all their enquiries and disputes. They endeavour to find objections,
both to our abstract reasonings, and to those which regard matter of
fact and existence.

The chief objection against all _abstract_ reasonings is derived from
the ideas of space and time; ideas, which, in common life and to a
careless view, are very clear and intelligible, but when they pass
through the scrutiny of the profound sciences (and they are the chief
object of these sciences) afford principles, which seem full of
absurdity and contradiction. No priestly _dogmas_, invented on purpose
to tame and subdue the rebellious reason of mankind, ever shocked common
sense more than the doctrine of the infinitive divisibility of
extension, with its consequences; as they are pompously displayed by all
geometricians and metaphysicians, with a kind of triumph and exultation.
A real quantity, infinitely less than any finite quantity, containing
quantities infinitely less than itself, and so on _in infinitum_; this
is an edifice so bold and prodigious, that it is too weighty for any
pretended demonstration to support, because it shocks the clearest and
most natural principles of human reason.[32] But what renders the matter
more extraordinary, is, that these seemingly absurd opinions are
supported by a chain of reasoning, the clearest and most natural; nor is
it possible for us to allow the premises without admitting the
consequences. Nothing can be more convincing and satisfactory than all
the conclusions concerning the properties of circles and triangles; and
yet, when these are once received, how can we deny, that the angle of
contact between a circle and its tangent is infinitely less than any
rectilineal angle, that as you may increase the diameter of the circle
_in infinitum_, this angle of contact becomes still less, even _in
infinitum_, and that the angle of contact between other curves and their
tangents may be infinitely less than those between any circle and its