BEfore we come in point of Art to prove what we before promiſed, and to ſee whether our Antagoniſt have proved himſelf to be verus filius Artis, it will not be impertinent to take notice of his ſpecious words, high arrogancie, and large promiſes: That whatſoeuer he hath writ is undoubtedly true, and of learned Readers will be ſo approved, &c. But we, doubt not, to make the contrary appear, and to manifeſt to the world, that his aime hath been principally to delude them who underſtand not theſe Sciences, and we could wiſh his promiſed Aſtronomia Britannica, be not as deſective as his Anatomia Ʋraniae.

IN the Table of the Moons Aequation he would make the Reader believe we have followed Argol, a man very laborious in Calculations, but one (ſaith he) who hath given no reaſons for his doings: But this is not true, for there is a ſenſible variation, amounting ſomtimes to 7 or 8 minutes, nay many times more, as they who liſt to try ſhall finde; but becauſe his errour may be apparent, and his inſufficiencie appear, we have added the following operation from Argols Tables.

☾ being Perig. diſtant from the ☉ 30 degrees   s d ′ ″ Centrum Lunae 2 00 00 00 Argumentum medium 6 00 00 00 Aeqnatio centri add.   9 39 00 Scrup. proport.     19 30 Argumentum verum 6 09 39 00 Exceſſus     34 36 Pars pro ſcrup. prop.     11 15 Aequatio abſoluta add.   1 05 27

But according to Ʋrania Practica, 00 56 00 differing from Argoll 9′ 27″, whereas according to his judgement it ſhould be equall.

Laſtly, he ſaith, that in the Latitude of the Moon we haue meerly followed Lansberge, and ſo from the fragments of broken Authors have patcht up the Tables of the Luminaries motions, attiring the divine Urania in a partie-coloured veſture: But this is as falſe as the other, and though in the latter we come neer to Lansberge, (which makes him conjecture we had it from him) yet the Table is de novo of our Calculation, and the Theorie it ſelf, whereon its grounded, which is conſentaneous to the former.

In the beginning of Chap. 5. we finde him guilty of another errour, in imagining by the quality of the Table of the Moons Aequation, that we have followed a Theorie aequivalent to that of Copernicus, viz. A double Epicycle, the circumference of the one, carrying the center of the other; But we denie this to be true, for ſhould we grant it, it would follow that the Aequation of the Center, or ſecond Epicycle ſhould be ſwifter in the former ſemi-circle, and ſloweſt in the latter, and ſo the two inaequalities digeſted into one Table, would be ſenſibly diſconſonant to that which we have compoſed, being grounded upon a different Hypotheſis, as we would here have exemplified, had it been pertinent to anſwer every groundleſſe contradiction.

By your favour (Sir) you are (againe) miſtaken in ſuppoſing we have taken the whole excentricity 3577. which had we done, we ſhould willingly have acknowledged an offence, and undergone your cenſure, but wee have followed the proportion of bi-ſected excentricitie (though different from the Hypotheſis of Kepler) and that his errour herein may be apparent, we will here compare our numbers with his own Diagram. Pag. 25. and uſe his own manner of operation thus.

1. As Radius B. E. 1000000 to the Tangent of the Angle, BEA 15′—0″—4363. ſo BE 1017890 to B A 4441.

2. As E D 982110. to CD (equall to B A (4441. So the Radius E D 1000000 to the Tangent of the Angle, DEC 4522. whoſe Arch is 15′. 31″. (and not 16′. 7″. as he ſaith) which if the true Semidiameter of the Sun according to our Hypotheſis,

from which our Tables never differ more, which was the reaſon we followed Argoll and Eichſtade therein without further calculation, and now Maſter Shakerley, me thinks, you cannot have the impudence to own that Paper-kite ſo courſely deckt in your feathers, which flyes abroad, as unſeemly as an Owl at noon day.

Next he affirmes, That the Semidiameters of the Moon are not conſonant to the obſervations which have been made by Artiſts, eſpecially in Eclipſes of the Sun, and for an example inſtances the Obſervation of Clavius at Rome, Anno 1567. Aprill 9. and to the time of this Obſervation he formes a Caculation from our Tables, but yet he mentions not the moment of the obſcurations, though Clavius there tels him it was circa meridiem about noone, which, it ſeems, he is loath to make known, yet he cannot deny but that (according to our Tables) the Eclipſe was centrall there at the very moment of Obſervation, to which few Tables that have yet appeared, do better agree; but for the other Eclipſe of the Sun, which Clavius a little (before in the ſame page) ſpeaks of, which was in the yeer 1560 at Conimbrica in Luſitania about noon hee meddles not with, becauſe he knowes it ſpeaks much to the praiſe of our Tables (as doth the other) though much againſt his will.

CHap. 8. He comes to examine the diſtance of the Coeleſtiall bodies from the earth, wherein his malice and ignorance as much appears as before, but before we come to examine his miſtakes here, let us look back to the 24 pag. where are theſe words, Hence would likewiſe follow, that the Suns diſtance from the earth is not only infinite, but, if we may ſo ſay, a degree beyond infiniteneſs, and yet with much confidence they can proceed to determine the diſtance of the Sun from the earth in miles, whereas it appears by their Tables, no ſuch diſtance is ever poſſibly to be defined, and their very diſtances there ſet down, are not only diſconſonant to the truth, but alſo to their own erroneous aſſumptions.

What we have there ſaid concerning the intervals and diſtances of the Sun, Earth and other Planets, we are able to make the truth thereof demonſtratively appear, as we ſhall exemplifie, and ſhall here, by the verity of our calculation, ſufficiently prove him a meer Botcher, and by the way adviſe him to turn to the 3 Book of Lansbergs Ʋranometria, de errantium & in errantium Stellarum dimentione, and then, if he be not too much byaſſed to his own opinion, we dare undertake he ſhall ſoon be able, by thoſe ſimple Elements to make his own demonſtration, if he will have but reaſon to hang his dimenſions upon their proper and true Hypotheſis, and then he ſhall finde what we have ſaid, cum rei veritate ad amuſſim conſentire, to be no leſſe then truth. Now that the judicious may ſee his failings and unparalleld miſtakes, we ſhall ſhew him, as we promiſed, how to finde the true diſtance of the Sun from the earth according to our Tables, which for brevity ſake take thus.

In the following Scheme, A denotes the center of the earth, B C B the circumference thereof, A B its Semidiameter, D the place of the Sun in the Horizon, B D the line of the Suns appearance from the ſuperficies of the Earth B, therefore A D is the diſtance of the Sun from (A) the center of the earth, and the angle A D B is the Horizontall parallax of the Sun, therefore in the rectangle Triangle A B D is given (1) the ſide A B, the Semidiameter of the earth 1 part, (2) the angle oppoſite A D B 3′0″, hence is found the ſide A D: For,

As Radius A B, 10,00000 to the co-tang. of ADB 3′ 13,05915 So the ſide AB 1 Semidi. 0,00000 to the ſide AD 1146 ſerè 3,05915

And this is the true diſtance of the Sun from the earth in Semidiameters according to our Tables, which is not infinite, nor a degree beyond infiniteneſſe, as he ſurmiſes, and therefore from our Hypotheſis the diſtance of the Sun from the earth (in German miles) is 985560, and this gives the horizontall parallax of the Sun 3′ as before, and not 12′ as he imagines: and herein we deſire not to be our own judges, but ſhall refer it to the cenſure of profounder Artiſts then either Mr. Shakerley or our ſelves; but (that noble Mecaenas, and reſtaurator of Aſtronomy) Tycho Brahe, whom we followed therein (as appears pag. 174 and following,) he obſerved by his large and curious Inſtruments, his diſtance from the earth to be neer 4 Semidiameters greater, viz. 1150 Semidiameters: Now he that ſhall multiply this number by 860 ſhall have in the product 989000 German miles which is the true number we have ſet down; ſo likewiſe in Saturn, 10571 multiplyed by 860 giveth 9091060: in Jupiter 3990 multiplyed by 860 gives 3431400, and in Mars (likewiſe 1745 multiplyed by 860, gives 1500700.

Hence it appears how unjuſtly he hath charged us with that he can no way make good, but we could wiſh (becauſe he pretends to theſe Sciences) he could finde ſome hole to creepe out at, which we cannot yet eſpie.

Concerning his three Queries (or demands) we ſhall here forbeare to make any tedious repetition, in regard one of us intends ere long to publiſh ſomthing of that nature wherein we ſhall fully diſcuſs that matter; in the interim, we can but laugh at his folly, in demanding the Obſervations of others from us, which he underſtands not himſelfe. But leaving him herein, we next come to his Bug-bear-bundle, or briefe ſummary of non-ſenſe.

Although the precept to finde the Súns altitude were caſually omitted in the 6 Book, yet that defect may very well be ſupplyed by helpe of thoſe Tables there inſerted, which are ſufficient for this Kingdom and the Regions conterminate; and beſides, what is he that is but a meer Tyro in theſe Arts that cannot perceive how to work it, having ſo plain and perſpicuous an example as that is, Pag. 99. but to ſupply that defect, and to amplifie that there promiſed, we have added the following Example,

Let the time propoſed be the 2 of July 1649, at four of the clock in the afternoon, the Suns declination being 22 deg. Northwards, at which time the Suns Altitude above the Horizon is to be enquired: Therefore in the Diagram annexed, let the outward Circle thereof repreſent the Meridian of London, O P the Latitude thereof 51d 32′, whoſe complement is Z P 38d 28′, H O the Horizon, E Q the Aequinoctiall, D K the Suns parallel of Declination Northward, and Z S C N the Azimuth that the Sun is in at the time of the queſtion. In which Diagram (by the interſection of three great Circles) we have limited the oblique angled Triangle Z S P, in which we have given: Firſt, The ſide Z P 38d 28′ the complement of the Latitude, Secondly, the ſide S P 68d, the Suns diſtance from the Pole, or the complement of his Declination. Thirdly, the angle Z P S 60d, the time from noon 4 houres. And it is required to finde the ſide Z S, the complement of the Suns altitude above the Horizon H C O.

As the Radius 90d 10,0000000 to the co-ſine of Z P S 30d 9,6989700 So the Tangent of Z P 38d 28′, 9,9000865 to the Tangent of P R 21d 40′ 9,5990565

Which being ſubſtracted from the whole ſide S P, there remains the Arch S R 46d 20′ As the co-ſine of P R 68d 20′ 9,9681781 to the co-ſine of Z P 51d 32′ 9,8937452 So the co-ſine of R S 43d 40′ 9,8391396   19,7328848 to the co-ſine of Z S 35d 34′ 9,7647067

Which 35d 34′ is the altitude of the Sun above the Horizon.

TO the third and fourth Sections of his Muſter-roll we ſhall anſwer with brevity, in regard they are not worth the view of an Artiſt. To the firſt whereof (being the third in order) we ſay, and dare affirm by the pure Rules of undoubted Art, that the Suns excentricity cannot cauſe an alteration of above 3 or 4″ in the table of the hourely motion of the Moon from the Sun, and what errour this can produce in the uſe thereof let himſelf judge: and ſo the difference being inſenſible gave us good cauſe to omit it, as Copernicus, Maginus, Purbachius, Lansberge, Argoll, and diverſe others have done before us, being loth to trouble themſelves with ſuch nicities & needleſſe trifles.

In the next, where he ſaith The Suns horizontall parallax is not always 3′, but if this be his parallax in his mean diſtance, the Apogaean parallax is 2′ 53″, the Perigaeon parallax 3′ 7″, according to our Authors Excentricity. And here, indeed, he ſpeaks truer then he ſuppoſed, Ex falſa ſequitur verum, for henever dreamt of a biſected Excentricity, but we ſhal examine whether it be ſo according to the Excentricity which he ſets down, therefore in the Diagram of the 5 § reaſon thus.

1 As the Radius 100000, to the Tangent of the angle E 3′, (viz. 87,) So EB 103577 to AB 90.

2 As ED 94423 to DC 90 (being equall to AB,) So ED the Radius to the Tangent of the Angle at E 95, whoſe arch 3′ 13″ ſhould (according to the proportion he ſets down) be his Perigaeon Parallax, differing from his own judgement 6″, whereas it ſhould be equall.

WE are now arrived at the fifth and laſt Section of his Summary, where he is doubtfull Whether in our Tables we have uſed any reduction of the Moon from her Orbe to the Ecliptique, & contra, which he might have obſerved pag. 62, and pag. 87. and therefore might have ſaved this labour as well as all the reſt, for what he ſaith here, we knew long ſince, and have taught how to obtein it: but we doe not well conceive his meaning, where he ſaith, the middle of the Eclipſe is not the greateſt obſcuration, &c. Surely this (indeed) is ſtrange muſick in the ears of Ʋrania, and is not ſutable to her excellencie, for the proving whereof we deſire the Reader to peruſe Ptol, Lib. 6. Cap, 4. &c. Copernicus Lib. 4. Cap. 21, & 30. Purbachus Prop. 15. Tab. Eclip. Reinhold in Theor. Geo. Purbach. Stofl. Prop. 9, & 10. Eichſtad. Cap. 2, 3, 4, & 5, Paed. Aſtron. contin. Lanſberg à fol. 56. ad fol. 70. Precept. cal. motuum. But if he be not ſatisfied with theſe, we doubt not, but the learned Kepler and the expert Bullialdus will do it, for, we hope, he will have ſo much modeſty as to credit them though it be againſt himſelfe, and therefore ſhall adviſe him to turn to Precept 146. Tab. Rudolph. or to pag. 864. Epit. Aſtron. Cop. where Kepler tels him, Quod medium Eclipſis eſt maxima obſcuration that the middle of the Eclipſe is the greateſt obſcuration, and that is, Quando centrum Lunae eſt vel junctum centro umbrae, vel in perpendiculari illâ, ex centro umbrae in viam Lunae: when the center of the Moon is either joyned to the center of the ſhadow, or is in the perpendicular which comes from the center of the ſhadow, and falls upon the way of the Moon; the ſame ſaith Bullialdus, Lib. 5. fol. 214. Aſtron. Philol. yet are we not ignorant of that he ſeems to ſtumble at, pag. 865 Epit. Aſtron. where Kepler moſt excellently ſhews in what reſpects the places of the true Conjunction and greateſt obſcuration differ: Differunt enim in arcu minimo (as his own Author there tels him) duploreductionis Lunae loci ad Eclipticam, cujus area Luna in obſcuratione maximâ ſemper eſt vicinior nodo, quam centrum umbrae: and hereunto aſſents Bullialdus, Lib. 4. Cap. 7. De Reduct. Temp. where he alſo admits of a reduction of time from the true Oppoſition or Conjunction with the Sun to the greateſt obſcuration: one cauſe whereof is the difference of the place of the Moon in her Orbe from her place in the Ecliptique, which always differ, unleſſe the Moon be in the Nodes or Quarters: the other is cauſed by the inclination of the way of the Moon to the Zodiack, when ſhe is in the ſhadow of the earth, and this is all theſe Authors intend, and this we approve of, but (by Mr. Shakerleys favour) not of that he ſpeaks of. And in caſe we ſhould not obſerve this nice reduction he cavils at, what errour could it breed? Nay, did the learned Copernicus; Reinholdus, Noble Tycho, Eichſtade, Lansberge, or Longomontanus, ever ſo much as obſerve it? although as able and skilfull as our Antagoniſt, ſeeing reaſons may be given pro & con, as we could inſtance, but we doubt not but the judicious are already ſatisfied of the verity of our calculations, and alſo obſerve the fallacies of his erroneous affertions.

Thus have we diligently examin'd this learned (or rather wrangling) Diſcourſe wherein we finde him ſo unadviſedly raſh that we can but admire at his folly, eſpecially that ſuch a man as he, who profeſſeth himſelfe to be an Artiſt, ſhould ſo contumeliouſly and inconſiderately ſtrive to confute others, before he hath any ground for his ſo doing, and ſo plunge himſelfe into moſt infinite errours and groſſe abſurdities, even ſuch as may be diſcerned by every judicious Spectator, if he winke not on purpoſe; but we ſhall leave him as we found him even brim-full of malice; his aime being (as every one may perceive) purpoſely to ſmother thoſe tender buds which begin to appear in the fields of Ʋrania.