order to give a termination to bodies; and others eluded the force of
this reasoning by a heap of unintelligible cavils and distinctions. Both
these adversaries equally yield the victory. A man who hides himself,
confesses as evidently the superiority of his enemy, as another, who
fairly delivers his arms.

Thus it appears, that the definitions of mathematics destroy the
pretended demonstrations; and that if we have the idea of indivisible
points, lines and surfaces conformable to the definition, their existence
is certainly possible: but if we have no such idea, it is impossible we can
ever conceive the termination of any figure; without which conception
there can be no geometrical demonstration.

But I go farther, and maintain, that none of these demonstrations can
have sufficient weight to establish such a principle, as this of infinite
divisibility; and that because with regard to such minute objects, they
are not properly demonstrations, being built on ideas, which are not
exact, and maxims, which are not precisely true. When geometry decides
anything concerning the proportions of quantity, we ought not to look for
the utmost precision and exactness. None of its proofs extend so far. It
takes the dimensions and proportions of figures justly; but roughly, and
with some liberty. Its errors are never considerable; nor would it err at
all, did it not aspire to such an absolute perfection.

I first ask mathematicians, what they mean when they say one line or
surface is EQUAL to, or GREATER or LESS than another? Let any of them
give an answer, to whatever sect he belongs, and whether he maintains the
composition of extension by indivisible points, or by quantities
divisible in infinitum. This question will embarrass both of them.