The Complete Aristotle (eng.)

affirmatively or negatively, a syllogism will not be
possible, whether the major premiss is positive or negative,
indefinite or particular: e.g. if some B is or is not A, and all C
is B. As an example of a positive relation between the extremes
take the terms good, state, wisdom: of a negative relation, good,
state, ignorance. Again if no C is B, but some B is or is not A or
not every B is A, there cannot be a syllogism. Take the terms
white, horse, swan: white, horse, raven. The same terms may be
taken also if the premiss BA is indefinite.
    Nor when the major premiss is universal, whether affirmative or
negative, and the minor premiss is negative and particular, can
there be a syllogism, whether the minor premiss be indefinite or
particular: e.g. if all B is A and some C is not B, or if not all C
is B. For the major term may be predicable both of all and of none
of the minor, to some of which the middle term cannot be
attributed. Suppose the terms are animal, man, white: next take
some of the white things of which man is not predicated-swan and
snow: animal is predicated of all of the one, but of none of the
other. Consequently there cannot be a syllogism. Again let no B be
A, but let some C not be B. Take the terms inanimate, man, white:
then take some white things of which man is not predicated-swan and
snow: the term inanimate is predicated of all of the one, of none
of the other.
    Further since it is indefinite to say some C is not B, and it is
true that some C is not B, whether no C is B, or not all C is B,
and since if terms are assumed such that no C is B, no syllogism
follows (this has already been stated) it is clear that this
arrangement of terms will not afford a syllogism: otherwise one
would have been possible with a universal negative minor premiss. A
similar proof may also be given if the universal premiss is
negative.
    Nor can there in any way be a syllogism if both the relations of
subject and predicate are particular, either positively or
negatively, or the one negative and the other affirmative, or one
indefinite and the other definite, or both indefinite. Terms common
to all the above are animal, white, horse: animal, white,
stone.
    It is clear then from what has been said that if there is a
syllogism in this figure with a particular conclusion, the terms
must be related as we have stated: if they are related otherwise,
no syllogism is possible anyhow. It is evident also that all the
syllogisms in this figure are perfect (for they are all completed
by means of the premisses originally taken) and that all
conclusions are proved by this figure, viz. universal and
particular, affirmative and negative. Such a figure I call the
first.
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    Whenever the same thing belongs to all of one subject, and to
none of another, or to all of each subject or to none of either, I
call such a figure the second; by middle term in it I mean that
which is predicated of both subjects, by extremes the terms of
which this is said, by major extreme that which lies near the
middle, by minor that which is further away from the middle. The
middle term stands outside the extremes, and is first in position.
A syllogism cannot be perfect anyhow in this figure, but it may be
valid whether the terms are related universally or not.
    If then the terms are related universally a syllogism will be
possible, whenever the middle belongs to all of one subject and to
none of another (it does not matter which has the negative
relation), but in no other way. Let M be predicated of no N, but of
all O. Since, then, the negative relation is convertible, N will
belong to no M: but M was assumed to belong to all O: consequently
N will belong to no O. This has already been proved. Again if M
belongs to all N, but to no O, then N will belong to no O. For if M
belongs to no O, O belongs to no M: but M (as was said) belongs to
all N: O then will belong to no N: for the first figure has again
been formed. But since the negative relation is convertible, N will
belong to no O. Thus it will be the same syllogism that proves both
conclusions.
    It is possible to prove these results also by reductio ad
impossibile.
    It is clear then that a syllogism is formed when the terms are
so related, but not a perfect syllogism; for necessity is not
perfectly established merely from the original premisses; others
also are needed.
    But if M is predicated of every N and O, there cannot be a
syllogism. Terms to illustrate a positive relation between the
extremes are