The Complete Aristotle (eng.)

For the affirmative is destroyed by the
negative, and the negative by the affirmative. There remains the
proof of possibility. But this is impossible. For it has been
proved that if the terms are related in this manner it is both
necessary that the major should belong to all the minor and not
possible that it should belong to any. Consequently there cannot be
a syllogism to prove the possibility; for the necessary (as we
stated) is not possible.
    It is clear that if the terms are universal in possible
premisses a syllogism always results in the first figure, whether
they are affirmative or negative, only a perfect syllogism results
in the first case, an imperfect in the second. But possibility must
be understood according to the definition laid down, not as
covering necessity. This is sometimes forgotten.
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    If one premiss is a simple proposition, the other a problematic,
whenever the major premiss indicates possibility all the syllogisms
will be perfect and establish possibility in the sense defined; but
whenever the minor premiss indicates possibility all the syllogisms
will be imperfect, and those which are negative will establish not
possibility according to the definition, but that the major does
not necessarily belong to any, or to all, of the minor. For if this
is so, we say it is possible that it should belong to none or not
to all. Let A be possible for all B, and let B belong to all C.
Since C falls under B, and A is possible for all B, clearly it is
possible for all C also. So a perfect syllogism results. Likewise
if the premiss AB is negative, and the premiss BC is affirmative,
the former stating possible, the latter simple attribution, a
perfect syllogism results proving that A possibly belongs to no
C.
    It is clear that perfect syllogisms result if the minor premiss
states simple belonging: but that syllogisms will result if the
modality of the premisses is reversed, must be proved per
impossibile. At the same time it will be evident that they are
imperfect: for the proof proceeds not from the premisses assumed.
First we must state that if B’s being follows necessarily from A’s
being, B’s possibility will follow necessarily from A’s
possibility. Suppose, the terms being so related, that A is
possible, and B is impossible. If then that which is possible, when
it is possible for it to be, might happen, and if that which is
impossible, when it is impossible, could not happen, and if at the
same time A is possible and B impossible, it would be possible for
A to happen without B, and if to happen, then to be. For that which
has happened, when it has happened, is. But we must take the
impossible and the possible not only in the sphere of becoming, but
also in the spheres of truth and predicability, and the various
other spheres in which we speak of the possible: for it will be
alike in all. Further we must understand the statement that B’s
being depends on A’s being, not as meaning that if some single
thing A is, B will be: for nothing follows of necessity from the
being of some one thing, but from two at least, i.e. when the
premisses are related in the manner stated to be that of the
syllogism. For if C is predicated of D, and D of F, then C is
necessarily predicated of F. And if each is possible, the
conclusion also is possible. If then, for example, one should
indicate the premisses by A, and the conclusion by B, it would not
only result that if A is necessary B is necessary, but also that if
A is possible, B is possible.
    Since this is proved it is evident that if a false and not
impossible assumption is made, the consequence of the assumption
will also be false and not impossible: e.g. if A is false, but not
impossible, and if B is the consequence of A, B also will be false
but not impossible. For since it has been proved that if B’s being
is the consequence of A’s being, then B’s possibility will follow
from A’s possibility (and A is assumed to be possible),
consequently B will be possible: for if it were impossible, the
same thing would at the same time be possible and impossible.
    Since we have defined these points, let A belong to all B, and B
be possible for all C: it is necessary then that should be a
possible attribute for all C. Suppose that it is not possible, but
assume that B belongs to all C: this is false but not impossible.
If then A is not possible for C but B belongs to all C, then A is
not possible for all B: for a syllogism is formed in the third
degree. But it was