The Complete Aristotle (eng.)

if it is admissible
for no garment to be white, it is also admissible for nothing white
to be a garment. For if any white thing must be a garment, then
some garment will necessarily be white. This has been already
proved. The particular negative also must be treated like those
dealt with above. But if anything is said to be possible because it
is the general rule and natural (and it is in this way we define
the possible), the negative premisses can no longer be converted
like the simple negatives; the universal negative premiss does not
convert, and the particular does. This will be plain when we speak
about the possible. At present we may take this much as clear in
addition to what has been said: the statement that it is possible
that no B is A or some B is not A is affirmative in form: for the
expression ‘is possible’ ranks along with ‘is’, and ‘is’ makes an
affirmation always and in every case, whatever the terms to which
it is added, in predication, e.g. ‘it is not-good’ or ‘it is
not-white’ or in a word ‘it is not-this’. But this also will be
proved in the sequel. In conversion these premisses will behave
like the other affirmative propositions.
4
    After these distinctions we now state by what means, when, and
how every syllogism is produced; subsequently we must speak of
demonstration. Syllogism should be discussed before demonstration
because syllogism is the general: the demonstration is a sort of
syllogism, but not every syllogism is a demonstration.
    Whenever three terms are so related to one another that the last
is contained in the middle as in a whole, and the middle is either
contained in, or excluded from, the first as in or from a whole,
the extremes must be related by a perfect syllogism. I call that
term middle which is itself contained in another and contains
another in itself: in position also this comes in the middle. By
extremes I mean both that term which is itself contained in another
and that in which another is contained. If A is predicated of all
B, and B of all C, A must be predicated of all C: we have already
explained what we mean by ‘predicated of all’. Similarly also, if A
is predicated of no B, and B of all C, it is necessary that no C
will be A.
    But if the first term belongs to all the middle, but the middle
to none of the last term, there will be no syllogism in respect of
the extremes; for nothing necessary follows from the terms being so
related; for it is possible that the first should belong either to
all or to none of the last, so that neither a particular nor a
universal conclusion is necessary. But if there is no necessary
consequence, there cannot be a syllogism by means of these
premisses. As an example of a universal affirmative relation
between the extremes we may take the terms animal, man, horse; of a
universal negative relation, the terms animal, man, stone. Nor
again can syllogism be formed when neither the first term belongs
to any of the middle, nor the middle to any of the last. As an
example of a positive relation between the extremes take the terms
science, line, medicine: of a negative relation science, line,
unit.
    If then the terms are universally related, it is clear in this
figure when a syllogism will be possible and when not, and that if
a syllogism is possible the terms must be related as described, and
if they are so related there will be a syllogism.
    But if one term is related universally, the other in part only,
to its subject, there must be a perfect syllogism whenever
universality is posited with reference to the major term either
affirmatively or negatively, and particularity with reference to
the minor term affirmatively: but whenever the universality is
posited in relation to the minor term, or the terms are related in
any other way, a syllogism is impossible. I call that term the
major in which the middle is contained and that term the minor
which comes under the middle. Let all B be A and some C be B. Then
if ‘predicated of all’ means what was said above, it is necessary
that some C is A. And if no B is A but some C is B, it is necessary
that some C is not A. The meaning of ‘predicated of none’ has also
been defined. So there will be a perfect syllogism. This holds good
also if the premiss BC should be indefinite, provided that it is
affirmative: for we shall have the same syllogism whether the
premiss is indefinite or particular.
    But if the universality is posited with respect to the minor
term either