The Complete Aristotle (eng.)

and let A possibly not belong to any B, and
let B necessarily belong to all C. The syllogism will be perfect,
but it will establish a problematic negative, not an assertoric
negative. For the major premiss was problematic, and further it is
not possible to prove the assertoric conclusion per impossibile.
For if it were supposed that A belongs to some C, and it is laid
down that A possibly does not belong to any B, no impossible
relation between B and C follows from these premisses. But if the
minor premiss is negative, when it is problematic a syllogism is
possible by conversion, as above; but when it is necessary no
syllogism can be formed. Nor again when both premisses are
negative, and the minor is necessary. The same terms as before
serve both for the positive relation-white-animal-snow, and for the
negative relation-white-animal-pitch.
    The same relation will obtain in particular syllogisms. Whenever
the negative proposition is necessary, the conclusion will be
negative assertoric: e.g. if it is not possible that A should
belong to any B, but B may belong to some of the Cs, it is
necessary that A should not belong to some of the Cs. For if A
belongs to all C, but cannot belong to any B, neither can B belong
to any A. So if A belongs to all C, to none of the Cs can B belong.
But it was laid down that B may belong to some C. But when the
particular affirmative in the negative syllogism, e.g. BC the minor
premiss, or the universal proposition in the affirmative syllogism,
e.g. AB the major premiss, is necessary, there will not be an
assertoric conclusion. The demonstration is the same as before. But
if the minor premiss is universal, and problematic, whether
affirmative or negative, and the major premiss is particular and
necessary, there cannot be a syllogism. Premisses of this kind are
possible both where the relation is positive and necessary, e.g.
animal-white-man, and where it is necessary and negative, e.g.
animal-white-garment. But when the universal is necessary, the
particular problematic, if the universal is negative we may take
the terms animal-white-raven to illustrate the positive relation,
or animal-white-pitch to illustrate the negative; and if the
universal is affirmative we may take the terms animal-white-swan to
illustrate the positive relation, and animal-white-snow to
illustrate the negative and necessary relation. Nor again is a
syllogism possible when the premisses are indefinite, or both
particular. Terms applicable in either case to illustrate the
positive relation are animal-white-man: to illustrate the negative,
animal-white-inanimate. For the relation of animal to some white,
and of white to some inanimate, is both necessary and positive and
necessary and negative. Similarly if the relation is problematic:
so the terms may be used for all cases.
    Clearly then from what has been said a syllogism results or not
from similar relations of the terms whether we are dealing with
simple existence or necessity, with this exception, that if the
negative premiss is assertoric the conclusion is problematic, but
if the negative premiss is necessary the conclusion is both
problematic and negative assertoric. [It is clear also that all the
syllogisms are imperfect and are perfected by means of the figures
above mentioned.]
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    In the second figure whenever both premisses are problematic, no
syllogism is possible, whether the premisses are affirmative or
negative, universal or particular. But when one premiss is
assertoric, the other problematic, if the affirmative is assertoric
no syllogism is possible, but if the universal negative is
assertoric a conclusion can always be drawn. Similarly when one
premiss is necessary, the other problematic. Here also we must
understand the term ‘possible’ in the conclusion, in the same sense
as before.
    First we must point out that the negative problematic
proposition is not convertible, e.g. if A may belong to no B, it
does not follow that B may belong to no A. For suppose it to follow
and assume that B may belong to no A. Since then problematic
affirmations are convertible with negations, whether they are
contraries or contradictories, and since B may belong to no A, it
is clear that B may belong to all A. But this is false: for if all
this can be that, it does not follow that all that can be this:
consequently the negative proposition is not convertible. Further,
these propositions are not incompatible, ‘A may belong to no B’, ‘B
necessarily does not