Take the question why
proportionals alternate. The cause when they are lines, and when
they are numbers, is both different and identical; different in so far
as lines are lines and not numbers, identical as involving a given
determinate increment. In all proportionals this is so. Again, the
cause of likeness between colour and colour is other than that between
figure and figure; for likeness here is equivocal, meaning perhaps
in the latter case equality of the ratios of the sides and equality of
the angles, in the case of colours identity of the act of perceiving
them, or something else of the sort. Again, connexions requiring proof
which are identical by analogy middles also analogous.
The truth is that cause, effect, and subject are reciprocally
predicable in the following way. If the species are taken severally,
the effect is wider than the subject (e.g. the possession of
external angles equal to four right angles is an attribute wider
than triangle or are), but it is coextensive with the species taken
collectively (in this instance with all figures whose external
angles are equal to four right angles). And the middle likewise
reciprocates, for the middle is a definition of the major; which is
incidentally the reason why all the sciences are built up through
definition.
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