when the subject fails him, and entertains a notion of a compleat TIERCE
or OCTAVE, without being able to tell whence he derives his standard. A
painter forms the same fiction with regard to colours. A mechanic with
regard to motion. To the one light and shade; to the other swift and slow
are imagined to be capable of an exact comparison and equality beyond the
judgments of the senses.

We may apply the same reasoning to CURVE and RIGHT lines. Nothing is more
apparent to the senses, than the distinction betwixt a curve and a right
line; nor are there any ideas we more easily form than the ideas of these
objects. But however easily we may form these ideas, it is impossible to
produce any definition of them, which will fix the precise boundaries
betwixt them. When we draw lines upon paper, or any continued surface,
there is a certain order, by which the lines run along from one point to
another, that they may produce the entire impression of a curve or right
line; but this order is perfectly unknown, and nothing is observed but
the united appearance. Thus even upon the system of indivisible points,
we can only form a distant notion of some unknown standard to these
objects. Upon that of infinite divisibility we cannot go even this
length; but are reduced meerly to the general appearance, as the rule by
which we determine lines to be either curve or right ones. But though we
can give no perfect definition of these lines, nor produce any very exact
method of distinguishing the one from the other; yet this hinders us not
from correcting the first appearance by a more accurate consideration,
and by a comparison with some rule, of whose rectitude from repeated
trials we have a greater assurance. And it is from these corrections, and
by carrying on the same action of the mind, even when its reason fails
us, that we form the loose idea of a perfect standard to these figures,
without being able to explain or comprehend it.