There are some who pretend,[6] that equality is best defined by _congruity_, and that any two figures are equal, when upon the placing of one upon the other, all their parts correspond to and touch each other. In order to judge of this definition let us consider, that since equality is a relation, it is not, strictly speaking, a property in the figures themselves, but arises merely from the comparison which the mind makes betwixt them. If it consists therefore in this imaginary application and mutual contact of parts, we must at least have a distinct notion of these parts, and must conceive their contact. Now 'tis plain, that in this conception, we would run up these parts to the greatest minuteness which can possibly be conceived, since the contact of large parts would never render the figures equal. But the minutest parts we can conceive are mathematical points, and consequently this standard of equality is the same with that derived from the equality of the number of points, which we have already determined to be a just but an useless standard. We must therefore look to some other quarter for a solution of the present difficulty. There are many philosophers, who refuse to assign any standard of _equality_, but assert, that 'tis sufficient to present two objects, that are equal, in order to give us a just notion of this proportion. All definitions, say they, are fruitless without the perception of such objects; and where we perceive such objects we no longer stand in need of any definition. To this reasoning I entirely agree; and assert, that the only useful notion of equality, or inequality, is derived from the whole united appearance and the comparison of particular objects. 'Tis evident that the eye, or rather the mind, is often able at one view to determine the proportions of bodies, and pronounce them equal to, or greater or less than each other, without examining or comparing the number of their minute parts. Such judgments are not only common, but in many cases certain and infallible. When the measure of a yard and that of a foot are presented, the mind can no more question, that the first is longer than the second, than it can doubt of those principles which are the most clear and self-evident.