Page:Philosophical Transactions - Volume 001.djvu/303

 for a large Confutation: yet I am scarce inclined to believe, that any will bestow so much pains upon it. For, if that be true, which (in his Preface) he saith of himself, Aut solus insanio Ego, aut solus non insanio: it would either be Needless, or to no Purpose. For, by his own confession, All others, if they be not mad themselves, ought to think Him so; And therefore, as to Them, a Confutation would be needless; who, its like, are well enough satisfied already; at least out of danger of being seduced. And, as to himself, it would be to no purpose. For, if He be the Mad man, it is not to be hoped that he will be convinced by Reason: Or, if All We be so; we are in no capacity to attempt it.

But there is yet another Reason, why I think it not to need a Confutation. Because what is in it, hath been sufficiently confuted already; (and, so Effectually; as that he professeth himself not to Hope, that This Age is like to give sentence for him; what ever Nondum imbuta Posteritas may do.) Nor doth there appear any Reason, why he should again Repeat it, unless he can hope, That, what was at first False, may by oft Repeating, become True.

I shall therefore, instead of a large Answer, onely give you a brief Account, what is in it, &, where it hath been already Answered.

The chief of what he hath to say, in his first 10 Chapters, against Euclids Definitions, amounts but to this, That he thinks, Euclide ought to have allowed his Point some Bigness; his Line some Breadth; and his Surface, some Thickness.

But where in his Dialogues, pag. 151, 152. he solemnly undertakes to Demonstrate it; (for it is there, his 41th Proposition;) his Demonstration amounts to no more but this; That, unless a Line be allowed some Latitude; it is not possible that his Quadratures can be True. For finding himself reduced to these inconveniences;1. That his Geometrical Constructions, would not consist with Arithmetical calculations, nor with what Archimedes and others have long since demonstrated:2. That the Arch of a Circle must be allowed to be sometimes Shorter than its chord, and sometimes longer than its Tangent:3. That the same Straight Line must be allowed, at one place onely to Touch, and at another place to Cut the same Circle: (with others of like nature;) He findes it necessary, that these things may not seem Absurd, to allow his Lines some Breadth, (that so, as he speaks, While a Straight Line with its Out-side doth at one place Rh