lines, parallel to each other, and on the same plane; which is a
description, that explains a thing by itself, and returns in a circle.

It appears, then, that the ideas which are most essential to geometry,
viz. those of equality and inequality, of a right line and a plain
surface, are far from being exact and determinate, according to our
common method of conceiving them. Not only we are incapable of telling,
if the case be in any degree doubtful, when such particular figures are
equal; when such a line is a right one, and such a surface a plain one;
but we can form no idea of that proportion, or of these figures, which is
firm and invariable. Our appeal is still to the weak and fallible
judgment, which we make from the appearance of the objects, and correct
by a compass or common measure; and if we join the supposition of any
farther correction, it is of such-a-one as is either useless or
imaginary. In vain should we have recourse to the common topic, and
employ the supposition of a deity, whose omnipotence may enable him to
form a perfect geometrical figure, and describe a right line without any
curve or inflexion. As the ultimate 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 be 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