The Complete Aristotle (eng.)

universal premiss is
negative or affirmative. First let the universal be necessary, and
let A belong to all B necessarily, but let B simply belong to some
C: it is necessary then that A belongs to some C necessarily: for C
falls under B, and A was assumed to belong necessarily to all B.
Similarly also if the syllogism should be negative: for the proof
will be the same. But if the particular premiss is necessary, the
conclusion will not be necessary: for from the denial of such a
conclusion nothing impossible results, just as it does not in the
universal syllogisms. The same is true of negative syllogisms. Try
the terms movement, animal, white.
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    In the second figure, if the negative premiss is necessary, then
the conclusion will be necessary, but if the affirmative, not
necessary. First let the negative be necessary; let A be possible
of no B, and simply belong to C. Since then the negative statement
is convertible, B is possible of no A. But A belongs to all C;
consequently B is possible of no C. For C falls under A. The same
result would be obtained if the minor premiss were negative: for if
A is possible be of no C, C is possible of no A: but A belongs to
all B, consequently C is possible of none of the Bs: for again we
have obtained the first figure. Neither then is B possible of C:
for conversion is possible without modifying the relation.
    But if the affirmative premiss is necessary, the conclusion will
not be necessary. Let A belong to all B necessarily, but to no C
simply. If then the negative premiss is converted, the first figure
results. But it has been proved in the case of the first figure
that if the negative major premiss is not necessary the conclusion
will not be necessary either. Therefore the same result will obtain
here. Further, if the conclusion is necessary, it follows that C
necessarily does not belong to some A. For if B necessarily belongs
to no C, C will necessarily belong to no B. But B at any rate must
belong to some A, if it is true (as was assumed) that A necessarily
belongs to all B. Consequently it is necessary that C does not
belong to some A. But nothing prevents such an A being taken that
it is possible for C to belong to all of it. Further one might show
by an exposition of terms that the conclusion is not necessary
without qualification, though it is a necessary conclusion from the
premisses. For example let A be animal, B man, C white, and let the
premisses be assumed to correspond to what we had before: it is
possible that animal should belong to nothing white. Man then will
not belong to anything white, but not necessarily: for it is
possible for man to be born white, not however so long as animal
belongs to nothing white. Consequently under these conditions the
conclusion will be necessary, but it is not necessary without
qualification.
    Similar results will obtain also in particular syllogisms. For
whenever the negative premiss is both universal and necessary, then
the conclusion will be necessary: but whenever the affirmative
premiss is universal, the negative particular, the conclusion will
not be necessary. First then let the negative premiss be both
universal and necessary: let it be possible for no B that A should
belong to it, and let A simply belong to some C. Since the negative
statement is convertible, it will be possible for no A that B
should belong to it: but A belongs to some C; consequently B
necessarily does not belong to some of the Cs. Again let the
affirmative premiss be both universal and necessary, and let the
major premiss be affirmative. If then A necessarily belongs to all
B, but does not belong to some C, it is clear that B will not
belong to some C, but not necessarily. For the same terms can be
used to demonstrate the point, which were used in the universal
syllogisms. Nor again, if the negative statement is necessary but
particular, will the conclusion be necessary. The point can be
demonstrated by means of the same terms.
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    In the last figure when the terms are related universally to the
middle, and both premisses are affirmative, if one of the two is
necessary, then the conclusion will be necessary. But if one is
negative, the other affirmative, whenever the negative is necessary
the conclusion also will be necessary, but whenever the affirmative
is necessary the conclusion will not be necessary. First let both
the premisses be affirmative, and let A and B belong to all C, and
let AC be necessary. Since then B belongs to all C, C also