9.79560710 The double whereof is the Angle MBH 1. 51. 10. which being Subtracted from 360 the remainer 358. 08. 50. is the estimate middle motion of the Sun from which subtracting the Aphelion before found 65. 49. 53. the remainer 292. 18. 57. is the mean Anomaly by which the absolute AEquation may be found according to the former operation Z. ME+MH 203576. Co. ar 4.69127343 X. ME-MH 196424 5.29321855 Tang. ½ Anom 56. 09. 28. 10.17359517 Tang. ½ X. 55. 12. 18. 10.15808715 Differ 00. 57. 10.  Doubled 1. 54. 20 which added to the middle motion before found gives the ☉ true place ♈ 00. 3′ 10″ which exceeds the observation 3′ 10″ therefore I deduct the same from the middle motion before found and the remainer 358. 05. 50. is the middle motion at the time of the observation of Hipparchus to which if you add the middle motion of the Sun for 53245 days or for 323 AEgyptian years 131 days 280. 46. 08′ the Summ rejecting the whole Circles is 278. 51. 48 the Suns mean Longitude in the beginning of the Christian AEra 6. But one observation is not sufficient whereby to state the middle motion for any desired Epocha we will therefore examine the same by another observation made by Albategnius at Aracta in the year of Christ 882 March 15. hours 22. 21. but in the Meridian of London at 18 hours 58′ The motion of the Aphelion for 881 years 74 days is 3. 806068653737 which being added to the place thereof in the beginning of the Christian AEra the place at the time of the observation will be found to be 22. 785538148578 that is reduced Deg. 82. 01′ 40″ And hence the AEquation according to the former operations is Deg. 2. 01′ 16″ which being deducted from a whole Circle the remainer 357 d. 58′ 44″ is the estimate middle motion at that time from which deducting the Aphelion deg 82. 01. 40. the remainer 275. 57. 04 is the mean anomaly and the AEquation answering thereto is deg 2. 02′ 18″ which being added to the middle motion before found gives the ☉ place ♈ 00. 01′ 02″ which exceeds the observation 01′ 02″ therefore deduct the same from the middle motion before found the remainer 357. 57′ 22″ is the middle motion of the ☉ at the time of the observation from which deducting the middle motion for 881 years 74 days 18 hours 58 minutes viz. 80d. 06′ 10″ the remainer 277 deg 51′ 12″ is the ☉ mean Longitude in the beginning of the Christian AEra By the first observation it is deg 278. 51′ 48″ By the second 277. 51. 12 Their difference is 1. 00. 36 He that desires the same to this or any other Epocha to more exactness must take the pains to compare the Collection thereof from sundry Observations with one another this is sufficient to shew how it is to be found Here therefore I will only add the measures set down by some of our own Nation and leave it to the Readers choice to make use of that which pleaseth him best The ☉ mean Longitude in the beginning of the Christian AEra according to Vincent Wing is 9. 8d. 00′ 31″ Tho. Street is 9. 7. 55. 56 Iohn Flamsted is 9. 7. 54. 39 By our first Computation 9. 8. 51. 48 By our second 9. 7. 51. 12 In the Ensuing Tables of the ☉ mean Longitude we have made use of that measure given by Mr. Flamsted a little pains will fit the Tables to any other measure CHAP. XI Of the quantity of the Tropical and Sydereal Year THe year Natural or Tropical so called from the Greek word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 which signifies to turn because the year doth still turn or return into it self is that part of time in which the ☉ doth finish his course in the Zodiack by coming to the same point from whence it began 2. That we may determine the true quantity thereof we must first find the time of the ☉ Ingress into the AEquinoctial Points about which there is no small difference amongst Astronomers and therefore an absolute exactness is not to be expected it is well that we are arrived so near the Truth as we are Leaving it therefore to the scrutiny of after Ages to make and compare sundry Observations of the ☉ entrance into the AEquinoctial Points it shall suffice to shew here how the quantity of the Tropical year may be determined from these following observations 3. Albategnius Anno Christi 882 observed the ☉ entrance into the Autumnal AEquinox at Aracta in Syria to be Sept. 19. 1 hour 15′ in the Morning But according to Mr. Wings correction in his Astron. Instaur Page 44 it was at 1 hour 43′ in the Morning and therefore according to the ☉ middle motion the mean time of this Autumnal AEquinox was Sept. 16. 12 h. 14′ 25″ that is at London at 8 h. 54′ 25″ 4. Again by sundry observations made in the year 1650. the second from Bissextile as that of Albategnius was the true time of the ☉ ingress into ♎ was found to be Sept. 12. 14 h. 40′ and therefore his ingress according to his middle motion was Sept. 10. 13 h. 02. 5. Now the interval of these two observations is the time of 768 years in which space by subtracting the lesser from the greater I find an anticipation of 5 days 9 hours 52′ 25″ which divided by 768 giveth in the quotient 10′ 55″ 39 which being subtracted for 365 days 6 hours the quantity of the Julian year the true quantity of the Tropical year will be 365 days 5 hours 49′ 04″ 21‴ Others from other observations have found it somewhat less our worthy countryman Mr. Edward Wright takes it to be 365 d. 5 hours 48′ Mr. Iohn Flamsted
government the several Provinces are 1. Peloponnesus 2. Achaia 3. Epirus 4. Albania 5. Macedon 6. Thrace 7. The Islands of the Propontick 8. AEgean and 9. The Ionian Seas and 10. finally the Isle of Crete And thus I have given you a brief description of those Countries which are comprehended in the Continent of Europe the Islands in this part of the world are many I will mention only some few These two in the British and Northern Ocean known by the names of Great Britain and Ireland are the most famous to which may be added Greenland In the Mediterranaen Sea you have the Islands of Sicilia Sardinia Corsica and Crete which is now called Candia the greater and the less As for the other Islands belonging to this part of the world the Reader may expect a more particular description from them who have or shall write more largely of this subject This we deem sufficient for our present purpose Let this then suffice for the description of the first part of the World called Europe CHAP. IV. Of Asia ASia is bound on the West with the Mediteranean and AEgaean Seas the Hellespont Propontis Thracian Bosphorus and the Euxine Sea the Palus Maeotis the Rivers Tanais and Duina a Line being drawn from the first of the two said Rivers unto the other by all which it is parted from Europe on the North it hath the main Scythick Ocean but on the East the Indian Ocean and Mare del Eur by which it is separated from America on the South the Mediterranean or that part of it which is called the Carpathian Sea washing the shoars of Anatolia and the main Southern Ocean passing along the Indian Persian and Arabian Coasts and finally on the south-west the red Sea or Bay of Arabia by which it is parted from Affrick Environed on all sides with the Sea or some Sea like Rivers except a narrow Isthmus in the south-west which joyns it to Africk and the space of ground whatsoever it be between Duina and Tanais on the North-west which unites it to Europe 2. It is situated East and West from the 52 to the 169 degree of Longitude and North and South from the 82 degree of Latitude to the very AEquator some of the Islands only lying on the South of that Circle so that the longest summers day in the southern parts is but twelve hours but in the most northern parts hereof almost four whole Months together 3. This Country hath heretofore been had in special honour 1. For the creation of Man who had his first making in this part of the World 2. Because in this part of it stood the Garden of Eden which he had for the first place of his habitation 3. Because here flourished the four first great Monarchies of the Assyrians Babylonians Medes and Persians 4. Because it was the Scene of almost all the memorable Actions which are recorded by the pen-men of the Scriptures 5. Because our Saviour Christ was borne here and here wrought his most divine Miracles and accomplished the great work of our Redemption 6. And finally because from hence all Nations of the World had their first beginning on the dispersion which was made by the Sons of Noah after their vain attempt at Babel 4. This part of the World for the better understanding of the Greek and the Roman Stories and the estate of the Assyrian Babylonian and the Persian Monarchies to which the holy Scriptures do so much relate we shall consider as divided into the Regions of 1. Anatolia or Asia minor 2. Cyprus 3. Syria 4. Arabia 5. Chaldea 6. Assyria 7. Mesopotamia 8. Turcomania 9. Media 10. Persia. 11. Tartaria 12. China 13. India and 14. the Oriental Islands Anatolia or Asia minor Anatolia or Asia minor is bounded on the East with the River Euphrates by which it is parted from the greater Asia on the West with the Thracian Bosphorus Propontis Hellespont and the AEgean Sea by which it is parted from Europe on the North with Pontus Euxinus called also the black Sea and Mare Maggiore and on the South by the Rhodian Lydian and Pamphilian Seas several parts of the Mediterranean So that it is a Demi-Island or Peninsula environed on all sides with water excepting a small Isthmus or Neck of Land extending from the head of Euphrates to the Euxine Sea by which it is joyned to the rest of Asia It reacheth from the 51 to the 72 degree of Longitude and from the 36 to the 45 degree of Latitude and lyeth almost in the same position with Italy extending from the middle Parallel of the fourth Clime to the middle Parallel of the sixth so that the longest summers day in the Southern Parts is about 14 hours and a half and one hour longer in those parts which lie most towards the North. The Provinces into which it was divided before the Roman Conquest were 1. Bithynia 2. Pontus 3. Paphlagonia 4. Galatia 5. Cappadocia 6. Armenia Major Minor 7. Phrygia minor 8. Phrygia major 9. Mysia the greater and the less 10. Asia specially so called comprehending AEolis and Ionia 11. Lydia 12. Caria 13. Lycia 14. Lycaonia 15. Pisidia 16. Pamphylia 17. Isauria 18. Cilicia 19. The Province of the Asian Isles whereof the most principal are 1. Tenedos 2. Chios 3. Samos 4. Choos 5. Icaria 6. Lesbos 7. Patmos 8. Claros 9 Carpathos 10. Rhodes Cyprus Cyprus is situated in the Syrian and Cilician Seas extended in length from East to West 200 miles in breadth 60 the whole compass reckoned 550 distant about 60 miles from the rocky Shores of Cilicia in Asia minor and about one hundred from the main Land of Syria It is situated under the fourth Climate so that the longest day in Summer is no more than 14 hours and a half Divided by Ptolemy into the 4 provinces of 1. Paphia 2. Amathasia 3. Lepathia 4. Salamine Syria Syria is bounded on the East with the River Euphrates by which it is parted from Mesopotamia on the West with the Mediterranean Sea on the North with Cilicia and Armenia minor parted from the last by mount Taurus and on the South with Palestine and some parts of Arabia The length hereof from Mount Taurus to the Edge of Arabia is said to be 525 Miles the breadth from the Mediterranean to the River Euphrates 470 Miles drawing somewhat near unto a Square The whole Country was antiently divided into these six parts 1. Phoenicia 2. Palestine 3. Syria specially so called 4. Comagena 5. Palmyrene and Caelosyria or Syria Cava Arabia Arabia hath on the East Chaldaea and the Bay or Gulf of Persia on the West Palestine some part of Egypt and the whole course of the red Sea on the North the River Euphrates with some parts of Syria and Palestine and on the South the main southern Ocean It is in circuit about 4000 Miles but of so unequal and heteregeneous Composition that no general Character can be given of it and therefore we
90 beginneth again with 10. 20. 30 c. is for that the use of this Meridian in reference to its Division in Degrees requireth no more than that Number 12. The Horizon is a great Circle without the Globe which divides the upper part of Heaven from the lower so that the one half is always above that Circle and the other under it 13. The Poles of this Circle are two the one directly over our Heads and is called the Zenith the other is under feet and is called the Nadir 14. The Horizon is either Rational or Sensible 15. The Rational Horizon is that which divideth the Heavens and the Earth into two equal parts which though it cannot be perceived and distinguished by the eye yet may be conceived iâ— our minds in which respect all the Stars may be conceived to rise and set as in our view 16. The Visible Horizon is that Circle which the eye doth make at its farthest extent of sight when the body in any particular place doth turn it self round Of these two Circles there needeth no more to be said at present only we may observe that it was ingeniously devised by those who first thought upon it to set one Meridian and one Horizon without the Globe to avoid the confusion if not the impossibility of drawing a several Meridian and a several Horizon for every place which must have been done if this or the like device had not been thought upon 17. Besides these two great Circles without the Globe there are 4 other great Circles drawn upon the Globe it self besides the Meridian 1. The AEquator or Equinoctial Circle 2. The Zodiack 3. The AEquinoctial Colure 4. Solstitial Colure And these four Circles are immâ—table that is in whatsoever part of the World you are these Circles have no variation as the other two have 18. The AEquator is a great Circle drawn upon the Globe in the middle between the two Poles and plainly dividing the Globe into two equal parts 19. The AEquator is the measure of the Motion of the Primum Mobile for 15 Degrees of this Circle do always arise in an hours time the which doth clearly shew that the whole Heavens are turned round by equal intervals in the space of one day or 24 hours 20. In this Circle the Declinations of the Stars are computed from the mid-Heaven towards the North or South 21. This Circle gives denomination to the AEquinox for the Sun doth twice in a Year and no more cross this Circle to wit when he enters the first points of Aries and Libra and then he maketh the Days and the Nights equal His entrance into Aries is in March and is called the Vernal Equinox and his entrance into Libra is in September and is called the Autumnal Equinox 22. And from one certain point in this Circle the Longitude of Places upon the Earth are reckoned and the Latitude of Places are reckoned from this Circle towards the North or the South Poles 23. The Zodiack is a great Circle drawn upon the Globe cutting the AEquinoctial Points at Oblique Angles for although it divides the whole World into two equal parts in reference to its own Poles yet in reference to the Poles of the World it hath an Oblique Motion 24. The Poles of this Circle are as far distant from the Poles of the World as the greatest Obliquity thereof is from the Equinoctial that is 23 Degrees and 31 Minutes or thereabouts 25. This Circle doth differ from all other Circles upon the Globe in this other Circles to speak properly have Longitude assigned them but no Latitude but this hath both Whereas other Circles are in reference to their Longitude or Rotundity only divided into 360 Degrees this Circle in respect of its Latitude is supposed to be divided into 16 Degrees in Latitude 26. The Zodiack then in respect of Longitude is commonly divided into 360 Degrees as other Circles are but more peculiarly in respect of its self it is divided into 12 Parts called Signs and each Sign into 30 Degrees and 12 times 30 do make 360. 27. The 12 Signs into which the Zodiack is divided have these Names and Characters Aries ♈ Taurus ♉ Gemini ♊ Cancer ♋ Leo ♌ Virgo â™ Libra ♎ Scorpio â™ Sagittarius â™ Capricornus ♑ Aquarius â™’ and Pisces ♓ 28. These two Circles of the Equator and Zodiack are crossed by two other great Circles which are called Colures They are drawn through the Poles of the World and cut one another as well as the Equator at Right Angles One of them passeth through the Intersections of the Equinoctial points and is called the Equinoctial Colure The other passeth through the points of the greatest distance of the Zodiack from the Equator and is called the Solstitial Colure 29. The other great Circles described upon the Globe are the Meridians Where we must not think much to hear of the Meridians again That of Brass without the Globe is to serve all turns and the Globe is framed to apply it self thereto The Meridians upon the Globe will easily be perceived to be of a new and another use 30. The Meridians upon the Globe are either the great or the less Not that the great are any greater than the less for they have all one and the same center and equally pass through the Poles of the Earth But those which are called less are of less use than that which is called the great 31. The great is otherwise called the fixt and first Meridian to which the less are second and respectively moveable The great Meridian is as it were the Landmark of the whole Sphere from whence the Longitude of the Earth or any part thereof is accounted And it is the only Circle which passing through the Poles is graduated or divided into Degrees not the whole Circle but the half because the Longitude is to be reckoned round about the Earth 32. The lesser Meridians are those black lines which you see to pass through the Poles and succeeding the great at 10 and 10 Degrees as in most Globes or at 15 and 15 Degrees difference as in some Every place never so little more East or West than another hath properly a several Meridian yet because of the huge distance of the Earth from the Heavens there is no sensible difference between the Meridians of places that are less than one Degree of Longitude asunder and therefore the Geographers as well as the Astronomers allow a new Meridian to every Degree of the Equator which would be 180 in all but except the Globes were made of an extream and an unusual Diameter so many would stand too thick for the Description Therefore most commonly they put down but 18 that is at 10 Degrees distance from one another the special use of the lesser Meridians being to make a quicker dispatch in the account of the Longitudes Others set down but 12 at 15 Degrees difference aiming at this That the Meridians might be distant
T. 72. 195. 10.49327695 t ½ X Cru 69. 306. 10.42281009 2. Operation cs ½ Z 80. 49596. Comp. Arith. 0.78170174 cs ½ X 56. 97096. 9.73628614 Their Sum 10.51798788 t ½ ♈ T. 72. 195. 10.49327695 t ½ Z Cru 84. 34. 11.01126483 1. Arch. 69. 306. Their Sum is 53.740 is the Point of the Ecliptick for the Second House For the Cusp of the Third House In the Oblique angled Spherical Triangle ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 we have 1. ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 174. 39. The half whereof is 87. 195. The Angls ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 are the same with those of the Eleventh House s ½ Z. 72. 85437. Comp. Arith. 0.01977580 s ½ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 49. 32937. 6.88000800 Their Sum 9.89978389 t ½ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 87. 195. 11.30984054 For the Eleventh House For the Cusp of the Twelfth House In the Oblique angled Spherical Triangle ♈ KF we have given 1. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 K. 84. 39. The half whereof is 42. 195. 2. ♈ Kt. 137.46692  3. K ♈ t. 23.525 To find ♈ t. Z. 160.99192 ½ Z. 80.49596 X. 113.94192 ½ X. 56.97096 s ½ Z. 80. 49596. Comp. Arith. 0.00601663 s ½ X. 56. 97096. 9.92351651 t ½ ♈ K. 42. 195. 9.95740882 t ½ X Cru 37. 625. 9.88694196 2. Operation cs ½ Z. 80. 49596. Comp. Arith. 0.78170174 cs ½ X. 56. 97096. 9.73628614 t ½ ♈ K. 42. 195. 9.95740882 t ½ Z Cru 71. 496. 10.47539670 1. Arch. 37. 625. Their Sum 113.6691 is the Point of the Ecliptick for the Twelfth House For the Cusp of the Ascendant In the Oblique angled Spherical Triangle ♈ AG we have 1. ♈ A. 114. 39. The half whereof is 57. 195. 2. ♈ AZ 141. 5333. The Complement of HAAE 38. 46667. 3. A 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 y. 23. 525.  Z. 165.05833 ½ Z. 82.51916 X. 118.00833 ½ X. 59.00416 s. ½ Z. 82. 51916. Comp. Arith. 0 0037162◠s. ½ X. 59. 00416. 9.93313477 t ½ ♈ A. 57. 195. 10.19072348 t ½ X. 53. 296. 10.12757454 2. Operation t ½ X Cru 86. 468. 11.20962043 2. Operation cs ½ Z. 72. 85437. Comp. Arith. 0.53012277 cs ½ X. 49. 32937. 9.81395860 Their Sum 10.34408137 t ½ ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 87. 195. 11.39984054 t ½ X Cru 88. 729. 11.65392191 1. Arch. 86. 468. Their Sum 175.197 is the Point of the Ecliptick for the Third House And thus we have not only erected a Figure for the Time given but composed a Table for the general erecting of a Figure in that Eatitude for by adding together the first and second Numbers in each Proportion for the first second and third Houses there is composed two Numbers for each House to each of which the Artificial Tangent of half the Ascension of each House being added their Aggregates are the Tangents of two Arches which being added together do give the distance of the Cusp of the House from the first Point of Aries as in the preceding Operations hath been shewed Only note That if the Ascension of any House be more than a Semicircle you must take the Tangent of half the Complement to a whole Circle And to find the Cusp of the House you must also take the Complement of the Sum of the Arches added together The Numbers according to the former Operations which do constitute a Table of Houses for the Latitude of London 51. 53 are as followeth  11 and 3 Houses Ascendant 12 and 2 Houses 1. Oper. 9.89978389 9.93685106 9.92953314 2. Oper. 10.34408137 10.59682651 10.51798788 The Six Oriental Houses by the preceding Operations The opposite Houses are in the opposite Signs and Degrees 10 House ♈ 26.311 11 House ♊ 10.803 12 House ♋ 23.691 Ascendant ♌ 11.693 2 House ♠3.740 3 House ♠25.197 4 House ♎ 26.311 5 House ♠10.803 9 House ♑ 23.691 7 House ♒ 11.693 8 House ♓ 3.740 9 House ♓ 25.197 A Figure of the Twelve Coelestial Houses ASTRONOMY THE Second Part OR AN ACCOUNT OF THE Civil Year With the Reason of the Difference Between the JULIAN GREGORIAN Calendars And the manner of Computing the Places of the SVN and MOON LONDON Printed for Thomas Passinger at the Three Bibles on London-Bridge 1679. AN INTRODUCTION TO Astronomy The Second Book CHAP. I. Of the Year Civil and Astronomical HAving shewed the Motion of the Primum Mobile or Doctrine of the Sphere which I call the Absolute Part of Astronomy I come now unto the Comparative that is to shew the Motion of the Stars in reference to some certain Distinction of Time 2. And the Distinction of Time is to be considered either according to Nature or according to Institution 3. The Distinction of Time according to Nature is that space of Time in which the Planets do finish their Periodical Revolutions from one certain Point in the Zodiack to the same again and this in reference to the Sun is called a Year in reference to the Moon a Month. 4. The Sun doth pass through the Zodiack in 365 Days 5 Hours and 49 Minutes And the Moon doth finish her course in the Zodiack and return into Conjunction with the Sun in 29 Days 12 hours 44 Minutes and 4 Seconds And from the Motion of these two Planets the Civil Year in every Nation doth receive its Institution 5. Twelve Moons or Moneths is the measure of the Common Year in Turkey in every Moneth they have 29 or 30 Days in the whole Year 354 Days and in every third Year 355 Days 6. The Persians and Egyptians do also account 12 Moneths to their Year but their moneths are proportioned to the Time of the Suns continuance in every of the Twelve Signs in their Year therefore which is Solar there are always 365 Days that is eleven Days more than the Lunar Year 7. And the Iulian Year which is the Account of all Christendom doth differ from the other in this that by reason of the Sun's Excess in Motion above 365 Days which is 5 Hours 49 Minutes it hath a Day intercalated once in 4 Years and by this intercalation it is more agreeable to the Motion of the Sun than the former and yet there is a considerable difference between them which hath occasioned the Church of Rome to make some further amendment of the Solar Year but hath not brought it to that exactness which might be wished 8. This intercalation of one Day once in 4 Years doth occasion the Sunday Letter still to alter till 28 Years be gone about The Days of the Week which use to be signed by the seven first Letters in the Alphabet do not fall alike in every Common Year but because the Year consisteth of 52 Weeks and one Day Sunday this Year will fall out upon the next Year's Monday and so forward for seven years but every fourth year consisting of 52 weeks and two days doth occasion the Sunday Letter to alter till four times seven years that is till 28 years
be gone about This Revolution is called the Cycle of the Sun taking its name from the Sunday Letter of which it sheweth all the Changes that it can have by reason of the Bissextile or Leap-year To find which of the 28 the present is add nine to the year of our Lord because this Circle was so far gone about at the time of Christs Birth and divide the whole by 28 what remaineth is the present year if nothing remain the Cycle is out and that you must call the last year of the Cycle or 28. 9. This Intercalation of one day in four years doth occasion the Letter F to be twice repeated in February in which Moneth the day is added that is the Letter F is set to the 24 and 25 days of that Moneth and in such a year S. Matthias day is to be observed upon the 25 day and the next Sunday doth change or alter his Letter from which leaping or changing such a year is called Leap-year aud the number of days in each Moneth is well expressed by these old Verses Thirty days hath September April June and November February hath 28 alone All the rest have thirty and one But when of Leap-year cometh the Time Then days hath February twenty and nine That this year is somewhat too long is acknowledged by the most skilful Astronomers as for the number of days in a year the Emperours Mathematicians were in the right for it is certain that no year can consist of more than 365 days but for the odd hours it is as certain that they cannot be fewer than five nor yet so many as six so then the doubt is upon the minutes 60 whereof do make an hour a small matter one would think but how great in the consequence we shall see The Emperours year being more than 10 minutes greater than the Suns will in 134 years rise to one whole day and by this means the Vernal or Spring Equinox which in Iulius Caesar's time was upon the 24 of March is now in our time upon the 10 of March 13 days backward and somewhat more and so if it be let alone will go back to the first of March and first of February and by degrees more and more backward still 10. To reform this difference some of the late Roman Bishops have earnestly endeavoured And the thing was brought to that perfection it now standeth by Gregory the Thirteenth in the year 1582. His Mathematicians whereof Lilius was the Chief advised him thus That considering there had been an Agitation in the Council of Nice somewhat concerned in this matter upon the motion of that Question about the Celebration of Easter And that the Fathers of the Assembly after due deliberation with the Astronomers of that time had fixed the Vernal Equinox at the 21 of March and considering also that since that time a difference of ten whole days had past over in the Calendar that is that the Vernal Equinox which began upon the 21 of March had prevented so much as to begin in Gregorie's days at the 10 of the same they advised that 10 days should be cut off from the Calendar which was done and the 10 days taken out of October in the year 1582. as being the moneth of that year in which that Pope was born so that when they came to the fifth of the moneth they reckoned the 15 and so the Equinox was come up to its place again and happened upon the 21 of March as at the Council of Nice But that Lilius should bring back the beginning of the year to the time of the Nicene Council and no further is to be marvelled at he should have brought it back to the Emperours own time where the mistake was first entered and instead of 10 cut off 13 days however this is the reason why these two Calendars differ the space of 10 days from one another And thus I have given you an account of the year as it now stands with us in England and with the rest of the Christian World in respect of the Sun some other particulars there are between us and them which do depend upon the motion of the Moon as well as of the Sun and for the better underderstanding of them I will also give you a brief account of her revolution But first I will shew you how the day of the moneth in any year propounded in one Couutry may be reduced to its correspondent time in another 11. Taking therefore the length of the year to be in several Nations as hath been before declared if we would find what day of the moneth in one Conntry is correspondent to the day of that moneth given in another there must be some beginning to every one of these Accounts and that beginning must be referred to some one as to the common measure of the rest 12. The most natural beginning of All Accounts is the time of the Worlds Creation but they who could not attain to the Worlds Beginning have reckoned from their own as the Romans from the building of Rome the Greeks from their Olympicks the Assyrians from Nabonassar and all Christians from the Birth of Christ the beginning of which and all other the most notable Epochaes we have ascertained to their correspondent times in the Julian Period which Scaliger contrived by the continual Multiplication of those Circles all in former time of good use and two of them do yet remain the Circles yet in use are those of the Sun and Moon the one to wit the Sun is a Circle of 28 years and the Circle of the Moon is 19 as shall be shewed hereafter The third Circle which now serves for no other use than the constituting of the Julian Period is the Roman Indiction or a Circle of 15 years if you multiply 28 the Circle of the Sun by 19 the Circle of the Moon the Product is 532 which being multiplied by 15 the Circle of the Roman Indiction the Product is 7980 the Number of years in the Julian Period whose admirable condition is to distinguish every year within the whole Circle by a several certain Character the year of the Sun Moon and Indiction being never the same again until the revolution of 7980 years be gone about the beginning of this Period was 764 Julian years before the most reputed time of the Worlds Creation which being premised we will now by Example shew you how to reduce the years of Forreigners to our Julian years and the contrary 1. Example I desire to know at what time in the Turkish Account the fifth of Iune in the year of our Lord 1640. doth fall The Julian years complete are 1648 and are thus turned into days by the Table of days in Julian years 1000 Julian years give days 365250 600 Julian years give days 219150 40 Julian years give days 14610 8 Years give days 2922 May complete 151 Days 5 The Sum is 602088 Now because the Turkish Account began Iuly 16. Anno
order E F G A B c. and when you come to the Golden Number 8 set the Letter C and there continue the Letters till you come to C again because when the Golden Number is 16 which in the Calendar is set to the eighth day of March is new Moon and the fourteenth day of that Moon doth fall upon the twenty first to which the Dominical Letter is C upon which the Feast of Easter cannot happen and therefore in the third Column containing the day in which the Feast of Easter is to be observed is also void But in the next place immediately following to wit against the letter D is set March 22 because if the fourteenth day of the Moon shall fall upon the twenty first of March being Saturday the next day being Sunday shall be the Feast of Easter To the Letters following E F G A B c. are set 23 24 25 and so orderly to the last of March and so forward till you come to the twenty fifth of April by which Table thus made the Feast of Easter may be found until the Calendar shall be reformed For having found the Golden Number in the first Column the Dominical Letter for the Year next after it doth shew the Feast of Easter as in the former Example the Golden Number is 3 and the Dominicall Letter D therefore Easter day is upon April 19. The other moveable Feasts are thus found Advent Sunday is always the nearest Sunday to St. Andrews whether before or after Septuagesima Sunday is Nine Weeks before Easter Sexagesima Sunday is Eight Weeks before Easter Qainquagesima Sunday is Seven Weeks before Easter Quadragesima Sunday is Six Weeks before Easter Rogation Sunday is five Weeks after Easter Ascension day is Forty Days after Easter Whitsunday is Seven Weeks after Easter Trinity Sunday is Eight Weeks after Easter G. N. D. L. Easter XVI   V D 22 March  E 23 XIII F 24 II G 25  A 26 X B 27  C 28 XVIII D 29 VII E 30  F 31 XV G 1 April IV A 2  B 3 XII C 4 I D 5  E 6 IX F 7  G 8 XVII A 9 VI B 10  C 11 XIV D 12 III E 13  F 14 XI G 15  A 16 XIX B 17 VIII C 18  D 19  E 20  F 21  G 22  A 23  B 24  C 25 CHAP. IV. Of the Reformation of the Calendar by Pope Gregory the Thirteenth and substituting a Cycle of Epacts in the room of the Golden Number HItherto we have spoken of the Calendar which is in use with us we will now shew you for what reasons it is alter'd in the Church of Rome and how the Feast of Easter is by them observed The Year by the appointment of Iulius Caesar consisting of 365 days 6 hours whereas the Sun doth finish his course in the Zodiack in 365 days 5 hours 49 minutes or thereabouts it cometh to pass that in 134 Years or less there is a whole day in the Calendar more than there ought in 268 years 2 days more in 4002 years 3 days and so since Iulius Caesar's time the vernal Equinox hath gone backward 13 or 14 days namely from the 24 of March to the tenth Now because the Equinox was at the time of the Nicene Council upon the twenty first of March when the time for the observing of Easter was first universally established they thought it sufficient to bring the Equinox back to that time by cutting off 10 days in the Calendar as hath been declared and to prevent any anticipation for the time to come have appointed that the Leap-year shall be thrice omitted in every 400 Years to come and for memory sake appointed the first omission to be accounted from the Year 1600 not from 1582 in which the reformation was made because it was not only near the time in which the emendation was begun but also because the Equinox has not fully made an anticipation of 10 days from the place thereof at the time of the Nicene Council which was March 21. The Years then 1700 1800 1900 which should have been Bissextile Years are to he accounted common years but the Year 2000 must be a Bissextile In like manner the Years 2100 2200 2300 shall be common years and the Year 2400 Bissextile and so forward 2. Again because it was supposed that the Cycle of the Moon or Golden Number was so fixed that the new and full Moons would in every 19 years return to the same days again whereas their not returning the same hours but making an anticipation of one hour 27 minutes or thereabouts it must needs be that in 17 Cycles or little more than 300 Years there would be an anticipation of a whole day And hence it is evident that in 1300 Years since the Nicene Council the New and Full Moons do happen more than 4 days sooner than the Cycle of the Moon or Golden Number doth demonstrate Whence also it comes to pass that the fourteenth day of the Moon by the Cycle is in truth the eighteenth day and so the Feast of Easter should be observed not from the fifteenth day of the Moon to the twenty first but from the nineteenth to the twenty fifth 3. That the Moon therefore being once brought into order might not make any anticipation for the time to come it is appointed that a Cycle of 30 Epacts should be placed in the Calendar instead of the Golden Number answering to every day in the Year to shew the New Moons in these days not only for 300 Years or thereabouts but that there might be new Epacts without altering the Calendar to perform the same thing upon other days as need shall require 4. For the better understanding whereof to the Calendar in use with us we have annexed the Gregorian Calendar also In the first Column whereof you have 30 numbers from 1 to 30 save only that in the place of 30 you have this Asterisk * But they begin with the Calends of Ianuary and we continued and repeated after a Retrograde order in this manner * 29 28 27 c. and that for this cause especially that the number being given which sheweth the New Moons in every Month for one Year you might by numbring 11 upwards exclusively find the number which will shew the New Moons the Year following to wit the Number which falleth in the eleventh place 5. And these Numbers are called Epacts because they do in order shew those 11 days which are yearly to be added to the Lunar Year consisting of 354 days that it may be in conformity with the Solar Year consisting of 365 days To this purpose as hath been said concerning the Golden Number these Epacts being repeated 12 times and ending upon the twentieth day of December the same Numbers must be added to the 11 remaining days which were added to the first 11 days in the Month of Ianuary 6. And
because 12 times 30 do make 360 whereas from the first of Ianuary to the twentieth of December inclusively there are but 354 days you must know that to gain the other six days the numbers 25 and 24 are in every other Month both placed against one day namely to February 5 April 5 Iune 3 August 1 September 29 and November 27. But why these two Numbers are chosen rather then any other and why in these 6 Months the number 25 is sometimes writ to XVI sometimes to XXV in a common character and why the number 19 is set to the last day of December in a common Character shall be declared hereafter 7. Here only note that this Asterisk * is set instead of the Epact 30 because the Epact shewing the Number of days which do remain after the Lunation in the Month of December it may sometimes fall out that 2 Lunations may so end that the one may require 30 for the Epact and the other 0 which would if both were written cause some inconveniences and therefore this * Asterisk is there set that it might indifferently serve to both And the Epact 29 is therefore set to the second day of Ianuary because after the compleat Lunation in the second of December there are 29 days and for the like reason the Epact 28 is set against the third of Ianuary because after the compleat Lunation in the third of December there are then 28 days over and so the rest in order till you come to the thirtieth of Ianuary where you find the Epact 1. because after the compleat Lunation on the thirtieth day there is only one day over 8. And besides the shewing of the New Moons in every Month which is and may be done by the Golden Number the Epacts have this advantage that they may be perpetual and keep the same place in the Calendar in all future ages which can hardly be effected with the Golden Number for in little more then 700 years the New Moons do make an anticipation of one day and then it will be necessary to set the Golden Number one degree backward and so the Golden Number which at the time of the Nicene Council was set to the first of Ianuary should in 300 years be set to the last of December and so of the rest but the Epacts being once fixed shall not need any such retraction or commutation For as often as the New Moons do change their day either by Anticipation or by Suppression of the Bissextile year you shall not need to do any more than to take another rank of 19 Epacts insteed of those which were before in use For instance the Epacts which are and have been in use in the Church of Rome since the year of reformation 1582 and will continue till the year 1700 are these 10 following 1. 12. 23. 4. 15. 26. 7. 18. 29. 10. 21. 2. 13. 24. 5. 16. 27. 8. 19. And from the year 1700 the Epacts which will be in use are these * 11. 22. 3. 14. 25. 6. 17. 28. 9. 20. 1. 12. 23. 4. 15. 26. 7. 18. and shall continue not only to the year 1800 but from thence until the year 1900 also and although in the year 1800 the Bissextile is to be suppressed yet is there a compensation for that Suppression by the Moons Anticipation To make this a little more plain the motion of the Moon which doth occasion the change of the Epact must be more fully considered CHAP. V. Of the Moons mean Motion and how the Anticipation of the New Moons may be discovered by the Epacts THe Moon according to her middle motion doth finish her course in the Zodiack in 29 days 12 hours 44 minutes three seconds or thereabout and therefore a common Lunar year doth consist of 354 days 8 hours 48 minutes 38 seconds and some few thirds but an Embolismical year doth consist of 383 days 21 hours 32 minutes 41 seconds and somewhat more and therefore in 19 years it doth exceed the motion of the Sun 1 hour 27 minutes 33 seconds feré 2. Hence it cometh to pass that although the New Moons do after 19 years return to the same days yet is there an Anticipation of 1 hour 27 minutes 33 seconds And in twice 19 years that is in 38 years there is an Anticipation of 2 hours 55 minutes 6 seconds and after 312 years and a half there is an Anticipation of one whole day and some few Minutes And therefore after 312 years no new Moon can happen upon the same day it did 19 years before but a day sooner Hence it comes to pass that in the Julian Calendar in which no regard is had to this Anticipation the New Moons found out by the Golden Number must needs be erroneous and from the time of the Nicene Council 4 days after the New Moons by a regular Computation 3. And hence it follows also that if the Golden Number after 312 were upon due consideration removed a day forwarder or nearer the beginning of the Months they would shew the New Moons for 312 years to come And being again removed after those years a day more would by the like reason do the same again But it was thought more convenient so to dispose 30 Epacts that they keeping their constant places 19 of them should perform the work of the Golden Number until by this means there should be an Anticipation of one day And when such an Anticipation should happen those 19 Epacts being let alone other 19 should be used which do belong to the preceding day without making any alteration in the Calendar 4. And if this Anticipation would do the whole work nothing were more plain then to make that commutation of the 19 Epact once in 312 years but because the detraction of the Bissextile days doth variously interpose and cause the 19 Epacts sometimes to be changed into these that do precede sometimes into these that follow sometimes into neither but to continue still the same therefore some Tables are to be made by which we may know when the commutation was to be made and into what Epacts 4. First therefore there was made a Table called Tabula Epactarum Expansa in this manner First on the top were placed the 19 Golden Numbers in order beginning with the Number 3 which in the old Calendar is placed against the Calends of Ianuary and under every one of these Golden Numbers there are placed 30 Epacts all constituted from the lowest number in the first rank in which the Epact is 1 and in that first rank the Golden Number is 3 the rest from thence towards the right Hand are made by the constant addition of it and the casting away of 30 as often as they shall exceed that number only when you come to the 27 the Epact under the Golden Number 19 there must be added 12 instead of 11 that so the Epact following may be 9 not 8 for the Reasons already given in this Discourse concerning the
TNK 180 the Remainer is KG+TX 1. 15. 18. Therefore KG or TX 37. 39 whose Sine is HR Now then to find the Apogaeon As HA 46′ 13″ 5.12851105 To Rad. So HR 37′ 39″ 15.03948202 To Tang. HAR. 39 d. 10′.04″ 9.91097097 GAM 45 Apogaeon 95. 49. 56. Hence to find the excentricity AR. As the Sine HAR. 39. 10.04 9.80043756 To Rad. So HR 37.39 15.03948202 To RA. 1733.99 5.23904446 Or thus In the Triangle 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 we have given 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 As 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 37.39 5.03948202 To Rad. So 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 46. 13. 15.12851105 To Tang. R 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 50. 49.56 10.08902903 PAS 45. Apogaeon 95 deg 49′ 56″ as before Then for the Excentricity RA. As the Sine of R 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 50. 49. 56 9.88945938 Is to 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 46′ 13″ 5.12851105 So is Radius To RA. 1734.01 5.23905167 And this agreeth with the excentricity used by Mr. Street in his Astron. Carolina Pag. 23. But Mr. Wing as well by observation in former ages as our own in his Astron. Instaur Pag. 39. doth find it to be 1788 or 1791. The work by both observations as followeth 2. And first in the time of Ptolemy Anno Christi 139 by comparing many observations together he sets down for the measure nearest truth the interval between the vernal Equinox and the Tropick of Cancer to be days 93. hours 23. and minutes 03. And from the Vernal to the Autumnal Equinox days 186. hours 13. and minutes 5.  D. The apparent motion from ♈ to ♎ 90. 36.00 Middle motion for 93 d. 23 h. 3′ is 92. 36.42 The half Sum is GP 91. 18.21 Apparent motion from ♈ to ♎ 180. 00.00 Middle motion for 186 d. 13 h. 5′ is 183. 52.03 The half Sum is GEK 181. 56.02 The half of GEK is GE. 90. 58.01 And GP less GE is 00. 20.20 Whos 's Sum is AC 59146.  Again from GEK 181. 56. 02. deduct the Semicircle FED 180. the remainer is the summ DK and FG. 1. 56. 2. and therefore DK = FG. 58′ 01″ whose sign is BC. 168755. L is the place of the Aphelion and AB the Excentricity Now then in the Triangle ABC in the Fig. 6 we have given the two sides AC and BC. To find the Angle BAC and the Hypotenuse AB For which the proportions are As the side AC 59146 4.77192538 Is to the Radius 10.00000000 So is the side BC 168755 5.22725665 To Tang. BAC 70. 41. 10. 10.45533127 Secondly for AB As the Sine of BAC 70. 41. 10. 9.97484352 Is to the side AB 168755. 5.22725665 So is the Radius 10.00000000 To the Hypot AB 1788. 10. 5.25241313 Therefore the Aphelion at that time was in II 10. 41. 10. And the excentricity 1788. 3. Again Anno Christi 1652 the Suns place by observation was found to be as followeth April 24. hours 10. ♉ 15 October 27. hours 7. 10′ ♠15 Ianuary 24. hours 11 20′ ♒ 15 Iuly 27. hours 16.30 ♌ 15 Hence it appeareth that the Sun is running through one Semicircle of the Ecliptick that is from ♉ 15 to ♠15. 185 days 21 hours and 10′ And through the other Semicircle from ♒ 15 to ♌ 15 days 184. hours 5. therefore the Suns mean motion according to the practice in the last example from ♉ 15 to ♠15 is 181. 30. 26. and from ♒ 15 to ♌ 15. 181. 16. 30. Now then in Fig. 7. if we subtract the semicircle of the Orb KMH 180. from WPV 181. 36. 26. the remainer is the sum of KW and HV 1. 36. 26. the Sine of half thereof 48′ 13″ is equal to AC 140252. Again the mean motion of the Sun in his Orb from ♒ 15 to ♉ 15 is the Arch SKP. 181. 16. 30. whose excess above the Semicircle being bisected is 38. 15. whos 's Sine CB. 111345. now then in the Triangle ABC to find the Angle BAC the proportion is As the side AC 140252 5.14690906 Is to the Radius 10.00000000 So is the Side CB 111345 5.04667072 To Tang. BAC 38. 36. 21 9.89966166 Which being deducted out of the Angle 69 A ♌ 45 it leaveth the Angle 69 AL 6. 33. 39. the place of the ☉ Aphelion sought and this is the quantity which we retain And for the excentricity BC. As the Sum of BAC 38. 26. 21 9.79356702 Is to the Radius 10.00000000 So is the side BC 111345 5.04667072 To the Hypot AB 179103 5.25310370 So then Anno Christi 1652. Aphel 96. 33.39 Anno Christi 139. the Aphelion 70. 41.10 Their difference is 25. 52.29 And the difference of time is 1513 Julian years Hence to find the motion of the Aphelion for 2. years say I if 1513 years give 25. 52.29 what shall one year give and the answer is 00 d. 01′ 01″ 33‴ 56 iv 44v. that is in Decimal numbers 0. 00475. 04447. 0555. And the motion for 1651 years 7. 84298. 4208862 which being deducted from the place of the Aphelion Anno Christi 1652 26. 82245. 3703703. The remainer viz. 18. 97946. 9494841 is the place thereof in the beginning of the Christian AEra which being reduced is 68 deg 19. min. 33. sec. 56. thirds 4. The Earths middle motion Aphelion and Excentricity being thus found we will now shew how the same may be stated to any particular time desired and this must be done by help of the Sun or Earths place taken by observation In the 178 year then from the death of Alexander Mechir the 27 at 11 hours P. M. Hipparcus found in the Meridian of Alexand. that the Sun entered ♈ 0. the which Vernal Equinox happened in the Meridian of London according to Mr. Wings computation at 9 hours 14′ and the Suns Aphelion then may thus be found The motion of the Aphelion for one year was before found to be 0. 00475. 04447. 0555. therefore the motion thereof for one day is 0. 00001. 501491722. The Christian AEra began in the 4713 year compleat of the Julian Period in which there are days 1721423. The AEra Alexandri began November the twelfth in the year 4390 of the Julian Period in which there are 1603397 days And from the death of Alexander to the 27 of Mechir 178 there are days 64781 therefore from the beginning of the Julian Period to the 178 year of the AEra Alexandri there are days 1668178 which being deducted from the days in the Christian AEra 1721423 the remainer is 53245 the number of days between the 178 year after the death of Alexander Mechir 27 and the beginning of the Christian AEra Or thus From the AEra Alexandri to the AEra Christi there are 323 Julian years and 51 days that is 118026 days And from the AEra Alexandri to the time of the observation there are 64781 days which being deducted from the former the remainer is 53245 as before Now then if you multiply the motion of the
5 h. 29′ Mr. Tho. Street 5 h. 49′ 01″ taking therefore the Tropical year to consist of 365 days 5 hours 49 Minutes the Suns mean motion for one day is 0 deg 59′ 8″ 19‴ 43 iv 47 v. 21 vi 29 vii 23 viii or in decimal Numbers the whole Circle being divided into 100 degrees the ☉ daily motion is 0. 27379. 08048. 11873. 6. The Sydereal or Starry year is found from the Solar by adding the Annual Motion of the eighth Orb or praecession of the AEquinoctial Points thereunto that praecession being first converted into time 7. Now the motion of the fixed Stars is found to be about 50″ in a years time as Mr. Wing hath collected from the several observations of Timocharis Hipparchus Tycho and others and to shew the manner of this Collection I will mention onely two one in the time of Timocharis and another in the time of Tycho 8. Timocharis then as Ptolemy hath it in his Almagist sets down the Virgins Spike more northwardly than the AEquinoctial 1 deg 24′ the time of this observation is supposed to be about 291 years before Christ the Latitude 1 deg 59′ South and therefore the place of the Star was in ♠21 d. 59′ And by the observation of Tycho 1601 current it was in ♎ 18. 16′ and therefore the motion in one year 50″ which being divided by 365 days 6 hours the quotient is the motion thereof in a days time 00′ 8‴ 12 iv 48 v. 47 vi 18 vii 30 viii 13 ix and in decimal Numbers the motion for a year is 00385. 80246. 91358. The motion for a day 00001. 05626. 95938. 9. Now the time in which the Sun moveth 50″ is 20′ 17″ 28‴ therefore the length of the sydereal year is 365 days 6 hours 9′ 17″ 28‴ And the Suns mean motion for a day 59′ 8″ 19‴ 43 iv 47 v. 21 vi 29 vii 23 viii converted into time is 00. 03′ 56″ 33‴ 18 iv 55 v. 9 vi 23 vii 57 viii which being added to the AEquinoctial day 24 hours giveth the mean solar day 24 hours 3. ′ 56″ 33‴ 18 iv 55. 9. 23. 57. 10. And the daily motion of the fixed Stars being converted into time is 32 iv 51 v. 15 vi 9 vii 14 viii 24 ix and therefore the AEquinoctial day being 24 hours the sydereal day is 24 hours 00′ 00″ 00‴ 32 iv 51. 15. 9. 14 24. 11. Hence to find the praecession of the AEquinoctial Points or Longitude of any fixed Star you must add or subtract the motion thereof from the time of the observation to the time given to or from the place given by observation and you have your desire Example The place of the first Star in Aries found by Tycho in the year 1601 current was in ♈ 27 d. 37′ 00. and I would know the place thereof in the beginning of the Christian AEra The motion of the fixed Stars for 1600 years 22 d. 13′ 20″ Which being deducted from the place found by observ 27. 37. 00 The remainer 5. 231. 40 is the place thereof in the beginning of the Christian AEra 12. Having thus found the ☉ middle motion the motion of the Aphelion and fixed Stars with their places in the beginning of the Christian AEra we will now set down the numbers here exhibited AEra Christi Mr. Wing from the like observations takes the ☉ motion to be as followeth The ☉ mean Longitude 9. 8. 00. 31 Place of Aphelion 2. 8. 20. 03 The Anomaly 06. 29. 40. 28 The which in decimal Numbers are The ☉ mean Longitude 77. 22460. 86419 Place of the Aphelion 18. 98171. 29629 The Anomaly 58. 24289. 56790 The mean motions for one year The ☉ mean Longitude 99. 93364. 37563. 34 The Aphelion 00. 00475. 04447. 05 The ☉ mean Anomaly 99. 92889. 33116. 29 The ☉ mean motions for one day The ☉ mean Longitude 00. 27379. 08048. 11 The Aphelion 00. 00001. 30149. 17 The mean Anomaly 00. 27377. 77898. 94 And according to these measures are the Tables made shewing the ☉ mean Longitude and Anomaly for Years Months Days and Hours CHAP. XII The Suns mean motions otherwise stated SOme there are in our present age that will not allow the Aphelion to have any motion or alteration but what proceeds from the motion of the fixed Stars the which as hath been shewed do move 50 seconds in a year and hence the place of the first Star in Aries in the beginning of the Christian AEra was found to be ♈ 5. 23d. 40. Now then if from the place of the Aphelion Anno Christi 1652 as was shewed in the tenth Chapter deg 96. 33′ 39. we deduct the motion of the fixed Stars for that time 28. 19. 12. the remainer 68. 14. 27 is the constant place of the Aphelion but Mr. Street in his Astronomia Carolina Page 23 makes the constant place of the Aphelion to be 68d. 20. 00 and the ☉ excentricity 1732. The place of the Sun observed ♈ 0. 33. 19 The praecession of AEquinox 0. 27. 27. 22 The Earths Sydereal Longitude 5. 03. 05. 57 The place of the Aphelion Subtract 8. 08. 20. 00 The Earths true Anomaly 8. 24. 45. 57 AEquation Subtract 1. 58. 47 The remainer is the Estimate M. Anom 8. 22. 47. 10 AEquation answering thereto add 1. 58. 27 The Earths true Anomaly 8. 24. 45. 37 The place of the Aphelion 8. 08. 20. 00 Praecession of the AEquinox 0. 27. 27. 22 Place of the Sun ♈ 00. 32. 59 But the place by observation ♈ 00. 33. 19 The difference is 001. 001. 20 Which being added to the mean Anom 8. 22. 47. 10 The mean Anomaly is 8. 22. 47. 30 The absolute AEquation 1. 58. 27 The true Anomaly 8. 24. 45. 57 Agreeing with observation  And so the mean Anomaly AEra Christi is 6. 23. 19. 56. But Mr. Flamsted according to whose measure the ensuing Tables are composed takes the mean Anomaly AEra Christi to be 6. 24. 07. 091. The place of the Aphelion to be 8 08. 23. 50. And so the Praecession of the AEquinox and Aphelion in the beginning of the Christian AEra 8 13. 47. 30. in decimal Numbers AEra Christi The Suns mean Anomaly 56. 69976. 85185 The Suns Apogaeon and Praec AEq. 20. 49768. 51851 The ☉ mean motions for one Year The ☉ mean Longitude 99. 93364. 37563. 34 The Praecession of AEquin 00385. 80246. 91 The ☉ mean Anomal 99. 92978. 57316. 43 The ☉ mean Motions for one Day The ☉ mean Longitude 00. 27379. 08048. 11 The Praecession of AEqui 00. 00001. 05699. 30 The ☉ mean Anom 00. 27378. 02348. 81 CHAP. XIII How to Calculate the Suns true place by either of the Tables of middle motion VVRite out the Epocha next before the given time and severally under that set the motions belonging to the years months and days compleat to the hours scruples current every one under his like only remember that in the Bissextile years after the end of Frebruary
or 146 days 53 revolutions 0 Signes 7 degrees 56 minutes 45 Seconds And the Apogaeon from the AEquinox 5 Signes 12 degrees 46 minutes And hence the daily motion of her mean Anomaly will be found to be 13 d. 03′ 53″ 57‴ 09 iv 58 v. 46 vi Of her Apogaeon 0. 06. 41. 04. 03. 25. 33. And according to these Measures if you deduct the motion of the ☽ mean Anomaly for 1641 years April 4. hours 13. 37′ viz. 8. 22. 02. 00. from 3. 121. 35. 26 The remainer is 6. 201. 33. 26 from which abating 20′ 41″ the ☽ mean Anom AEra Chr. 6. 20. 12. 45.  In like manner the motion of her Apogaeon for the same time is 6. 05. 311. 57 which being deducted from 3. 17. 25. 57 The remainer is 9. 11. 55. 56 To which if you add 21.04 The Sum 91. 121. 15200 is the place of the ☽ Apogaeon in the beginning of the Christian AEra  CHAP. XVI Of the finding of the place and motion of the Moons Nodes ANno Christi 1652 March 28 hour 22. 16′ the Sun and Moon being in conjunction Mr. Street in Page 33 computes the ☽ true place in the Meridian of London to be in ♈ 19. 14. 18 with latitude North 46′ 15″ And Anno Christi 1654 August 1. hour 21. 19′ 30″ was the middle of a Solar Eclipse at London at which time the Moons true place was found to be in ♌ 18. 58′ 12″ with North Latitude 32′ 01″ 1654 August 1. 21. 19′ 30″ ☽ place ♌ 18. 58. 12 1652 March 28. 22. 16. 00 ☽ place ♈ 19. 14. 18 From the first observation to the second there are 27 years 4 months 5 days 23 hours 03′ 30″ Mean motion of the Nodes in that time deg 45. 19. 41 The true motion of the ☽ 119. 43. 54 Their Summ is in Fig. 11. The angle DPB 165. 03. 35 Therefore in the oblique angled Spherical Triangle DPB we have given BP 89. 13. 45 the complement of the Moons Latitude in the first Observation 2. PD 89. 27. 50 the complement of the Moons Latitude in the second observation and the angle DPB 165. 03. 35 whose complement to a Semicircle is DPF 14. 56. 25. The angle PBD is required 1. Proportion As the Cotangent of PD 89. 27. 50 9.97114485 Is to the Radius 10.00000000 So is the Cosine of DPF 14. 56. 25 9.98506483 To the tang of PF 89. 26. 42 12.01191998 BP 89. 13. 45  Their Z is FPB 178. 40. 27. whose complement Is the Arch FG 1. 19. 33. 2. Proportion As the Sine of FP 89. 26. 42. Co. ar 0.00002037 Is to the Cotang of DPF 14. 56. 25 10.57376158 So is the Sine of FG 1. 19. 33 8.36418419 To the Cotang of FGD 85. 02. 56 8.93796614 FGD = PBD inquired  And in the right angled Spherical Triangle BA ☊ right angled at A we have given AB 046′ 15″ the Latitude in the first observation and the Angle AB ☊ = PBD 85. 02. 56. to find A ☊ the Longitude of the Moon from the ascending Node As the Cot. of AB ☊ 85. 02. 56 8.93796614 Is to the Radius 10.00000000 So is the Sine of AB 0 46′ 15″ 8.12882290 To the tang of A ☊ 8. 49. 17 9.19085676 2. To find the Angle A ☊ B. As the tang of AB 0. 46. 15 8.12886212 Is to the Radius 10.00000000 So is the Sine of A ☊ 8. 49. 17 9.18569718 To the Cotang of A ☊ B 5. 0. 41 11.05682506 The angle of the ☽ orbite with the Ecliptick  The first observed place of the ☽ ♈ 19. 14. 18 A ☊ Subtract 8. 49. 17 There rests the true place of the ☊ ♈ 10. 25. 01 The retrograde motion whereof in 4 Julian years or 2461 days is by other observations found to be Sign 2. deg 17. 22′ 06″ and therefore the daily motion deg 0. 03′ 10″ 38‴ 11 iv 35 v. And the motion thereof for 1651 years March 28. h. 22. 16′ viz. Sign 8. deg 18. 26′ 58″ being added to the place of the Node before found Sig. 0. 10. 25 01. Their Sum is the place thereof in the beginning of the Christian AEra Sign 8. deg 28. 51′ 59″ But the Rudolphin Tables as they are corrected by Mr. Horron and reduced to the Meridian of London do differ a little from these measures for according to these Tables the Moons mean motions are AEra Christi The Moons mean Longitude is Sign 04. deg 02. 25. 55 The Moons Apogaeon Sign 09. deg 13. 46. 59 The Moons mean Anomaly Sign 06. deg 18. 38. 56 The Moons Node Retrograde Sign 08. deg 28. 33. 16 And according to these measures the Moons mean motions in decimal Numbers are AEra Christi The Moons mean Longitude deg 34. 00887.345677 The Moons Apogaeon deg 78. 82862.654320 The Moons mean Anomaly deg 55. 18024.691357 The Moons Node Retrograde deg 74. 69845.679010 The ☽ mean motion for one year The Moons mean Longitude deg 35. 94001. 44893. 1 The Moons Apogeaon deg 11. 29551. 126365 The Moons mean Anomaly deg 24. 64450. 322566 The Moons Node Retrograde deg 05. 36900. 781604 The ☽ mean motion for one day The Moons mean Longitude deg 03. 66010. 962873 The Moons Apogaeon deg 00. 03094. 660620 The Moons mean Anomaly deg 03. 62916. 302253 The Moons Node Retrograde deg 00. 01470. 961045 And according to these measures are the Tables made shewing the Moons mean Longitude Apogaeon Anomaly and Node retrograde for Years Months Days and Hours And hence to compute the Moons true place in her Orbit I shall make use of the Method which Mr. Horron in his Posthumas works lastly published by Mr. Flamsted in which from the Rudolphin Tables he sets down these Dimensions The Moons mean Semidiameter deg 00. 15′ 30″ Her mean distance in Semid of the Earth Deg. 11. 47. 22 The half whereof deg 5. 53. 41. he adds 45 the whole is deg 50. 53. 41 Whos 's Artificial cotangent is 9.91000022 And the double thereof makes this standing Numb 9.82000044  Greatest 6685. 44  The Moons Mean 5523. 69 Excentricity  Least 4361. 94  And her greatest variation 00. 36′ 27″ These things premised his directions for computing the Moons place are as followeth CHAP. XVII How to Calculate the Moons true place in her Orbit TO the given time find the true place of the Sun or his Longitude from the Vernal AEquinox as hath been already shewed 2. From the Tables of the Moons mean motions write out the Epocha next before the given time and severally under that set the motions belonging to the years months and days compleat and to the hours and scruples current every one under his like only remember that in the Bissextile years after the end of February the days must be increased by one Unite then adding them all together the Summ shall be the Moons mean motions for the time given But in her Node Retragrade you must leave out the Radix or
according to the title the Sum or difference is the true place of the Node which being deducted from the place of the Moon in her Orb the Remainer shall be the Augment of Latitude or Distance of the Moon from the Node or Leg A ☊ 2. With the Augment of Latitude enter the Table of the Moon 's Latitude and take thence her Simple and Latitude and Increase answering to it Then say as the whole excess of Latitude 18′ or in Decimals 30. is to the Inclination of the Monethly limit So is the increase of Latitude to the Part Proportional which being added to the simple Latitude will give you the true Latitude of the Moon 3. With the same Augment of Latitude enter the Table of Reduction and take thence the Reduction and Inclination answering thereto Then say again as 18′ 00″ or 0. 30. is to the Inclination of the Monethly limit So is the increase of Reduction to the Part Proportional which being added to the simple Reduction shall give the true to be added to or subtracted from the place of the Moon in the Ecliptick Example By the former Chapter we found the mean motion of the Node to be 95. 96094 which reduced to the Degrees and Parts of the common Circle is 345.459384 And the Suns true place to be 345.291334 Their difference is the distance ☉ à ☊ 168050 with which entring the Table Entituled Tabula AEquationis Nodorum Lunae I find the Node to need no Equation and the Inclination limitis menstrui to be deg 00. 30. The place of the ☽ in her Orbit 55.698954 The Nodes true place subtract 345.459384 The Augment of Latitude 70.239570 2. With this Augment of Latitude I enter the Table shewing the Moons simple Latitude and thereby find her simple Latitude to be Degrees 04. 70476. North And the increase 00.28234 And therefore the Moons true Latitude is deg 4.98610 3. With the same Augment of Latitude I enter the Table of Reduction and thereby find the Reduction to be 00.06955 And the increase of Reduction to be deg 00.00855 And therefore the whole Reduction to be sub 00.07810 From the ☽ place in her Orbit 55.69895 The ☽ true place in the Ecliptick 55.62085 That is in Sexagenary Numbers 8. 25. 37′ 15″ CHAP. XIX To find the Mean Conjunction and Opposition of the Sun and Moon TO this purpose we have here exhibited a Table shewing the Moons mean motion from the Sun the construction whereof is this By the Tables of the Moons mean motions her mean Longitude AEra Christi is 34.0088734567 The ☉ mean Anomaly 56.6997085185 Praecession of the AEquinox 20.4976851851 Their Sum is the ☉ mean longit AEra a Christi 77.4973937036 Which being deducted from the ☽ mean longitude the remainer is the Moons mean 56.8114797531 distance from the Sun in the beginning of the Christian AEra  In like manner the Moons mean distance from the Sun in a year or a day is thus found ☉ Anomaly for a year 99.9297857316 Praecession of the AEquinox 0038580246 Their Sum subtract 99.9336437562 From the ☽ mean Longitude 35.9400144893 Moons distance from the ☉ 36.0063707331 Moons distance from the Sun in a days time ☉ mean Anomaly 27378.02348 Praecession of the AEquinox 1.05699 Their Sum subtract 27379.08047 From the ☽ mean Longitude 03. 66010.96287 ☽ Daily motion from the ☉ 03. 38631.88240 And according to these measures are the Tables made shewing the Moons mean motion from the Sun by which the mean conjunction of the ☽ and Moon may be thus computed To the given year and Month gather the middle motions of the Moon from the Sun and take the complement thereof to a whole Circle from which subtracting continually the nearest lesser middle motions the day hour and minute enfuing thereto is the mean time of the Conjunction Example Anno Christi 1676. I would know the time of the mean Conjunction or New Moon in October Epocha 1660 32.697283 Years Compl. 15. 50.254463 Septemb. Compl. 24.465038 1. day for Leap-year 03.386318 Their Sum is the Moons motion from the ☉ 10.803102 Complement to a whole Circle 89.196898 Days 26 Subtract 88.044289 Hours 8. substract 1.152609 1.128772 Minutes 10 Subtract 0.023837 0.023516 The Remainer giveth 8″ .00321 Therefore the mean Conjunction in October 1676. was the 26 day 10 min. 8 seconds after 8 at night And to find the mean opposition To the complement of the middle motion add a semicircle and then subtract the nearest lesser middle motions as before the day hour and minute ensuing thereto shall be the mean opposition required Example Anno Christi 1676. I desire to know the mean opposition in November Epocha 1660 32.697283 Years Compl. 15 50.254463 October Compl. 29.440922 1 day for Leap-year 03.386318 The ☽ mean motion from the ☉ 15.778986 Complement to a whole Circle 84.221014 To which add a Semicircle 50. The Sum is 34.221014 Day 10 subtract 33.863188 Hours 2. .357826 .282193 Minutes 32. .075633 .075251 The Remainer giveth 9 seconds .000382 Therefore the Full Moon or mean Opposition of the Sun and Moon was November the 10th Hours 2 32′ 09″ The like may be done for any other And here I should proceed to shew the manner of finding the true Conjunction or Opposition of the Sun and Moon but there being no decimal Canon yet extant suitable to the Tables of middle motions here exhibited I chuse rather to refer my Reader to Mr. Street's Astronomia Carolina for instructions in that particular and what else shall be found wanting in this Subject AN INTRODUCTION TO Geography OR The Fourth Part of COSMOGRAPHY CHAP. I. Of the Nature and Division of Geography GEOGRAPHY is a Science concerning the measure and distinction of the Earthly Globe as it is a Spherical Body composed of Earth and Water for that both these do together make but one Globe 2. And hence the parts of Geography are two the one concerns the Earthy part and the other the Water 3. The Earthy part of this Globe is commonly divided into Continents and Islands 4. A Continent is a great quantity of Land not separated by any Sea from the rest of the World as the whole Continent of Europe Asia and Africa or the Continents of France Spain and Germany 5. An Island is a part of Earth environed round about with some Sea or other as the Isle of Britain with the Ocean the Isle of Sicily with the Mediterranean and therefore in Latine it is called Insula because it is scituate in Salo in the Sea 6. Both these are subdivided into Peninsula Isthmus Promontorium 7. Peninsula quasi pene insula is a tract of land which being almost encompassed round by water is joyned to the main land by some little part of Earth 8. Isthmus is that narrow neck of Land which joyneth the Peninsula to the Continent 9. Promontorium is a high mountain which shooteth it self into the Sea the outmost end whereof is called a Cape or Foreland as the Cape of Good Hope in Africk 10. The
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
and Gallick Ocean Those of most note are these six 1. Oleron 2. Reâ— 3. Iarsey 4. Gernsey 5. Sarke 6. Aldernay on the shores of Normandy of which the four last are under the Kings of England 15. Italy once the Empress of the greatest part of the then known World is compassed with the Adriatick Ionian and Tyrrhenian Seas except it be towards France and Germany from which it is parted by the Alpes so that it is in a manner a Peninsula or a Demi-Island But more particularly it hath on the East the lower part of the Adriatick and the Ionian Sea by which it is divided from Greece on the West the River Varus and some part of the Alpes by which it is parted from France on the North in some part the Alpes which divide it from Germany and on the other part of the Adriatick which divides it from Dalmaria and on the South the Tyrrhenian and Tuscan Seas by which it is separated from the main Land of Africa 16. It containeth in length from Augusta Praetoria now called Aost at the foot of the Alpes unto Otranto in the most Eastern Point of the Kingdom of Naples 1020 miles in breadth from the River Varo which parts it from Provence to the mouth of the River Arsia in Friuli where it is broadest 410 miles about Otranto where it is narrowest not above 25 miles and in the middle parts from the mouth of Peseara in the Adriatick or upper Sea to the mouth of Tiber in the Tuscan or lower Sea 126 miles The whole compass by Sea reckoning in the windings and turnings of the shore comes to 3038 miles which added to the 410 which it hath by Land make up in all 3448 miles but if the Coasts on each side be reckoned by a straight Line then as Castaldo computes it it comes to no more than 2550 miles 17. The whole Country lieth under the first and sixth Climates of the Northern temperate Zone which it wholly taketh up so that the longest day in the most Northern Parts is 15 hours and three first parts of an hour the longest in the Southern Parts falling short a full hour of that length 18. Italy as it stands now is divided into the Kingdoms of Naples Sicily and Sardinia 2. The Land or Patrimony of the Church 3. The great Dukedom of Tuscany 4. The Common-wealths of Venice Genoa and Luca. 5. The Estates of Lombardy that is the Dukedoms of 1. Mâ—llain 2. Mantua 3. Modena 4. Parma 5. Montferrat and the Principality of Piedmont 19. To the Peninsula of Italy belong the Alpes aridge of Hills wherewith as with a strong and defensible Rampart Italy is assured against France and Germany They are said to be five days Journey high covered continually with Snow from the whiteness whereof they took this name it doth contain the Dukedom of Savoy the Seigniory of Geneva the Country of Wallisland Switzerland and the Grisons 20. Belgium or the Netherlands is bounded on the East with Westphalin Gulick Cleve and the Land of Triers Provinces of the higher Germany on the West with the main Ocean which divides it from Britain on the North with the River Ems which parts it from East-Friezeland on the South with Picardie and Campagne two French Provinces upon the South-East with the Dukedom of Lorrain 21. It is in compass 1000 Italian or 280 German miles and is situated in the Northern temperate Zone under the seventh eighth and ninth Climates the longest day in the midst of the seventh Climate where it doth begin being 16 hours iu the beginning of the ninth Climate increased to 16 hours 3 quarters or near 17 hours 22. It containeth those Provinces which in these later Ages were possessed by the House of Burgundy that is the Lordship of West-Friezeland given to the Earls of Holland by Charles the Bald the Earldom of Zutphen united unto that of Gelder by Earl Otho of Nassau and finally the Estate of Groening Over-Yssel and some part of Vtrecht by Charles the Fifth As it stands now divided between the Spaniards and the States it containeth the Provinces of 1. Flanders 2. Artois 3. Hainault 4. The Bishoprick of Cambray 5. Namur 6. Luxemburg 7. Limbourg 8. Luyckland or the Bishoprick of Leige 9. Brabant 10. Marquisate 11. Meohlin The rest of the Netherlands which have now for sometime withdrawn their obedience from the Kings of Spain are 1. Holland 2. Zeland 3. West-Friezeland 4. Vtrecht 5. Over-Yssel 6. Gelderland 7. Zutphen 8. Groening 23. Germany is bounded on the East with Prussia Poland and Hungary on the West with France Switzerland and Belgium on the North with the Baltick Seas the Ocean and some part of Denmark on the South with the Alps which part it from Italy 24. The length from East to West that is from the Vistula or Weissel to the Rhine is estimated at 840 Italian miles the breadth from North to South that is from the Ocean to the Town of Brixen in Tyrol 740 of the same miles So that the Figure of it being near a Square it may take up 3160 miles in compass or thereabouts Situate in the Northern temperate Zone between the middle Parallels of the sixth and tenth Climates the longest day in the most Southern Parts being 15 hours and an half and in the most Northern 17 hours and a quarter 25. The Principal Parts of this great Continent are 1. Cleveland 2. The Estates of the three spiritual Electors Colen â—â—â—ntz and Triers 3. The Palatinate of the Rhine 4. Alsatia 5. Lorrain 6. Suevia or Schwaben 7. Bavaria 8. Austria and its Appendices 9. The Confederation of Waderaw 10. Franconia 11. Wirtenberg 12. Baden 13. The Palatinate of Northgoia or the Upper Palatinate 14. Bohemia and the Incorporate Provinces 15. Pomerania 16. Mecklenburg 17. The Marquisate of Brandenburg 18. Saxony and the Members of it 19. The Dukedom of Brunswick and Lunenburg 20. The Lantgravedom of Hassia 21. Westphalen 22. East-Friezeland 26. Denmark or Danemark reckoning in the Additions of the Dukedom of Holstein and the great Continent of Norway with the Isles thereof now all united and incorporated into one Estate is bounded on the East with the Baltick Sea and some part of Sweden on the West with the main Western Ocean on the North-East with a part of Sweden full North with the main frozen Seas and on the South with Germany from which it is divided on the South-West by the River Albis and on the South-East by the Trave a little Isthmus or neck of Land uniting it to the Continent 27. It lieth partly in the Northern temperate Zone and partly within the Arctick Circle extending from the middle Parallel of the tenth Clime or 55 degree of Latitude where it joyneth with Germany as far as the 71 degree where it hath no other bound but the frozen Ocean by which account the longest day in the most Southern Parts is 17 hours and a quarter but in the Parts extreamly North they have no Night for
two whole Moneths three Weeks one Day and about seven hours as on the other side no day for the like quantity of time when the Sun is most remote from them in the other Tropick 28. The whole Body of the Estate consisteth chiefly of three Members viz. 1. The Dukedom of Holstein containing Waggerland Dilmarsh Starmaria and Holstein especially so called 2. The Kingdom of Denmark comprehending both Iuitlands part of Scandia and the Hemodes or Baltick Islands 3. The Kingdom of Norway consisting of Norway it self and the Islands of the Northern Ocean 29. Swethland is bounded on the East with Muscovy on the West with the Doferine Hills which divide it from Norway on the North with the great frozen Ocean spoken of before on the South with Denmark Liefland and the Baltick Sea 30. It is situate under the same Parallels and Degrees with Norway that is from the first Parallel of the 12 Clime where the Pole is elevated 58 degrees 26 minutes as far as to the 71 degree of Latitude by which account the longest day in the Southern Point is but 18 hours whereas on the farthest North of all the Countrey they have no Night for almost three whole Moneths together 31. The whole Kingdom is divided into two Parts the one lying on the East the other on the West of the Bay or Gulf of Bodener being a large and spacious branch of the Baltick Sea extending from the most Southerly Point of Gothland as far as to Lapland on the North. According to which Division we have the Provinces of 1. Gothland 2. Sweden lying on the West side of the Gulph 3. Lapland shutting it up upon the North. 4. Bodia or Bodden 5. Finland on the East side thereof 6. The Sweedish Islands where it mingleth with the rest of the Baltick Seas 32. Russia is bounded on the East by Tartary on the West with Livonia and Finland from which it is divided by great mountains and the River Poln on the North by the frozen Ocean and some part of Lapland and on the South by Lituania a Province of the Kingdom of Poland and the Crim Tartar inhabiting on the Banks of Palus Maeotis and the Euxine Sea It standeth partly in Europe and partly in Asia the River Tanais or Don running through it the common boundary of those great and noted parts of the world 33. It is scituate North within the Artick Circle so far that the longest day in Summer will be full six months whereas the longest day in the southern parts is but 16 hours and an half 34. It is divided into the Provinces of 1. Moscovy specially so called 2. Snolâ—usio 3. Masaisky 4. Plesco 5. Novagrod the great 6. Corelia 7. Blarmia 8. Petzora 9. Condora 10 Obdora 11. Iugria 12. Severia 13. Permia 14. Rozan 15. Wiathka 16. Casau 17. Astracan 18. Novogordia inferiour 10. The Morduits or Mordua 20. Worotime 21. Tuba 22. Wolodomir 23. Duina 24. the Russian Islands 35. Poland is bounded on the East with Russia and the Crim-Tartar from whom it is parted by the River Borysthenes on the West with Germany on the North with the Baltick Sea and some part of Russia on the South with the Carpathian Mountains which divide it from Hungary Transilvania and Moldavia It is of figure round in compass 2600 miles scituate under the 8 and 12 Climates so that the longest day in the southern parts is but 16 hours and about 18 hours in the parts most North. 36. The several Provinces of which this Kingdom doth consist are 1. Livonia 2. Samogitia 3. Lituania 4. Volkinia 5. Podolia 6. Russia nigra 7. Massovia 8. Podlassia 9. Prussia 10. Pomerellia 11. Poland specially so called 37. Hungary is bounded on the East with Transilvania and Walachia on the West with Sterria Austria and Moravia on the North with the Carpathian mountains which divide it from Poland and on the South with Sclavonia and some part of Dacia it extendeth in length from Presburg along the Danow to the borders of Transilvania for the space of 300 English miles and 190 of the same miles in breadth 38. It lieth in the Northern temperate Zone betwixt the middle parallels of the 7 and 9 Climates so that the longest Summers day in the Southern parts is but 15 hours and an half and not above 16 hours in the parts most North. 40. This Country is commonly divided into the upper Hungary and the lower the upper lying on the North of the River Danow the lower lying on the South of that River comprehending all Pannonia inferior and part of Superior and is now possessed by the King of Hungary and the Great Turk who is Lord of the most part by Arms and Conquest 04. Sclavonia is bounded on the East with Servia Macedonia and Epirus from which it is parted by the River Drinus and a line drawn from thence unto the Adriatick on the West with Carniola in Germany and Istria in the Seigniory of Venice from which last it is divided by the River Arsia on the North with Hungary on the South with the Adriatick Sea 41. It is scituate in the Northern temperate Zone between the middle Parallels of the sixth and seventh Climates so that the longest day in Summer is about 15 hours and an half 42. This Country as it came at last to be divided between the Kings of Hungary and the State of Venice is distinguished into 1. Windischland 2. Croatia 3. Bosnia 4. Dalmatia 5. Liburnia or Cantado di Zara and 6. The Sclavonian Islands 43. Dacia is bounded on the East with the Euxine Sea and some part of Thrace on the West with Hungary and Sclavonia on the North with Podolia and some other members of the Realm of Poland on the South with the rest of Thrace and Macedonia 44. It lieth on both sides of the Danow fronting all along the upper and the lower Hungary and some part of Sclavonia extended from the 7 Climate to the 10 so that the longest Summers day in the most northern parts thereof is near 17 hours and in the most southern 15 hours 3 quarters 45. The several Provinces comprehended under the name of Dacia are 1. Transilvania 2. Moldavia 3. Walachia 7. Rascia 5. Servia 6. Bulgaria the first four in old Dacia on the North side of the Danow the two last in new Dacia on the South thereof 45. Greece in the present Latitude and extent thereof is bounded on the East with the Propontick Hellespont and AEgean Seas on the West with the Adriatick on the North with Mount Haemus which parteth it from Bulgaria Servia and some part of Illyricum and on the South with the Sea Ionian so that it is in a manner a Peninsula or Demi-Island environed on three sides by the Sea on the fourth only united to the rest of Europe 46. It is scituate in the northern temperate Zone under the fifth and sixth Climates the longest day being 15 hours 47. In this Country formerly so famous for learning and
 Hours 1 04.16666667 2 08.33333333 3 12.5 4 16.16666667 5 20.83333333 6 25.0 7 29.16666667 8 33.33333333 9 37.5 10 41.66666667 11 45.83333333 12 50. 13 54.16666667 14 58.33333333 15 62.5 16 66.66606667 17 70.83333333 18 75.00 19 79.16660667 20 83.33333333 21 87.5 22 91.66666667 23 95.83333333 24 100.00000000  Minutes 1 0.06944444 2 0.13888888 3 0.20833333 4 0.27777777 5 0.34722222 6 0.41666666 7 0.48611111 8 0.55555555 9 0.625 10 0.69444444 11 0.76388888 12 0.83333333 13 0.90277777 14 0.97222222 15 1.04166666 16 1.11111111 17 1.18055555 18 1.25 19 1.31944444 20 1.38888888 21 1.45833333 22 1.52777777 23 1.59722222 24 1.66666666 25 1.73611111 26 1.80555555 27 1.875 28 1.94444444 29 2.01388888 30 2.08333333 The Decimal parts of a Day and the contrary Seconds  Minutes Seconds .00115740 31 2.15277777 .03587963 .00231481 32 2.22222222 .03703704 .00347222 33 2.29166666 .03819444 .00462962 34 2.36111111 .03935185 .00578703 35 2.43055555 .04050926 .00694444 36 2.5 .04166666 .00810184 37 2.56944444 .04282407 .00925925 38 2.63888888 .04398148 .01041660 39 2.70833333 .04513888 .01157405 40 2.77777777 .04629629 .01273148 41 2.84722222 .04745370 .01388888 42 2.91666666 .04861111 .01504630 43 2.98611111 0497685â— .01620371 44 3.05555555 .05092592 .01736111 45 3.125 .05208333 .01851853 46 3.19444444 .05324074 .01967593 47 3.26388888 .05439814 .02083333 48 3.33333333 .05555555 .02199074 49 3.40277777 .05671296 .02314810 50 3.47222222 .05787037 .02430555 51 3.54166666 .05902777 .02546295 52 3.61111111 .06018518 .02662037 53 3.68055555 06134â—59 .02777777 54 3.75 .0625 .02893518 55 3.81944444 .06365741 .03009259 56 3.88888888 .06481481 .03125000 57 3.95833333 .06597222 .03240741 58 4.02777777 .06712963 .03356482 59 4.09722222 .06828704 .03472222 60 4.16666666 .06944444 A Catalogue of some of the most eminent Cittes and Towns in England and Ireland wherein is shewed the difference of their Meridian from London with the hight of the Pole Names of Citties Differ Merid. Hight Pole St. Albons 0 1 s 55.55 Barwick 0 6 s 55.49 Bedford 0 2 s 52.18 Bristol 0 11 s 51.32 Boston 0 0 53.2 Cambridge 0 1 a 52.17 Canterbury 0 5 a 51.27 Carlile 0 10 s 54.57 Chester 0 11 s 53.20 Coventry 0 4 s 52.30 Carmarthen 0 17 s 52.2 Chichester 0 3 s 50.56 Colchester 0 5 a 52.4 Darby 0 5 s 53.6 Dublin in Ireland 0 26 s 53.11 Duresmâ— 0 5 s 54.45 Dartmouth 0 15 s 50.32 Eely 0 1 a 52.20 Granthaâ— 0 2 s 52.58 Glocester 0 9 s 52.00 Halefax 0 6 s 52.49 Hartford 0 1 s 52.50 Hereford 0 11 s 52.14 Huntington 0 1 s 52.19 Hull 0 1 s 53.58 Lancaster 0 11 s 54.08 Leicester 0 4 s 52.40 Lincoln 0 1 s 53.12 Middle of the Isle of Man 0 17 s 54.22 Nottingham 0 4 s 53.03 Newark 0 3 s 53.02 Newcastle 0 6 s 54.58 N. Luffingham 0 3 s 52.41 Norwich 0 4 a 52.44 Northampton 0 4 s 52.18 Oxford 0 5 s 51.54 Okenham 0 3 s 52.44 Peterborough 0 2 s 52.35 Richmond 0 6 s 54.26 Rochester 0 3 a 51.28 Ross 0 10 s 52.07 St. Michaels Mount in Cornwal 0 23 s 50.38 Stafford 0 8 s 52.55 Stamford 0 2 s 52.41 Shrewsbury 0 11 s 52.48 Tredah in Ireland 0 27 s 53.28 uppingham in Rutland 0 3 s 52.40 Warwick 0 6 s 52.25 Winchester 0 5 s 50.10 Waterford in Ireland 0 27 s 52.22 Worcester 0 9 s 52.20 Yarmouth in Suffolk 0 6 a 52.45 York 0 4 s 54.00 London 0 00 51.32 The Suns mean Longitude and mean Anomaly in AEgyptian Years  ☉ Mean Longitude ☉ Mean Anomaly 1 99.9336437563 99.9288933116 2 99.8672875126 99.8577866232 3 99.8009312690 99.7866799348 4 99.7345750253 99.7155732465 5 99.6682187816 99.6444665581 6 99.6018625380 99.5733598697 7 99.5355062943 99.5022531814 8 99.4691500506 99.4211464930 9 99.4027938070 99.3600398046 10 99.3364375633 99.2889331162 100 93.3643756334 92.8893311628 1000 33.6437563341 28.8933116289 The Suns Mean Anomaly and Praecession of the AEquinox 8 in 1 AEgyptian Years Year ☉ Mean Anomaly Praecession AEquinox 1 99.9297857316 00.0038580246 2 99.8595714632 00.0077160493 3 99.7893571949 00.0115740740 4 99.7191429265 00.0154320987 5 99.6489286582 00.0192901234 6 99.5787143898 00.0231481481 7 66.5085001114 00.0270061728 8 99.2978573164 00.0308641975 9 99.3680715847 00.0347222221 10 99.2978573164 00.0385802469 100 92.9785731642 00.3858024691 1000 99.7857316427 03.8580246913 The Suns mean Longitude and mean Anomaly in Julian Years  ☉ Mean Longitude ☉ Mean Anomaly 1 99.9336437563 99.9288933116 2 99.8672875126 99.8577866232 3 99.8009312689 99.7866799348 B 4 00.008365830 99.9892901234 5 99.9420095864 99.9181834350 6 99.875633427 99.8470767466 7 99.8092970990 99.7759700583 B 8 00.0167316602 99.9785802468 9 99.9503754165 99.9074735584 10 99.8840191728 99.8363668700 11 99.8176629291 99.7652591816 B 12 00.0250974903 99.9678703702 13 99.9587412466 99.8967636818 14 99.8923850029 99.8256569934 15 99.8260287592 99.7545503050 B 16 00.0334633205 99.9571604936 17 99.9671070768 99.8860548052 18 99.9007508331 99.8149481168 19 99.8343945894 99.7438414284 B 20 00.0418291506 99.9164506171 40 00.0836583012 99.8929012342 60 00.1254874518 99.8393518513 80 00.1673166024 99.7858024684 100 00.2091457530 99. 73225308â—5 200 00.4182015060 99.4645061710 300 00.6274372590 99.1967592565 400 00.8365830120 98.9290123420 500 01.0457287650 98.6612654275 600 01.2548745180 98.3935185130 700 01. 4640â—02710 98.1257715985 The ☉ mean Longitude and Anomaly AEra ☉ mean Longitude ☉ mean Anomaly Chr. 77. 22400.86419 58. 24289.56790 1600 80. 54891.97529 53. 95880.62961 1620 80. 59074.89035 53. 90525.69132 1640 80. 63257.80541 53. 85170.75303 1660 80. 67440.72047 53. 79815.81474 1680 80. 71623.63553 53. 74460.87645 1700 80. 75806.55059 53. 69105.93816 1720 80. 79989.46665 53. 63750.99987 1740 80. 84172.38171 53. 58396.06158 1760 80. 88265.29677 53. 53041.12329  ☉ mean Lon. in Mon. ☉ mean Ano. in Mo. Ianu. 08. 48751.49488 08. 48711.14867 Febr. 16. 15365.74832 16. 15288.96037 Mar. 24. 64117.24320 24. 64000.10904 April 32. 85489.65760 32. 85333.47872 May 41. 34241.15248 41. 34044.62739 Iune 49. 55613.56688 49. 55377.99708 Iuly 58. 04365.06176 58. 04089.14575 Aug. 66. 53116.55664 66. 52800.29442 Sept. 74. 74488.97104 74. 74133.66410 Octo. 83. 23240.46592 85. 22844.81277 Nov. 91. 44612.88032 91. 44178.18245 Dec. 99. 93364.37563 99. 92889.33116 In Anno â—issentili post Februarium adde unum diem unius dies motum The Suns mean Longitude and mean Anomaly in Days  ☉ mean Longitude ☉ mean Anomaly 1 0.2737908048 0.2737777898 2 0.5475816096 0.5475555796 3 0.8213724144 0.8213333694 4 1.0951632192 1.0951111592 5 1 3â—89540240 1.3688889490 6 1.6427448288 1.6426667388 7 1.9165356336 1.9164445286 8 2.1903264384 2.1902223184 9 2.4641172432 2.4640001082 10 2.7379080480 2.7377778980 11 3.0116988528 3.0115556878 12 3.2854896576 3.2853334776 13 3.5592804624 3.5591112674 14 3.8330712672 3.8328890572 15 4.1068620720 4.1066668470 16 4.3806428768 4.3804446368 17 4.6544436816 4.6542224266 18 4.9282344864 4.9280002164 19 5.2020252912 5.2077780062 20 5.4758160960 5.4755557960 21 5.7496069008 5.7493335858 22 6.0233977056 6.0231113756 23 6.2971885104 6.2968891654 24 6.5709793152 6.5706669552 25 6.8447701200 6.8444447450 26 7.1185609248 7.1182225348 27 7.3923517296 7.3920003246 28 7.6661425344 7.6957781144 29 7.9399333392 7.9395559042 30 8.2137241440 8.2133336940 31 8.4875149488 8.4871114838 The Suns mean Longitude and mean Anomaly in Days  ☉ Mean Longitude ☉ Mean Anomaly 1 0.0114079502 0.0114074079 2 0.0228159004 0.0228148158 3 0.0342238506 0.0342222237 4 0.0456318008 0.0456296316 5 0.0570397510 0.0570370395 6 0.0684477012 0.0684444474 7 0.0798556514 0.0798518553 8 0.0912636016 0.0912592632 9 0.1026715518