of indivisible points, and denying their idea; and it is on this latter
principle, that the second answer to the foregoing argument is founded.
It has been pretended [L'Art de penser.], that though it be impossible
to conceive a length without any breadth, yet by an abstraction without
a separation, we can consider the one without regarding the other; in
the same manner as we may think of the length of the way betwixt two
towns, and overlook its breadth. The length is inseparable from the
breadth both in nature and in our minds; but this excludes not a partial
consideration, and a distinction of reason, after the manner above
explained.

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 mat