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ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A93028	The anatomy of Urania practica or, a short mathematicall discourse; laying open the errors and impertinencies delivered in a treatise lately published by Mr. Vincent Wing, and Mr. William Leybourne, under the title of Urania practica. By Jeremy Shakerley philomath.	Shakerley, Jeremy, fl. 1651.	1649 (1649)	Wing S2911; Thomason E1366_1; ESTC R209254	23,878	48

motions of Mars To these reasons I may adde also the continued Observations of Tycho in Eclipses which cleer the Moon of any secondary inequality at the time of Defect which is the true not mean Syzigia of the Luminaries But to this I cannot impute any great force the difference being so little as it is hardly to be distinguished from those many irregularities which attend on the propinquity of the Moon to the Earth and of us in these Nothern Regions by reason of the great obliquity of our Sphear more perceived Nor can we as yet think the manifold motions of this inconstant Torrella so throughly known as we can for the present build any certainty hereon I doubt not but that Astronomia Brittannica now by the blessing of God almost brought to perfection will shortly take away many doubts herein which have hithereto puzled divers Artists And I doubt not but I shall discover some things concerning the Moons motions which may be usefull for Astronomers in this subject and more rationall then those impertinencies our Authors have here delivered for they are out of all possibility of being excused that in such a cleer Sun-shine will impudently adventure to set out their dim Lanthorn for a guide to the young Practitioner through these mysterious Laborinths especially such a worthy Luminary as Kepler having long since put all out of doubt and taught Truth to move in her own Orb not impedited by the adventitious remora's of humane fancy CHAP. VI. A demonstrative examination of our Authors Tables of Eclipses WE now come to the touch stone of our Authors judgment and will by God's help lay open those many absurdities which would follow should we admit of our Authors Tables This speculation is not ordinary for obvious to every young Practitioner yea the intricacies hereof have entangled many profounder Artists then either Master Wing Master L●y●ourn or my Self few of those many Authors ● ch to this day have appeared the publick Champions of Urania have had a full knowledge hereof excepting Kepler the late Ballialdus and the noble genius of our worthy Country-man Master Jeremy Horrox 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 from whose remains I have gathered the most of what I shall write in this Chapter Those who have presumed of their own sufficiency to be able to demonstrate those dimensions which are requisite for the calculation of Eclipses have used thereto a Diagram said to be invented by Hipparchus which they have severally commented on Amongst the rest the late famous Lansberge hath in his Uranometrie made a large discourse thereof but so simply as he may be ashamed to spend those brasts upon so insufficient a piece Yet hath his greatest fault been that he hath not fitted his numbers to those Theoremes or Elements in his Uranometrie as by him that will compare his numbers with the following Diagram may be seen But the like cannot so well be said of Copernicus Tycho Longomontanus c. by whom it is likely this demonstrative way was rather omitted then not conceived for they perceiving their Observations not to answer fully the rigid Theoremes hereof took more care to satisfie their Observations then Demonstrations But the greatest cause of this difference being the inconstancy of Physical causes which still interposed themselves they are not altogether to be excused as not professing to deliver the accidentall inconstancies of the Phaenomena but the true and demonstrative Principles of Art But the divine Kepler both understood the excellency of this Diagram and hath fitted the Precepts of his Rudolphine Tables hereto He mentions oft a book of his own entituled Hipparchus wherein the demonstrations hereof are contained The Book I have not seen perhaps it is not yet published I shall onely at this time touch some few things herein that concern my present purpose referring the Reader for the rest to Astronomia Brittannica where it is fully demonstrated and the manifold uses thereof declared In the Diagram annexed let A be the center of the Sun C of the Perigaean shadow H of the Apogaean shadow B of the Earth so is the apparent Semidiameter of the Sun ABE of the Perigaean shadow CBP of the Apogaean shadow HBN the vertex of the Conical shadow D the Semiangle thereof BDG the axis BD let the lines GF PK NO be paralel to DA the Semidiameter of the Earth BG the Center of the Moon L the Semidiameter of the Moon in the change LBM the Horizontal Paralax of the Sun BAG of the Moon BLG whence we thus proceed I. The Semiangle of the Cone of the shadow is alwayes lesse then the Sun 's apparent Semidiameter and the difference of these is the Sun 's Horizontall Paralax The former part is proved from an opticall principle Idem objectum quo proprius cerniter eo majus apparet so that the Semidiameter of the Sun being beheld from B appears greater then if it be beheld from D in regard B is neerer the object then D. The Sun's Semidiameter apparent is ABE AGE the Sun 's Horizontall Paralax is BAG GAF Now in regard the two lines AD and FG are paralel it is necessary that ADE should be equall to FGE therefore AGE-FGE-AGF-BAG the Sun 's Horizontall Paralax II. The Semiangle of the Cone of the shadow is equall to the difference of the Moon 's Horizontall Paralax and the Semidiameter of the shadow Let us take the Moon in her Apogaeum and opposition to the Sun her Horizontall Paralax is BHG whereto BNG is equall the Semidiamiter apparent of the shadow HBN now BNG HBN ONP which by reason of the Paralellisme of the lines NO and DA is equall to the angle ADE which is the Semiangle of the Cone of the shadow If we take also the Moon in her Perigaeum her Horizontall Paralax is BCG whereto BPG is equall the apparent Semidiameter of the shadow is CBP now BPG BPK KPG which by reason of the Paralellism of the lines PK and DA is equall to the angle ADE the Semiangle of the Cone of the shadow Nor need any one think our demonstration invalid or insufficient for that we have assumed the angles BCG and BPG to be equall whereas indeed they are not 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 precisely so For I shall shew how inconsiderable a difference this is and how far it avoids our Observation For if we take the angle ADE or which is the same KPG to be 12 min. o sec which follows from our Authors numbers for by the first Theoreme AGE 15 min. o sec AGF 3 min. o sec FGE ADE 12 min. o sec the naturall Tangent thereof is 349067 KG We shall also from our Authors Tables take the apparent Semidiameter of the shadow CBP or BPK to be 47 min. o sec which is the greatest they set down It s Tangent is BK 1367260. the sum of the angles is BPG 59 min. o sec the sum of the Tangents is BG 1716327. whereto answers the angle BCG 58 min. 59. sec 50

the yeers of our Lord is onely of all the following Centenaries to be Bissextile the rest of the Centenaries onely common yeers of 365. dayes whereby it fals out the Gregorian Accompt every 400. yeers gains three dayes of what the Iulian loses The differences of the two Accompts in some succeeding Centenaries we have here exhibited in this Table   An. Dō ad da Anno Domini Add days Anno dom Ad da. From the 5. of October 1582. 10.   From the 24 of February 1700. 11. 2500. 17. 3300 23 1800. 12. 2600. 18. 3400 24 1900. 13. 2700. 19. 3500 25 2100. 14. 2900. 20. 3700 26 2200. 15. 3000. 21. 3800 27 2300. 16. 3100. 22. 3900 28 Thus by omitting the intercalation in these yeers the Dominical Letter and Epact which depend on the number of dayes in each yeer come to be changed and by reason of the former the number of direction and consequently the movable Feasts cannot by my Authors rules be truly perpetually gathered all which with some other inconveniencies had been here more fully insisted on if we had not thought this that hath been said sufficient for the ingenious whereby to correct and amend these imperfections and that Origanus in the first part of his Introduction to his Ephemerides hath saved our Pen that labour which hasts to discoveries of further concernment CHAP. III. The inequality of the Precession of the Equinoctiall points examined WHat may be happy to Urania and gratefull to her true and legitimate Favourites we now adventure upon the Sun and Moons Motions A large current of considerations doth charge us and we are likely to have more matter then convenience to prosecute it yet shall my unwillingnesse to trouble the Reader with more then is needfull for our present purpose and my hope of a future fitter opportunity to dilate my conceits upon this subject prevail with the urgency of the matter and confine my Discourse to its intended limits The first occasion that invites our Pen to consider hereof is given by our Authors pag. 52. where mention is made of a mean and true Equinox in these words So shall you have the true motion of the Sun ab Aequinoctio vero for in these tables the Sun 's mean motion is reckoned from the true Equinox and not from the mean Whereby we may gather that our Authors admit of an inequality of the Precession of the Equinoctial points The manner whereof with the cause of its admission into Astronomy and lastly the validity thereof because none of these are by our Authors so much as touched it will not be inconvenient here in as brief a way as may be to deliver After that noble Dane Tycho Brahe had to the glory of Art and joy of Artists with incredible pains and diligence perfected that elaborate table of the fixed Stars and rectified it to his own time a further and necessary care of perpetuating it induced him to consider what helps might be drawn from ancient Observations to this purpose and perceiving by those accounts that were taken of their places first by Hipparchus afterwards by Ptolomey Albategnius Arzabel Copernicus and some others that they had not onely motions but unequall motions and inconstancy in their latitudes in severall ages he was forced to devise some way whereby these motions might be regulated to prove consentaneous to the observations of all ages The Theory of this inequality is according to the famous Astronomer Chr. S. Longomontanus in this manner Longomontanus Theric lib. 1. Let A be the Pole of tke Ecliptick BC that part of the Arctick circle of the Ecliptick which the Pole of the earth in B hath run by its equall motion upon the center of the Ecliptick since the Creation This Arch measures also the Precession of the Equinoxes and progressive motion of the fixed Stars BA is 23. degr 42. min the Zodiacks mean obliquity DGE the small circle regulating the obliquity of the Zodiack AD its radius 10. min. 53. sec By which it appears both how the Zodiack changeth its obliquity and also how the Equinoctiall points and consequently every severall point in the Zodiack do inequally anticipate for when the Pole of the Aequator which is carried in the circle EDG is at E or G the obliquity is in its mean deviations and is equall to AB 23. degr 42. min. But the equation of the Equinoxes is the greatest GBA 27. min. 5. sec and is to be substracted at G added at E wnen the Pole of the Aequator is at D the obliquity is least and is equall to DB 23. degr 31. min. 7. sec but when the Pole of the Aequator is at F the obliquity B F is greatest and is 23. degr 52. min. 53. sec and in both these cases there is no aequation of the Equinoxes by reason of the coincidence of the lines BA and BG This is the artifice Longomontanus hath used to satisfie appearances with which if we should Phiscally consider I doubt we should finde it more ingenuous then true for it is scarcely tolerable for any Astronomers to devise circles and imaginary motions where with to fill the heavens and withdraw the eye of man from a perfect consideration of the wisdome and power of his Creator which best appears in the simplicity and uniformity of these Coelestiall essences yet might this Hypothesis have been allowed yea highly commended if any good to Astronomy had come thereby more then a needlesse multiplication of uncertainties We will consider in a few words the validity and necessity of this Hypothesis to perform what it promiseth Of the necessity hereof ancient observations can give us no certainty for from Proclus to our times for above a thousand years the Aequinoctiall points have made a certain and equall Precession agreeable to that rule of motion which Timocharis and Hipparchus observed above 1800. yeers agoe if we onely except Ptolomey Therefore if any Circulation more then annuall and diurnall if those be to be admitted have befaln to the Poles of the aequator whereby it hath been so enormiously removed from its scituation it was betwixt the times of Hipparchus and Ptolomey in the space of lesse then three hundred yeers and was again restored in the time betwixt Ptolomey and Preclus in other three hundred yeers Wherefore without injury we may doubt of the certainty of Ptolomies observations and the rather for that he himself seems to imply as much by these words Non in tropicis tantum Observation bus sed in Aequinoctiabus error accidere po●est qui ad quartam unius diei partem se extendat Quod si ●nim in 3600 tantum particula as if that were little or nothing Aequatoris situs aut Instrumentis divisio arecta raratione deficiat illam in Latitudine sive Decliatione ac ☉ ad aequatorem accessu ad aequabit quarta circiter unius gradus pars in Zodiaco Longitudine c. Praeterquam quod majus erratum esse

Authors prescriptions for the use of them we will here briefly deliver Our Authors have in the Table of the Suns equations followed the Theorie of Longomontanus or some equivolent thereto for there are divers onely a little though almost insensibly increasing the Eccentricity of the Sun making the proportion of the radius of the Suns orbe to the radius of his epicycle as is 100000. to 3577. to which Eccentricity in that hypothesis their equations of the Sun agree But for what reason they have made this change themselves doe not show nor can I conjecture In the Tables of the Moons equations they have followed Argol a man very laborious in calculations but one who hath not to my knowledge given any reason for what he hath done He hath omitted the variation of the Moone induced thereto as he saith by Observations I will not question his doings because I know not what Observations he used but certainly if there had not been a necessity for it Tycho had never retained it into the Theory of the Moone nor had it been confirmed by the after doings of I ongemontanus Kepler and the industrious and expert Bullialdus especially it causing so great a difference in the Moones place extending it selfe to 40 min. 30 sec according to Tycho but according to Kepler a fourth part more And although Keplers variation may be justly thought too bigge notwithstanding he seems to deduce it from Physicall and Archetypicall demonstrations which he so much affected yet in a Mathematicall eye which attends precisenesse the variation is not altogether contemptible In the latitude of the Moon our Authors have meerly followed Lansberge and together with him rejected the inequality of motion in the Moones Nodes of which I will nor dispute the demonstration thereof depending upon such dubious Principles as Authors are not satisfied thereof Tycho making the period of this inequality menstruall with whom herein Argol and Bullialdus also agre Kepler annuall yet all since Tycho admitting thereof excepting onely Lansherg of whose corruption and depravation of ancient Observations so wresting them to his purpose he that is not satisfied may finde him sufficiently characterized by Phocylides in his forementioned booke Thus from the fragments of broken Authors have our Authors patcht up their Tables of the Luminaries motions which however they will be sufficient to represent Coelestiall Observations I much doubt and am fearfull that our Authors have done the divine Vrania wrong in attiring her simple excellence in such a particoloured vesture CHAP. V. Whether the second inequalitie of the Moon have dependance of the Sunnes mean or true and apparent place BY the quality of that table of the Moones equations our Authors have set downe occasion is given me to imagine they have therein followed a Theorie equivolent to that of Copernicus viz a double Epicycle the circumference of the one carrying the Center of the other Yet however the two inequalities which are by Copernicus attributed to these Epicycles are here by our Authors digested into one Table which without question were of great concernment to him that desires speedinesse in calculation if the Artist could be assured of its exactnesse and agreement with the Heavens and those legitimate and Physicall Theories which may be thence deduced But whereas it appeares by the Precepts which guide us to the use of this Table that the mean distance of the Luminaries is one of the steps wherby we attain the Moons equation we may and not without just cause suspect it of error It is true that in those Theories of the Planets which were used before Tycho had happily confuted the solidity of Caelestiall Orbs there might be some appearance of reason why the Centers of those solid Spheres rather then the Centers of the eccentricke Circles should regulate those other inequalities which depended thereon they being supposed in that age not imaginary but reall points and therefore sufficient whereon to build a connexion of mosions But after that Tycho had by the helpe of his exact Instruments found the existence of temporary and fading Lights within that Circuit which was supposed to be free from generation and corruption and thereby solidly refuted the solidity of those Orbs and Spheres so laboriously demonstrated by Ptolemie Proclus Peurbachius and others this disclosure gaue the minde liberty to thinke of more rational wayes then the old multiplicity of Circles and Motions whereby to salve caelestiall appearances And hereby it came to be known that the Causes of Motions were meerly Physicall and dapended not upon the variety of Orbs but followed that simple and uniforme course Nature had assigned them and respected not those imaginary Centers which prudent Antiquity had for want of other helpes devised for them but the very body of the Sun the fountaine of Motion and common node of all their Orbs. Why then the Moon which though a secondary Planet yet hath relation to the Suns course should receive the Lawes of her extra-sysygiall inaequality from the Suns mean motion I cannot see These reasons will evince she contrary 1. The mean motion of the Sun as also of any other Planet is not in nature but onely devised to regulate those exorbitances and deviations from equality to which their apparent motions are subject 2. Observations testifie that the longest line of every Primary Theory which exactly bisects the orbe into two semicircles equall in the quantity and celerity of the same parts passeth by the center of the Sun in which the Aphelian lines of the primary Planets concur 3. The orbite of every primary Planet is intersected by the Eclipticke in places opposite by the center of the Sun and not by any point without it 4. The fountaine of motion and the generall antecedent to the particular relative inequalities of the Planets ought rather to be in the most excellent body then any where without it for these reasons first because the moving force cannot reside in any Mathematicall point such as this is imagined to be but requires a body the more fully to exercise his operating power Secondly it is most cnnsentaneous to reason that the moving force should be in the Center of the world where it is evident the Sunne is there being rest in the superficies or sphere of the fixed Stars and motion in the intermediate places 5. The cause why Copernius and Tycho supposed the two Centers viz. of the Orbe and of the Eccentrick to be different things in themselves is not sufficiently Mathematicall they being drawn hereto by the desire of making their Hypotheses equivalent to those of Ptolomie But it was not necessary to follow the steps of Ptolomie so diligently for Ptolomie made not every part of his Hypothesis from observations but grounded many things upon a fore-conceived opinion that the motions of the Planets were equall through every portion of their own circles which Observations do sufficiently evince to be untrue as may appear by famous Kepler in his learned Comentaries of the