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 be more extended.