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
worse of the two yet not so bad but that our Dissenting Brethren have I hope some better Arguments to justifie their Non-conformity than what I see published in a little Book without any name to it concerning two Easters in one Year by the General Table saith this learned man who owneth the Feast of Easter was to be observed Anno 1674. upon the 19 day of April so the Almanacks for that Year as well as the General Table set before the Book of Common Prayer but by the Rule in the said Book of Common Prayer given the Feast of Easter should have been upon the twelfth of April for Easter-Day must always be the first Sunday after the first Full Moon which happeneth next after the one and twentieth day of March and if the Full Moon happen upon a Sunday Easter-Day is the Sunday after Now in the Year 1674. the 19 of April being Friday was Full Moon therefore by this Rule Easter-Day should be the twelfth and by the Table and the Common Almanacks April the tenth but this learned man must know that the mistake is in himself and not in the Rule or Table set down in the Book of Common Prayer for if he please to look into the Calendar he will find that the Golden Number Three which was the Golden Number for that Year is placed against the last day of March and therefore according to the supposed motion of the Moon that Day was New Moon and then the Full Moon will fall upon the fourteenth day of April and not upon the tenth and so by consequence the Sunday following the first Full Moon after the 21 day of March was the nineteenth of April and not the twelfth And thus the Rule and the Table in the Book of Common Prayer for finding the Feast of Easter are reconciled and when Authority shall think sit the Calendar may be corrected and all the moveable Feasts be observed upon the days and times at first appointed but till that be a greater difference than one Week will be found in the Feast of Easter between the Observation thereof according to the Moons true motion and that upon which the Tables are grounded for by the Fathers of the Nicene Council it was appointed that the Feast of Easter should be observed upon the Sunday following the first Full Moon after the Vernal Equinox which then indeed was the 21 of March but now the tenth and in the Year 1674. Wednesday the 11 of March was Full Moon and therefore by this Rule Easter-Day should have been upon March the fifteenth whereas according to the Rules we go by it was not till April the nineteenth The Tables of the Sun and Moons middle motions are neither made according to the usual Sexagenary Forms nor according to the usual Degrees of a Circle and Decimal Parts but according to a Circle divided into 100 Degrees and Parts and this I thought good to do to give the World a taste of the excellency of Decimal Numbers which if a Canon of Sines and Tangents were fitted to it would be found much better as to the computing the Places of the Planets but as to the Primum Mobile by reason of the general dividing a Circle into 360 Degrees I should think such a Canon with the Decimal Parts most convenient and in some cases the common Sexagenary Canon may be very useful and indeed should wish and shall endeavour to have all printed together one Table of Logarithms will serve them all and two such Canons one for the Study and another for the Pocket would be sufficient for all Mathematical Books in that kind and then men may use them all or either of them as they shall have occasion or as every one is perswaded in his own mind What I have done in this particular as it was for mine own satisfaction so I am apt to believe that it will be pleasing to many others and although I shall leave every one to abound in his own sense yet I cannot think that Custom should be such a Tyrant as to force us always to use the Sexagenary form if so I wonder that men did not always use the natural Canon if no alteration may be admitted what reason can be given for the use of Logarithms and if that be found more ready than the natural in things of this kind where none but particular Students are concerned I should think it reasonable to reduce all things hereafter into that form which shall be found most ready and exact now the Part Proportional in the Artificial Sines and Tangents in the three first Degrees cannot be well taken by the common difference and the way of finding them otherwise will not be so easie in the Sexagenary Canon as in either of the other and this me thinks should render that Canon which divides each Degree into 100 Parts more acceptable but thus to retain the use of Sines Degrees and Decimal Parts doth not to me seem convenient and to reckon up a Planets middle motion by whole Circles will sometimes cause a Division of Degrees by 60 which hath some trouble in it also but if a Circle be divided into 100 Degrees this inconvenience is avoided and were there no other reason to be given this me thinks should make such a Canon to be desirable but till I can find an opportunity of publishing such an one I shall forbear to shew any further uses of it and for what is wanting here in this subject I therefore refer thee to Mr. Street's Astronomia Carolina and the several Books written in English by Mr. Wing The fourth Part of this Treatise is an Introduction unto Geography in which I have given general Directions for the understanding how the habitable part of the World is divided in respect of Longitude and Latitude in respect of Climes and Parallels with such other Particulars as will be found useful unto such as shall be willing to understand History in which three things are required The time when and this depends upon Astronomy the place where and this depends upon Geography and the Person by whom any memorable Act was done and this must be had from the Historical narration thereof and he that reads History without some knowledge in Astronomy and Geography will find himself at a loss and be able to give but a lame account of what he reads but after the learning of these Arts of Grammar I mean so much thereof as tends to the understanding of every ones Native Language Arithmetick Geometry and Astronomy a Child may proceed profitably to Rhetorick and Logick the reading of History and the learning of the Tongues and sure there is no studious and ingenious man but will stand in need of some Recreation and therefore if Musick in the Worship and Service of God be not Argument enough to allow that a place among the Arts let that poor end of Delight and Pleasure be her Advocate and although that all men have not Voyces yet I can
00 7 48 E 43 25 8 92 F 80 00 6 08 G 59 25 9 73 5. Having thus taken the Angles and Distances in the Field to protract the same on Paper or Parchment cannot be difficult for if you draw a Line at pleasure as EB representing the Diameter of your Instrument about the middle thereof as at A mark a Mark and opening your Compasses to 60 Degrees in your Line of Chords upon A as a Center describe a Circle then lay your Field book before you seeing that your first Observattion cut no Degrees there are no Degrees to be marked out in the Circle but the Degrees at C are 40.75 which being taken from your Line of Chords you must set them from H to I and draw the Line AI. the Degrees at D are 96 which must in like manner be set from I to K and so the rest in order This done observe by your Field-book the length of every Line as the Line AB at your first Observation was 11 Chains and 36 Links which being by your Scale set from A will give the Point B in the Paper the second distance being set upon AI will give the Point C and so proceeding with the rest you will have the Points BCDEF and G by which draw the Lines BC. CD DE EF. FG and GB and so at last you have the Figure of the Field upon your Paper as was required And what is here done at one station may be done at two or more by measuring one or two distances from your first station taking at every station the Degrees and distances to as many Angles as are visible at each station And as for taking the the Plot of a-Field by Intersection of Lines he that doth but consider how the distances of several Objects may be taken at two stations will be able to do the other also and therefore I think it needless to make any illustration by example CHAP. XII How to take the Plot of a Wood Park or other Champion Plain by going round the same and making Observation at every Angle BY these Directions which have been already given may the Plot of any Field or Fields be taken when the Angles may be seen alone or more stations within the Field which though it is the case of some Grounds it is not the case of all now where observation of the Angles cannot be observed within they must be observed without and although this may be done by the plain Table yet as I judge it may be more conveniently done by the Theodolite in these cases thereof I chiefly commend that Instrument I know some use a Mariners Compass but the working with a Needle is not only troublesom but many times uncertain yet if a Needle be joyned with the Theodolite the joynt Observations of the Angles may serve to confirm one another 2. Suppose the Fig. 32. to be a large Wood whose Plot you desire to take Having placed your Instrument at the Angle A lay your Ruler on the Diameter thereof turning the whole Instrument till through the Sights you espy the Angle at K then fasten it there and turn your Ruler upon the Center till through the Sights you espy your second Mark at B the Degrees cut by the Ruler do give the quantity of that Angle BAK suppose 125 Degrees and the Line AB 6 Chains 45 Links which you must note in your Field-book as was shewed before 3. Then remove your Instrument to B and laying your Ruler upon the Diameter thereof turn it about till through the Sights you can espy your third mark at C and there fasten your Instrument then turn the Ruler backward till through the Sights you see the Angle at A the Degrees cut by the Ruler being 106.25 the quantity of the Angle ABC and the Line BC containing 8 Chains and 30 Links which note in your field-Field-book as before 4. Remove your Instrument unto C and laying the Ruler on the Diameter thereof turn the Instrument about till through the Sights you see the Angle at D and fixing of it there turn the Ruler upon the Center till you see your last station at B and observe the Degrees cut thereby which suppose to be 134 Degrees and the Line CD 6 Chains 65 Links which must be entered into your Field-book also and because the Angle BCD is an inward Angle note it with the Mark for your better remembrance 5. Remove your Instrument unto D and Iaying the Ruler on the Diameter turn the Instrument about till through the Sights you see the Angle at E and there fixing your Instrument turn your Ruler backward till you espy the Mark at C where the Degrees cut are suppose 68.0 and the Line DE 8 Chains and 23 Links 6. Remove your Instrument unto E and laying the Ruler on the Diameter turn the Instrument about till through the Sights you see the Angle at F and there fix it then turn the Ruler backward till you see the Angle at D where the Degrees cut by the Ruler suppose to be 125 and the Line EF 7 Chains and 45 Links 7. Remove your Instrument unto F and laying your Ruler upon the Diameter turn the Instrument about till through the Sights you see the Angle at G where fix the same and turn the Ruler backward till you see the Angle at E where the Degrees cut by the Ruler are 70 and the Line FG 4 Chains 15 Links which must be set down with this or the like Mark at the Angle 8. Remove your Instrument unto G and laying your Ruler upon the Diameter turn the Instrument about till through the Sights you see the Angle at H where fix the same and turn the Ruler backward till you see the Angle at F where the Degrees cut by the Ruler are 65.25 and the Line GH 5 Chains 50 Links 9. Remove your Instrument in like manner to H and K and take thereby the Angles and Distances as before and having thus made observation at every Angle in the Field set them down in your Field-book as was before directed the which in our present Example will be as followeth A 151.00 6.45 B 106.25 8.30 C 134.00 6.65 D 68.00 8.23 E 125.00 7.45 F 70.25 4.15 G 65.25 5.50 H 130.00 6.50 K 140.00 11.00 The taking of the inward Angles BCD and EFG was more for Conformity sake than any necessity you might have removed your Instrument from B to D from E to G the Length of the Lines BC. CD EF and G would have given by protraction the Plot of the Field without taking these Angles by observation many other compendious ways of working there are which I shall leave to the discretion of the Ingenious Practitioner 10. The Angles and Sides of the Field being thus taken to lay down the same upon Paper Parchment another Instrument called a Protractor is convenient the which is so well known to Instrument-makers that I shall not need here to describe it the chief use is to lay down Angles
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