— 205 —
Therefore Demonstrations in Numbers the most precise.       §4. The Clearness and Distinctness of each mode of Number from all
others, even those that approach nearest, makes me apt to think,
that Demonstrations in Numbers, if they are not more evident and
exact, than in Extension, yet they are more general in their use, and
— 206 —
more determinate in their Application. Because the Ideas of Numbers
are more precise, and distinguishable than in Extension; where
every Equality and Excess are not so easie to be observed, or
measured; because our Thoughts cannot in Space arrive at any
determined smallness beyond which it cannot go, as an Unite; and
therefore the quantity or proportion of any the least Excess cannot
be discovered, which is clear otherwise in Number, where, as has
been said, 91 is as distinguishable from 90, as from 9000, though 91
be the next immediate Excess to 90. But it is not so in Extension,
where whatsoever is more than just a Foot, or an Inch, is not
distinguishable from the Standard of a Foot, or an Inch; and in
Lines which appear of an equal length, one may be longer than
the other by innumerable Parts: Nor can any one assign an Angle,
which shall be the next biggest to a right one.
Locke Hum II, 16, §4, pp. 205-206