Mathematics so difficult and tedious. Hence, if we can make it appear
that no finite extension contains innumerable parts, or is infinitely
divisible, it follows that we shall at once clear the science of Geometry
from a great number of difficulties and contradictions which have ever
been esteemed a reproach to human reason, and withal make the attainment
thereof a business of much less time and pains than it hitherto has been.

124. Every particular finite extension which may possibly be the object
of our thought is an idea existing only in the mind, and consequently
each part thereof must be perceived. If, therefore, I cannot perceive
innumerable parts in any finite extension that I consider, it is certain
they are not contained in it; but, it is evident that I cannot
distinguish innumerable parts in any particular line, surface, or solid,
which I either perceive by sense, or figure to myself in my mind:
wherefore I conclude they are not contained in it. Nothing can be plainer
to me than that the extensions I have in view are no other than my own
ideas; and it is no less plain that I cannot resolve any one of my ideas
into an infinite number of other ideas, that is, that they are not
infinitely divisible. If by finite extension be meant something distinct
from a finite idea, I declare I do not know what that is, and so cannot
affirm or deny anything of it. But if the terms "extension," "parts,"
&c., are taken in any sense conceivable, that is, for ideas, then to say
a finite quantity or extension consists of parts infinite in number is so
manifest a contradiction, that every one at first sight acknowledges it
to be so; and it is impossible it should ever gain the assent of any
reasonable creature who is not brought to it by gentle and slow degrees,
as a converted Gentile to the belief of transubstantiation. Ancient and
rooted prejudices do often pass into principles; and those propositions
which once obtain the force and credit of a principle, are not only
themselves, but likewise whatever is deducible from them, thought