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 {291} Touch the Circle, it may with its
In-side at another place Cut it_, &c.) But I shou'd sooner take this to be
a _Confutation of His Quadratures_, than a _demonstration of the Breadth of
a _(Mathem