The Complete Aristotle (eng.)

B, then B will belong to no C: and this (as we saw) is the
middle figure. Consequently, since all syllogisms in the middle
figure can be reduced to universal syllogisms in the first figure,
and since particular syllogisms in the first figure can be reduced
to syllogisms in the middle figure, it is clear that particular
syllogisms can be reduced to universal syllogisms in the first
figure. Syllogisms in the third figure, if the terms are universal,
are directly made perfect by means of those syllogisms; but, when
one of the premisses is particular, by means of the particular
syllogisms in the first figure: and these (we have seen) may be
reduced to the universal syllogisms in the first figure:
consequently also the particular syllogisms in the third figure may
be so reduced. It is clear then that all syllogisms may be reduced
to the universal syllogisms in the first figure.
    We have stated then how syllogisms which prove that something
belongs or does not belong to something else are constituted, both
how syllogisms of the same figure are constituted in themselves,
and how syllogisms of different figures are related to one
another.
8
    Since there is a difference according as something belongs,
necessarily belongs, or may belong to something else (for many
things belong indeed, but not necessarily, others neither
necessarily nor indeed at all, but it is possible for them to
belong), it is clear that there will be different syllogisms to
prove each of these relations, and syllogisms with differently
related terms, one syllogism concluding from what is necessary,
another from what is, a third from what is possible.
    There is hardly any difference between syllogisms from necessary
premisses and syllogisms from premisses which merely assert. When
the terms are put in the same way, then, whether something belongs
or necessarily belongs (or does not belong) to something else, a
syllogism will or will not result alike in both cases, the only
difference being the addition of the expression ‘necessarily’ to
the terms. For the negative statement is convertible alike in both
cases, and we should give the same account of the expressions ‘to
be contained in something as in a whole’ and ‘to be predicated of
all of something’. With the exceptions to be made below, the
conclusion will be proved to be necessary by means of conversion,
in the same manner as in the case of simple predication. But in the
middle figure when the universal statement is affirmative, and the
particular negative, and again in the third figure when the
universal is affirmative and the particular negative, the
demonstration will not take the same form, but it is necessary by
the ‘exposition’ of a part of the subject of the particular
negative proposition, to which the predicate does not belong, to
make the syllogism in reference to this: with terms so chosen the
conclusion will necessarily follow. But if the relation is
necessary in respect of the part taken, it must hold of some of
that term in which this part is included: for the part taken is
just some of that. And each of the resulting syllogisms is in the
appropriate figure.
9
    It happens sometimes also that when one premiss is necessary the
conclusion is necessary, not however when either premiss is
necessary, but only when the major is, e.g. if A is taken as
necessarily belonging or not belonging to B, but B is taken as
simply belonging to C: for if the premisses are taken in this way,
A will necessarily belong or not belong to C. For since necessarily
belongs, or does not belong, to every B, and since C is one of the
Bs, it is clear that for C also the positive or the negative
relation to A will hold necessarily. But if the major premiss is
not necessary, but the minor is necessary, the conclusion will not
be necessary. For if it were, it would result both through the
first figure and through the third that A belongs necessarily to
some B. But this is false; for B may be such that it is possible
that A should belong to none of it. Further, an example also makes
it clear that the conclusion not be necessary, e.g. if A were
movement, B animal, C man: man is an animal necessarily, but an
animal does not move necessarily, nor does man. Similarly also if
the major premiss is negative; for the proof is the same.
    In particular syllogisms, if the universal premiss is necessary,
then the conclusion will be necessary; but if the particular, the
conclusion will not be necessary, whether the