This I am satisfyed with, and am willing to rest the controversy merely upon these ideas.

I desire therefore our mathematician to form, as accurately as possible, the ideas of a circle and a right line; and I then ask, 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 acknowledges the fallacy of geometrical demonstrations, when carryed beyond a certain degree 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.