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.