In refuting this answer I shall not insist on the argument, which I have
already sufficiently explained, that if it be impossible for the mind to
arrive at a minimum in its ideas, its capacity must be infinite, in order
to comprehend the infinite number of parts, of which its idea of any
extension would be composed. I shall here endeavour to find some new
absurdities in this reasoning.

A surface terminates a solid; a line terminates a surface; a point
terminates a line; but I assert, that if the ideas of a point, line or
surface were not indivisible, it is impossible we should ever conceive
these terminations: For let these ideas be supposed infinitely divisible;
and then let the fancy endeavour to fix itself on the idea of the last
surface, line or point; it immediately finds this idea to break into
parts; and upon its seizing the last of these parts, it loses its hold by
a new division, and so on in infinitum, without any possibility of its
arriving at a concluding idea. 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