te standard of these figures is derived
from nothing but the senses and imagination, it is absurd to talk of
any perfection beyond what these faculties can judge of; since the true
perfection of any thing consists in its conformity to its standard.

Now since these ideas are so loose and uncertain, I would fain ask any
mathematician what infallible assurance he has, not only of the more
intricate, and obscure propositions of his science, but of the most
vulgar and obvious principles? How can he prove to me, for instance,
that two right lines cannot have one common segment? Or that it is
impossible to draw more than one right line betwixt any two points?
should he tell me, that these opinions are obviously absurd, and
repugnant to our clear ideas; I would answer, that I do not deny, where
two right lines incline 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,