BOOK I PART II
if upon the conception of their contact he can
conceive them as touching in a mathematical
point, or if he must necessarily imagine them
to concur for some space. Whichever side he
chuses, he runs himself into equal difficulties.
If he affirms, that in tracing these figures in
his imagination, he can imagine them to touch
only in a point, he allows the possibility of that
idea, and consequently of the thing. If he says,
that in his conception of the contact of those
lines he must make them concur, he thereby ac-
knowledges the fallacy of geometrical demon-
strations, when carryed beyond a certain de-
gree of minuteness; since it is certain he has
such demonstrations against the concurrence
of a circle and a right line; that is, in other
words, he can prove an idea, viz. that of con-
currence, to be _incompatible with two other
ideas, those of a circle and right line; though at