menting its bulk; and afterwards, when it has encreased to
such a degree as to be really extended, it is still difficult for
the imagination to break it into its component parts, because of the
uneasiness it finds in the conception of such a minute object as a
single point. This infirmity affects most of our reasonings on the
present subject, and makes it almost impossible to answer in an
intelligible manner, and in proper expressions, many questions which may
arise concerning it.

III. There have been many objections drawn from the mathematics against
the indivisibility of the parts of extension: though at first sight that
science seems rather favourable to the present doctrine; and if it
be contrary in its DEMONSTRATIONS, it is perfectly conformable in its
definitions. My present business then must be to defend the definitions,
and refute the demonstrations.

A surface is DEFINed to be length and breadth without depth: A line
to be length without breadth or depth: A point to be what has neither
length, breadth nor depth. It is evident that all this is perfectly
unintelligible upon any other supposition than that of the composition
of extension by indivisible points or atoms. How else coued any thing
exist without length, without breadth, or without depth?

Two different answers, I find, have been made to this argument; neither
of which is in my opinion satisfactory. The first is, that the objects
of geometry, those surfaces, lines and points, whose proportions and
positions it examines, are mere ideas in the mind; I and not only never
did, but never can exist in nature. They never did exist; for no one
will pretend to draw a line or make a surface entirely conformable to
the definition: They never can exist; for we may produce demonstrations
from these very ideas to prove, that they are impossible.

But can anything be imagined more absurd and contradictory than this
reasoning? Whatever can be conceived by a clear and distinct idea
necessarily implies the possibility of existence; and he who pretends
to prove the impossibility of its existence by any argument derived from
the clear idea, in reality asserts, that we have no clear idea of
it, because we have a clear idea. It is in vain to search for a
contradiction in any thing that is distinctly conceived by the mind. Did
it imply any contradiction, it is impossible it coued ever be conceived.

There is therefore no medium betwixt allowing at least the possibility