other, the resemblance will at first strike the
eye, or rather the mind; and seldom requires a second examination. The
case is the same with contrariety, and with the degrees of any quality.
No one can once doubt but existence and non-existence destroy each
other, and are perfectly incompatible and contrary. And though it be
impossible to judge exactly of the degrees of any quality, such as
colour, taste, heat, cold, when the difference betwixt them is very
small: yet it is easy to decide, that any of them is superior or
inferior to another, when their difference is considerable. And this
decision we always pronounce at first sight, without any enquiry or
reasoning.

We might proceed, after the same manner, in fixing the proportions
of quantity or number, and might at one view observe a superiority
or inferiority betwixt any numbers, or figures; especially where the
difference is very great and remarkable. As to equality or any exact
proportion, we can only guess at it from a single consideration; except
in very short numbers, or very limited portions of extension; which are
comprehended in an instant, and where we perceive an impossibility of
falling into any considerable error. In all other cases we must settle
the proportions with some liberty, or proceed in a more artificial
manner.

I have already I observed, that geometry, or the art, by which we fix
the proportions of figures; though it much excels both in universality
and exactness, the loose judgments of the senses and imagination; yet
never attains a perfect precision and exactness. It's first principles
are still drawn from the general appearance of the objects; and that
appearance can never afford us any security, when we examine, the
prodigious minuteness of which nature is susceptible. Our ideas seem
to give a perfect assurance, that no two right lines can have a common
segment; but if we consider these ideas, we shall find, that they always
suppose a sensible inclination of the two lines, and that where the
angle they form is extremely small, we have no standard of a I @ right
line so precise as to assure us of the truth of this proposition. It is
the same case with most of the primary decisions of the mathematics.

There remain, therefore, algebra and arithmetic as the only sciences, in
which we can carry on a chain of reasoning to any degree of intricacy,
and yet preserve a perfect exactness and certainty. We are possest of a
precise standard, by wh