as Herefy; and that, by Confequence, the Popish Aftronomers have been driven into this terrible Dilemma, of either fubmitting to the Abfurdities of the Tychonian, or elfe of refigning themselves up to Imprisonment, if not to Death it felf for the true or Copernican Hypothefis: So dangerous is it, in that Church at least, if not in fome others, to admit of Truth not only in Divine, but even in Natural and Aftronomical Matters alfo!

(5.) There is one known fixed Proportion between the Periods and Distances of all the Heavenly Bodies from the Sun; I mean that the Squares of the Periods, are ever as the Cubes of the Distances; and this Proportion is fo univerfal, that it obtains not only in this general Syftem of the Primary Planets about the Sun, but in the particular Systems of the Secondary Planets about their Primaries, without the leaft Exception that we know of in the Universe: Which Proportion demonstrates, that the Annual Revolution belongs to the Earth, and not to the Sun.For as the Cube of the Moon's distance, which is 240,000 Miles, to the Cube of the Sun's diftance, which is 81,000.000 Miles, i, e. as I to 38,272.753, fo is the Square of the Moon's Period, or of less than 28 Days, which is about 784, to the Square of the Period of any Body moving about the Earth at the Sun's diftance in Days, or to 30,005.838,352, whofe Square Root, or 173,510 are therefore the Number of Days of the Solar Year, in cafe the Sun revolves about the Earth; which yet in reality are known to be but 365 Now this laft Number is contain'd no less than 475 Times in the former. So that if the Sun revolv'd about the Earth, from

that

Jupiter moves round this Circle

12 Months·

in twelve years

This Plate truly reprefents the Direction, Station, and Retrogradation of the Supe rior Planets, by the situation of the Earth and Jupiter, one of those Planets, during a whole years motion of the One, and a months motion of the Other; from their first. Position at 111, when Jupiter appears Direct, and near the Conjunction; at 2.2.2 and 3 when it continues Direct, the more flow in its motion; about 444, when it is Statis ionary; at 5.5.5 when it appears Retrograde, as alfo at 6.6.6/when it is in Op= position) and 777 till about 8.8.8 it is Stationary again: After which at 9.9.9 and 10.10.10 it becomes Direct again, and more swiftly so at u.. and 12.12.12. The Cafe of Saturn and Mars are much the same

1.Senex fulp

that Analogy and Harmony which is every where elfe obferved in the Heavens, the Year must be 475 Times as long as it now is. This Calculation feems to me to determine this Dispute in favour of the Copernican Syftem; according to which, the Proportion above-mentioned of the Cubes of the Distances, as the Squares of the Periodick Times, is known to agree to all the Planets, to the utmost exactness of Aftronomical Obfervations.

(6.) In Fact, the Earth has fuch an Annual Revolution about the Sun; as appears by all the Indications of fuch a Motion poffible: even by that of Parallax; which is the known Geometrical Foundation of the Science of Aftronomy. Thus if the Earth have an Annual Revolution about the Sun, it must affect the apparent Mo- See Fig.III. tions of all the other Planets and Comets, and, notwithstanding the Regularity of their feveral Motions in their own Orbits, must render the regular Motions, as to us, living upon the moving Earth, fometimes Direct, and that fwiftly or flowly; fometimes Stationary, and fometimes Retrograde, and that fwiftly or flowly alfo, and all this at fuch certain Periods, in fuch certain Places, for fuch certain Durations, and according to fuch certain Circumftances, as Geometry and Arithmetick will exactly determine, and not otherwife. Now that this is the real Cafe in Fact; and that every one of thefe Particulars are true in the Aftronomical World, all that are skilful in that Science do freely confefs; even those who, for Reafons already hinted at, do not think fit to declare openly for this Annual Revolution of the Earth, which is the natural, the certain Confequent of that Conceffion.

D 3

'Tis

'Tis true, fuch Perfons may pretend, that tho' thefe Phanomena be undoubted; and would be the undoubted Effects of fuch a Motion; yet that this Annual Revolution is not the undeniable, the strictly Geometrical Confequence of them; that they may poffibly be accounted for on other Hypothefes, and that on the Suppofition of certain complex Motions, deriv'd from (imaginary) Epicycles, and Eccentricks, and folid Orbs, &c. they may be folved without the introduction of this Annual Motion of the Earth. Now this I do not abfolutely deny, that if fuch precarious, aukward, immechanical, falfe, and abfurd Figments, were the true and real Laws of Nature, thefe Phænomena might poffibly be otherwife accounted for: But then I affirm, that fuch Hypothefes are indeed not at all the real Laws of Nature, but no better than meer precarious, aukward, immechanical, falfe, and abfurd Figments only; fuch indeed, as if they were allow'd in other Cafes, would take away all Certainty in all mixt Mathematicks at least, if not in Arithmetick and Geometry themselves; and would enable Men to evade the grand Foundation of Aftronomy, I mean that of the common Parallax it felf: These Phænomena being as truly Inftances of an Annual, as other known ones are of the Diurnal Parallax. I believe the skilful Aftronomers will know my meaning by this general intimation; but if not, I will eafily undertake to demonftrate, that those who, notwithstanding these Indications, or Demonstrations, do deny or doubt of the Earth's Annual Motion, may, in Confequence thereof, become Aftronomical Scepticks, and deny, or doubt of almost all the other Principles of Aftronomy,

and