Page:Philosophical Transactions - Volume 004.djvu/234



ince Mr. Hobbs thought himself obliged to make some Reply to Dr Wallis's confutation of what he had, not long since, publish't upon this Argument; Dr. Wallis made no stay at all to return this Answer and second refutation. Concerning which we shall give you a brief account, suggested by Dr. Wallis himself, of Mr. Hobbes's fundamental mistake in his late Quadrature of the Circle, referring the Reader to the Tract itself the Figure, which is therein the first.

Mr. Hobbs, considering, That, in case it should happen so luckily (which was not necessary) that Q Y (the base of a right angled Triangle Q Y A equal to the Sector L C A, and consequently the Square Q R S T equal to the Circle B C D E,) should, by the Arch C L, be cut just in the midst at P; then would, not only (which to his purpose was necessary) Q P L, C P Y, 'be equal each to other (because of A L P Y common both to the Triangle and the Sector,) but more-over (which was not necessary) each of them equal to the half of P A V, (supposing C A V taken equal, by construction, to L A P:) all which is true, in case of such a lucky hap:

And finding then (which is true also) that this could not All happen, unless that intersection at P, were in the line A O (drawn from the Center A to the middle of C G,) because this must needs pass through the middle of Q Y.

Concluded, That it so needs happen, or else it was impossible for Any right-angled Triangle, as Q Y A (like to, and part of G C A,) to be equal to the Sector L C A: because, in any other, as q y A the intersection of C L and q y at p, would not be just in the midst of q y; and therefore (which he suppos'd necessary, but was not) q p A not just the halfe of q y A.

Not considering (which is his fundamental mistake) that, if q p L and C p y be equal each to other (though neither of them be