The Complete Aristotle (eng.)

‘that’ belongs or that
to which it may belong; for the expression ‘A is possible of the
subject of B’ means that it is possible either of that of which B
is stated or of that of which B may possibly be stated. It makes no
difference whether we say, A is possible of the subject of B, or
all B admits of A. It is clear then that the expression ‘A may
possibly belong to all B’ might be used in two senses. First then
we must state the nature and characteristics of the syllogism which
arises if B is possible of the subject of C, and A is possible of
the subject of B. For thus both premisses are assumed in the mode
of possibility; but whenever A is possible of that of which B is
true, one premiss is a simple assertion, the other a problematic.
Consequently we must start from premisses which are similar in
form, as in the other cases.
14
    Whenever A may possibly belong to all B, and B to all C, there
will be a perfect syllogism to prove that A may possibly belong to
all C. This is clear from the definition: for it was in this way
that we explained ‘to be possible for one term to belong to all of
another’. Similarly if it is possible for A to belong no B, and for
B to belong to all C, then it is possible for A to belong to no C.
For the statement that it is possible for A not to belong to that
of which B may be true means (as we saw) that none of those things
which can possibly fall under the term B is left out of account.
But whenever A may belong to all B, and B may belong to no C, then
indeed no syllogism results from the premisses assumed, but if the
premiss BC is converted after the manner of problematic
propositions, the same syllogism results as before. For since it is
possible that B should belong to no C, it is possible also that it
should belong to all C. This has been stated above. Consequently if
B is possible for all C, and A is possible for all B, the same
syllogism again results. Similarly if in both the premisses the
negative is joined with ‘it is possible’: e.g. if A may belong to
none of the Bs, and B to none of the Cs. No syllogism results from
the assumed premisses, but if they are converted we shall have the
same syllogism as before. It is clear then that if the minor
premiss is negative, or if both premisses are negative, either no
syllogism results, or if one it is not perfect. For the necessity
results from the conversion.
    But if one of the premisses is universal, the other particular,
when the major premiss is universal there will be a perfect
syllogism. For if A is possible for all B, and B for some C, then A
is possible for some C. This is clear from the definition of being
possible. Again if A may belong to no B, and B may belong to some
of the Cs, it is necessary that A may possibly not belong to some
of the Cs. The proof is the same as above. But if the particular
premiss is negative, and the universal is affirmative, the major
still being universal and the minor particular, e.g. A is possible
for all B, B may possibly not belong to some C, then a clear
syllogism does not result from the assumed premisses, but if the
particular premiss is converted and it is laid down that B possibly
may belong to some C, we shall have the same conclusion as before,
as in the cases given at the beginning.
    But if the major premiss is the minor universal, whether both
are affirmative, or negative, or different in quality, or if both
are indefinite or particular, in no way will a syllogism be
possible. For nothing prevents B from reaching beyond A, so that as
predicates cover unequal areas. Let C be that by which B extends
beyond A. To C it is not possible that A should belong-either to
all or to none or to some or not to some, since premisses in the
mode of possibility are convertible and it is possible for B to
belong to more things than A can. Further, this is obvious if we
take terms; for if the premisses are as assumed, the major term is
both possible for none of the minor and must belong to all of it.
Take as terms common to all the cases under consideration
‘animal’-’white’-’man’, where the major belongs necessarily to the
minor; ‘animal’-’white’-’garment’, where it is not possible that
the major should belong to the minor. It is clear then that if the
terms are related in this manner, no syllogism results. For every
syllogism proves that something belongs either simply or
necessarily or possibly. It is clear that there is no proof of the
first or of the second.