But now, (after all our Physical, or Statical Considerations) the clearest Evidence for this Hypothesis (if it can be had) will be from Celestial Observations. As for instance; (see _Fig._ 5.) Supposing the Sun at S; the Earths place in its Annual Orb at T; and _Mars_ (in opposition to the Sun, or near it) at M: From whence _Mars_ should appear in the Zodiack at [gamma], and will at Full moon be seen there to be; the Moon being at C and the Earth at c; (and the like at the New-moon.) But if the Moon be in the First quarter at A, and the Earth at a: _Mars_ will be seen, not at [gamma], but at [alpha]; too slow: And when the Moon is at B, and the Earth at b, _Mars_ will be seen at [beta]; yet too slow: till at the {289} Full-moon, the Moon at C, the Earth at c, _Mars_ will be seen at [gamma], its true place, as if the Earth were at T. But then, after the Full, the Moon at D, the Earth at d; _Mars_ will be seen, not at [gamma], but at [delta], too forward: and yet more, when the Moon (at the last Quarter) is at E, the Earth at e, and _Mars_ seen at [epsilon]. If therefore _Mars_ (when in opposition to the Sun) be found (all other allowances being made) somewhat too backward before the Full moon, and somewhat too forward after the Full-moon, (and most of all, at the Quadratures:) it will be the best confirmation of the Hypothesis. (The like may be fitted to _Mars_ in other positions, _mutatis mutandis_; and so for the other Planets.) But this proof, is of like nature as that of the Parallaxis of the Earths Annual Orb to prove the Copernican Hypothesis. If it can be observed, it proves the Affirmative; but if it cannot be observed, it doth not convince the Negative, but only proves that the Semidiameter of the Earths Epicycle is so small as not to make any discernable Parallax. And indeed, I doubt, that will be the issue. For the Semidiameter of this Epicycle, being little more than the Semidiameter of the Earth it self, or about 1-1/3 thereof (as is conjectured, in the _Hypothesis_, from the Magnitudes and Distances of the Earth and Moon compared;) and there having not as yet been observed any discernable _Parallax_ of _Mars_, even in his neerest position to the Earth; it is very suspicious, that here it may prove so too. And whether any of the other Planets will be more favourable in this point, I cannot say. * * * * * _ANIMADVERSIONS of Dr. _Wallis_, upon Mr. _Hobs_'s late Book, _De Principiis & Ratiocinatione Geometrarum_._ These were communicated by way of Letter, written in _Oxford_, July 24. 1666. to an Acquaintance of the _Author_, as follows: Since I saw you last, I have read over Mr. _Hobs_'s Book _Contra Geometras_ (or _De Principiis & Ratiocinatione Geometrarum_) which you then shewed me. A New Book of _Old_ matter: Containing but a _Repetition_ of what he had before told us, more than once; and which hath been Answered long agoe.