The Complete Aristotle (eng.)

C, though not to all C: e.g. let B stand for
beautiful, and C for white. If beauty belongs to something white,
it is true to say that beauty belongs to that which is white; but
not perhaps to everything that is white. If then A belongs to B,
but not to everything of which B is predicated, then whether B
belongs to all C or merely belongs to C, it is not necessary that A
should belong, I do not say to all C, but even to C at all. But if
A belongs to everything of which B is truly stated, it will follow
that A can be said of all of that of all of which B is said. If
however A is said of that of all of which B may be said, nothing
prevents B belonging to C, and yet A not belonging to all C or to
any C at all. If then we take three terms it is clear that the
expression ‘A is said of all of which B is said’ means this, ‘A is
said of all the things of which B is said’. And if B is said of all
of a third term, so also is A: but if B is not said of all of the
third term, there is no necessity that A should be said of all of
it.
    We must not suppose that something absurd results through
setting out the terms: for we do not use the existence of this
particular thing, but imitate the geometrician who says that ‘this
line a foot long’ or ‘this straight line’ or ‘this line without
breadth’ exists although it does not, but does not use the diagrams
in the sense that he reasons from them. For in general, if two
things are not related as whole to part and part to whole, the
prover does not prove from them, and so no syllogism a is formed.
We (I mean the learner) use the process of setting out terms like
perception by sense, not as though it were impossible to
demonstrate without these illustrative terms, as it is to
demonstrate without the premisses of the syllogism.
42
    We should not forget that in the same syllogism not all
conclusions are reached through one figure, but one through one
figure, another through another. Clearly then we must analyse
arguments in accordance with this. Since not every problem is
proved in every figure, but certain problems in each figure, it is
clear from the conclusion in what figure the premisses should be
sought.
43
    In reference to those arguments aiming at a definition which
have been directed to prove some part of the definition, we must
take as a term the point to which the argument has been directed,
not the whole definition: for so we shall be less likely to be
disturbed by the length of the term: e.g. if a man proves that
water is a drinkable liquid, we must take as terms drinkable and
water.
44
    Further we must not try to reduce hypothetical syllogisms; for
with the given premisses it is not possible to reduce them. For
they have not been proved by syllogism, but assented to by
agreement. For instance if a man should suppose that unless there
is one faculty of contraries, there cannot be one science, and
should then argue that not every faculty is of contraries, e.g. of
what is healthy and what is sickly: for the same thing will then be
at the same time healthy and sickly. He has shown that there is not
one faculty of all contraries, but he has not proved that there is
not a science. And yet one must agree. But the agreement does not
come from a syllogism, but from an hypothesis. This argument cannot
be reduced: but the proof that there is not a single faculty can.
The latter argument perhaps was a syllogism: but the former was an
hypothesis.
    The same holds good of arguments which are brought to a
conclusion per impossibile. These cannot be analysed either; but
the reduction to what is impossible can be analysed since it is
proved by syllogism, though the rest of the argument cannot,
because the conclusion is reached from an hypothesis. But these
differ from the previous arguments: for in the former a preliminary
agreement must be reached if one is to accept the conclusion; e.g.
an agreement that if there is proved to be one faculty of
contraries, then contraries fall under the same science; whereas in
the latter, even if no preliminary agreement has been made, men
still accept the reasoning, because the falsity is patent, e.g. the
falsity of what follows from the assumption that the diagonal is
commensurate, viz. that then odd numbers are equal to evens.
    Many other arguments are brought to a conclusion by the help of
an hypothesis; these we ought to consider and mark out clearly. We
shall describe in the sequel their differences, and the various
ways in which