is far greater than an inch, and represented by it; and that when we say
a line is infinitely divisible, we must mean a line which is infinitely
great. What we have here observed seems to be the chief cause why, to
suppose the infinite divisibility of finite extension has been thought
necessary in geometry.

129. The several absurdities and contradictions which flowed from this
false principle might, one would think, have been esteemed so many
demonstrations against it. But, by I know not what logic, it is held that
proofs a posteriori are not to be admitted against propositions relating
to infinity, as though it were not impossible even for an infinite mind
to reconcile contradictions; or as if anything absurd and repugnant could
have a necessary connexion with truth or flow from it. But, whoever
considers the weakness of this pretence will think it was contrived on
purpose to humour the laziness of the mind which had rather acquiesce in
an indolent scepticism than be at the pains to go through with a severe
examination of those principles it has ever embraced for true.

130. Of late the speculations about Infinities have run so high, and
grown to such strange notions, as have occasioned no small scruples and
disputes among the geometers of the present age. Some there are of great
note who, not content with holding that finite lines may be divided into
an infinite number of parts, do yet farther maintain that each of those
infinitesimals is itself subdivisible into an infinity of other parts or
infinitesimals of a second order, and so on ad infinitum. These, I say,
assert there are infinitesimals of infinitesimals of infinitesimals, &c.,
without ever coming to an end; so that according to them an inch does not
barely contain an infinite number of parts, but an infinity of an
infinity of an infinity ad infinitum of parts. Others there be who hold
all orders of infinitesimals below the first to be nothing at all;