Page:Philosophical Transactions - Volume 004.djvu/84



Hen the Publisher intended to give notice to the World of Mr. Hobbes's Book very lately come abroad, concerning the Quadrature of the Circle &c. he soon found another, containing both that and the Confutation of it together.

The Author of this Confutation observeth two grand mistakes in Mr. Hobbs's Tract; the first in the Demonstration of his first Proposition, where these words, Aut ergo in Triangulo A C G, tiangulum rectangulum, cujus vertex sit A, æquale Sectori A C L sumi nullum potest; aut P Q L, C Y P, sunt æqualia, are upon our Authors Examination not at all prov'd, nor true. It seems, M. Hobbs had only prov'd, That If P Q L, C Y P, be equal, Then such a Triangle may be; but not the Converse, If those be not equall, then such a Triangle cannot be. For, if PQL be not equall, but a little bigger than CYP; and consequently, the Right-angled Triangle AYQ so much bigger than the Sector ACL; it is manifest, that a Line drawn parallel to the Base QY, a little nearer to the Vertex A, may cut off a like Right-angled Triangle (a little less then AYQ) which may be equall to the Sector ACL.

Billie; this (which overthrows all, in the examiners Iudgement) the other great mistake of M. Hobbs is alledged to be in the Demonstration of the second Proposition; where (supposing by the first Proposition a square found equall to a Circle) he argues, That, because the Square takes in as much of what is left out by the Circle, as the Circle takes in of what is left out by the Square; therefore a Cube answering to that Square, compar'd with a Sphere answering to that Circle, will doe so too: (which would have been well argued, saith the Examiner, of a Cylinder on that Circle, of equal height with a Cube on Rh