A science expands not by the interposition of fresh middle terms,
but by the apposition of fresh extreme terms. E.g. A is predicated
of B, B of C, C of D, and so indefinitely. Or the expansion may be
lateral: e.g. one major A, may be proved of two minors, C and E.
Thus let A represent number-a number or number taken
indeterminately; B determinate odd number; C any particular odd
number. We can then predicate A of C. Next let D represent determinate
even number, and E even number. Then A is predicable of E.
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Knowledge of the fact differs from knowledge of the reasoned fact.
To begin with, they differ within the same science and in two ways:
(1) when the premisses of the syllogism are not immediate (for then
the proximate cause is not contained in them-a necessary condition
of knowledge of the reasoned fact): (2) when the premisses are
immediate, but instead of the cause the better known of the two
reciprocals is taken as the middle; for of two reciprocally predicable
terms the one which is not the cause may quite easily be the better
known and so become the middle term of the demonstration. Thus (2) (a)
you might prove as follows that the planets are near because they do
not twinkle: let C be the planets, B not twinkling, A proximity.
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