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Prior Analytics - Book II 
each figure when the conclusion is converted; when a result contrary
to the premiss, and when a result contradictory to the premiss, is
obtained. It is clear that in the first figure the syllogisms are
formed through the middle and the last figures, and the premiss
which concerns the minor extreme is alway refuted through the middle
figure, the premiss which concerns the major through the last
figure. In the second figure syllogisms proceed through the first
and the last figures, and the premiss which concerns the minor extreme
is always refuted through the first figure, the premiss which concerns
the major extreme through the last. In the third figure the refutation
proceeds through the first and the middle figures; the premiss which
concerns the major is always refuted through the first figure, the
premiss which concerns the minor through the middle figure.
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It is clear then what conversion is, how it is effected in each
figure, and what syllogism results. The syllogism per impossibile is
proved when the contradictory of the conclusion stated and another
premiss is assumed; it can be made in all the figures. For it
resembles conversion, differing only in this: conversion takes place
after a syllogism has been formed and both the premisses have been
taken, but a reduction to the impossible takes place not because the
contradictory has been agreed to already, but because it is clear that
it is true. The terms are alike in both, and the premisses of both are
taken in the same way. For example if A belongs to all B, C being
middle, then if it is supposed that A does not belong to all B or
belongs to no B, but to all C (which was admitted to be true), it
follows that C belongs to no B or not to all B. But this is
impossible: consequently the supposition is false: its contradictory
then is true. Similarly in the other figures: for whatever moods admit
of conversion admit also of the reduction per impossibile.
All the problems can be proved per impossibile in all the figures,
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