contradictions and agreements of the ideas are all applicable to the
objects; and this we may in general observe to be the foundation of all
human knowledge. But our ideas are adequate representations of the most
minute parts of extension; and through whatever divisions and subdivisions
we may suppose these parts to be arrived at, they can never become
inferior to some ideas, which we form. The plain consequence is, that
whatever appears impossible and contradictory upon the comparison of
these ideas, must be really impossible and contradictory, without any
farther excuse or evasion.

Every thing capable of being infinitely divided contains an infinite
number of parts; otherwise the division would be stopt short by the
indivisible parts, which we should immediately arrive at. If therefore
any finite extension be infinitely divisible, it can be no contradiction
to suppose, that a finite extension contains an infinite number of parts:
And vice versa, if it be a contradiction to suppose, that a finite
extension contains an infinite number of parts, no finite extension can
be infinitely divisible. But that this latter supposition is absurd, I
easily convince myself by the consideration of my clear ideas. I first
take the least idea I can form of a part of extension, and being certain
that there is nothing more minute than this idea, I conclude, that
whatever I discover by its means must be a real quality of extension. I
then repeat this idea once, twice, thrice, &c., and find the compound
idea of extension, arising from its repetition, always to augment, and
become double, triple, quadruple, &c., till at last it swells up to a
considerable bulk, greater or smaller, in proportion as I repeat more or
less the same idea. When I stop in the addition of parts, the idea of
extension ceases to augment; and were I to carry on the addition in
infinitum, I clearly perceive, that the idea of extension must also
become infinite. Upon the whole, I conclude, that the idea of all