The number of fractions bring it no nearer the last division, than the first idea it formed.

Every particle eludes the grasp by a new fraction; like quicksilver, when we endeavour to seize it.

But as in fact there must be something, which terminates the idea of every finite quantity; and as this terminating idea cannot itself consist of parts or inferior ideas; otherwise it would be the last of its parts, which finished the idea, and so on; this is a clear proof, that the ideas of surfaces, lines and points admit not of any division; those of surfaces in depth; of lines in breadth and depth; and of points in any dimension.
The school were so sensible of the force of this argument, that some of them maintained, that nature has mixed among those particles of matter, which are divisible in infinitum, a number of mathematical points, in 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.