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 it is 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.
It is 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.
There are therefore three proportions, which the mind distinguishes in the general appearance of its objects, and calls by the names of greater, less and equal.