The Complete Aristotle (eng.)

Similarly also if the
minor premiss is negative. But if both premisses are negative, one
being assertoric, the other problematic, nothing follows
necessarily from these premisses as they stand, but if the
problematic premiss is converted into its complementary affirmative
a syllogism is formed to prove that B may belong to no C, as
before: for we shall again have the first figure. But if both
premisses are affirmative, no syllogism will be possible. This
arrangement of terms is possible both when the relation is
positive, e.g. health, animal, man, and when it is negative, e.g.
health, horse, man.
    The same will hold good if the syllogisms are particular.
Whenever the affirmative proposition is assertoric, whether
universal or particular, no syllogism is possible (this is proved
similarly and by the same examples as above), but when the negative
proposition is assertoric, a conclusion can be drawn by means of
conversion, as before. Again if both the relations are negative,
and the assertoric proposition is universal, although no conclusion
follows from the actual premisses, a syllogism can be obtained by
converting the problematic premiss into its complementary
affirmative as before. But if the negative proposition is
assertoric, but particular, no syllogism is possible, whether the
other premiss is affirmative or negative. Nor can a conclusion be
drawn when both premisses are indefinite, whether affirmative or
negative, or particular. The proof is the same and by the same
terms.
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    If one of the premisses is necessary, the other problematic,
then if the negative is necessary a syllogistic conclusion can be
drawn, not merely a negative problematic but also a negative
assertoric conclusion; but if the affirmative premiss is necessary,
no conclusion is possible. Suppose that A necessarily belongs to no
B, but may belong to all C. If the negative premiss is converted B
will belong to no A: but A ex hypothesi is capable of belonging to
all C: so once more a conclusion is drawn by the first figure that
B may belong to no C. But at the same time it is clear that B will
not belong to any C. For assume that it does: then if A cannot
belong to any B, and B belongs to some of the Cs, A cannot belong
to some of the Cs: but ex hypothesi it may belong to all. A similar
proof can be given if the minor premiss is negative. Again let the
affirmative proposition be necessary, and the other problematic;
i.e. suppose that A may belong to no B, but necessarily belongs to
all C. When the terms are arranged in this way, no syllogism is
possible. For (1) it sometimes turns out that B necessarily does
not belong to C. Let A be white, B man, C swan. White then
necessarily belongs to swan, but may belong to no man; and man
necessarily belongs to no swan; Clearly then we cannot draw a
problematic conclusion; for that which is necessary is admittedly
distinct from that which is possible. (2) Nor again can we draw a
necessary conclusion: for that presupposes that both premisses are
necessary, or at any rate the negative premiss. (3) Further it is
possible also, when the terms are so arranged, that B should belong
to C: for nothing prevents C falling under B, A being possible for
all B, and necessarily belonging to C; e.g. if C stands for
‘awake’, B for ‘animal’, A for ‘motion’. For motion necessarily
belongs to what is awake, and is possible for every animal: and
everything that is awake is animal. Clearly then the conclusion
cannot be the negative assertion, if the relation must be positive
when the terms are related as above. Nor can the opposite
affirmations be established: consequently no syllogism is possible.
A similar proof is possible if the major premiss is
affirmative.
    But if the premisses are similar in quality, when they are
negative a syllogism can always be formed by converting the
problematic premiss into its complementary affirmative as before.
Suppose A necessarily does not belong to B, and possibly may not
belong to C: if the premisses are converted B belongs to no A, and
A may possibly belong to all C: thus we have the first figure.
Similarly if the minor premiss is negative. But if the premisses
are affirmative there cannot be a syllogism. Clearly the conclusion
cannot be a negative assertoric or a negative necessary proposition
because no negative premiss has been laid down either in the
assertoric or in the necessary mode. Nor can the conclusion be a
problematic negative proposition. For if the terms are so