The agreement of the two ideas joined in that proposition is
perceived; but it is by the intervention of other ideas than those
which at first produced that perception. He remembers, i.e. he knows
(for remembrance is but the reviving of some past knowledge) that he
was once certain of the truth of this proposition, that the three
angles of a triangle are equal to two right ones. The immutability
of the same relations between the same immutable things is now the
idea that shows him, that if the three angles of a triangle were
once equal to two right ones, they will always be equal to two right
ones. And hence he comes to be certain, that what was once true in the
case, is always true; what ideas once agreed will always agree; and
consequently what he once knew to be true, he will always know to be
true; as long as he can remember that he once knew it. Upon this
ground it is, that particular demonstrations in mathematics afford
general knowledge. If then the perception, that the same ideas will
eternally have the same habitudes and relations, be not a sufficient
ground of knowledge, there could be no knowledge of general
propositions in mathematics; for no mathematical demonstration would
be any other than particular: and when a man had demonstrated any
proposition concerning one triangle or circle, his knowledge would not
reach beyond that particular diagram.
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