There are few or no mathematicians, who defend the hypothesis of
indivisible points; and yet these have the readiest and justest answer to
the present question. They need only reply, that lines or surfaces are
equal, when the numbers of points in each are equal; and that as the
proportion of the numbers varies, the proportion of the lines and
surfaces is also varyed. But though this answer be just, as well as
obvious; yet I may affirm, that this standard of equality is entirely
useless, and that it never is from such a comparison we determine objects
to be equal or unequal with respect to each other. For as the points,
which enter into the composition of any line or surface, whether
perceived by the sight or touch, are so minute and so confounded with
each other, that it is utterly impossible for the mind to compute their
number, such a computation will Never afford us a standard by which we
may judge of proportions. No one will ever be able to determine by an
exact numeration, that an inch has fewer points than a foot, or a foot
fewer than an ell or any greater measure: for which reason we seldom or
never consider this as the standard of equality or inequality.

As to those, who imagine, that extension is divisible in infinitum, it is
impossible they can make use of this answer, or fix the equality of any
line or surface by a numeration of its component parts. For since,
according to their hypothesis, the least as well as greatest figures
contain an infinite number of parts; and since infinite numbers, properly
speaking, can neither be equal nor unequal with respect to each other;
the equality or inequality of any portions of space can never depend on
any proportion in the number of their parts. It is true, it may be said,
that the inequality of an ell and a yard consists in the different
numbers of the feet, of which they are composed; and that of a foot and a
yard in the number of the inches. Bat as that quantity we call an inch in
the one is supposed equal to what we call an inch in the other, and as