upon each other with a sensible angle, but it is absurd to imagine them to
have a common segment. But supposing these two lines to approach at the
rate of an inch in twenty leagues, I perceive no absurdity in asserting,
that upon their contact they become one. For, I beseech you, by what rule
or standard do you judge, when you assert, that the line, in which I have
supposed them to concur, cannot make the same right line with those two,
that form so small an angle betwixt them? You must surely have some idea
of a right line, to which this line does not agree. Do you therefore mean
that it takes not the points in the same order and by the same rule, as
is peculiar and essential to a right line? If so, I must inform you, that
besides that in judging after this manner you allow, that extension is
composed of indivisible points (which, perhaps, is more than you intend)
besides this, I say, I must inform you, that neither is this the standard
from which we form the idea of a right line; nor, if it were, is there
any such firmness in our senses or imagination, as to determine when
such an order is violated or preserved. The original standard of a right
line is in reality nothing but a certain general appearance; and it is
evident right lines may be made to concur with each other, and yet
correspond to this standard, though corrected by all the means either
practicable or imaginable.

To whatever side mathematicians turn, this dilemma still meets them. If
they judge of equality, or any other proportion, by the accurate and
exact standard, viz. the enumeration of the minute indivisible parts,
they both employ a standard, which is useless in practice, and actually
establish the indivisibility of extension, which they endeavour to
explode. Or if they employ, as is usual, the inaccurate standard, derived
from a comparison of objects, upon their general appearance, corrected by
measuring and juxtaposition; their first principles, though certain and
infallible, are too coarse to afford any such subtile inferences as they