which is useless in practice, and actually
establish the indivisibility of extension, which they endeavour to
explode. Or if they employ, as is usual, the inaccurate standard,
derived from a comparison of objects, upon their general appearance,
corrected by measuring and juxtaposition; their first principles,
though certain and infallible, are too coarse to afford any such subtile
inferences as they commonly draw from them. The first principles are
founded on the imagination and senses: The conclusion, therefore, can
never go beyond, much less contradict these faculties.

This may open our eyes a little, and let us see, that no geometrical
demonstration for the infinite divisibility of extension can have so
much force as what we naturally attribute to every argument, which is
supported by such magnificent pretensions. At the same time we may learn
the reason, why geometry falls of evidence in this single point, while
all its other reasonings command our fullest assent and approbation.
And indeed it seems more requisite to give the reason of this exception,
than to shew, that we really must make such an exception, and regard
all the mathematical arguments for infinite divisibility as utterly
sophistical. For it is evident, that as no idea of quantity is
infinitely divisible, there cannot be imagined a more glaring absurdity,
than to endeavour to prove, that quantity itself admits of such a
division; and to prove this by means of ideas, which are directly
opposite in that particular. And as this absurdity is very glaring in
itself, so there is no argument founded on it which is not attended
with a new absurdity, and involves not an evident contradiction.

I might give as instances those arguments for infinite divisibility,
which are derived from the point of contact. I know there is no
mathematician, who will not refuse to be judged by the diagrams he
describes upon paper, these being loose draughts, as he will tell us,
and serving only to convey with greater facility certain ideas, which
are the true foundation of all our reasoning. This I am satisfyed with,
and am willing to rest the controversy merely upon these ideas. I desire
therefore our mathematician to form, as accurately as possible,
the ideas of a circle and a right line; and I then ask, if upon the
conception of their contact he can conceive them as touching in a
mathematical point, or if he must necessarily imagine them to concur
for some space. Whichever s