elude its force and evidence. It is not in demonstrations as in
probabilities, that difficulties can take place, and one argument
counter-ballance another, and diminish its authority. A demonstration, if
just, admits of no opposite difficulty; and if not just, it is a mere
sophism, and consequently can never be a difficulty. It is either
irresistible, or has no manner of force. To talk therefore of objections
and replies, and ballancing of arguments in such a question as this, is
to confess, either that human reason is nothing but a play of words, or
that the person himself, who talks so, has not a Capacity equal to such
subjects. Demonstrations may be difficult to be comprehended, because of
abstractedness of the subject; but can never have such difficulties as
will weaken their authority, when once they are comprehended.

It is true, mathematicians are wont to say, that there are here equally
strong arguments on the other side of the question, and that the doctrine
of indivisible points is also liable to unanswerable objections. Before I
examine these arguments and objections in detail, I will here take them
in a body, and endeavour by a short and decisive reason to prove at once,
that it is utterly impossible they can have any just foundation.

It is an established maxim in metaphysics, That whatever the mind clearly
conceives, includes the idea of possible existence, or in other words,
that nothing we imagine is absolutely impossible. We can form the idea of
a golden mountain, and from thence conclude that such a mountain may
actually exist. We can form no idea of a mountain without a valley, and
therefore regard it as impossible.

Now it is certain we have an idea of extension; for otherwise why do we
talk and reason concerning it? It is likewise certain that this idea, as
conceived by the imagination, though divisible into parts or inferior