out 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.

It is true, mathematicians pretend they give an exact definition of a
right line, when they say, it is the shortest way betwixt two points.
But in the first place I observe, that this is more properly the
discovery of one of the properties of a right line, than a just
deflation of it. For I ask any one, if upon mention of a right line he
thinks not immediately on such a particular appearance, and if it is not
by accident only that he considers this property? A right line can be
comprehended alone; but this definition is unintelligible without a
comparison with other lines, which we conceive to b