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. 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 varied. 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 'tis 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 enumeration, 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_, 'tis 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. 'Tis 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 inches. But as that quantity we call an inch in the one is supposed equal to what we call an inch in the other, and as 'tis impossible for the mind to find this equality by proceeding _in infinitum_ with these references to inferior quantities, 'tis evident that at last we must fix some standard of equality different from an enumeration of the parts.