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