The Complete Aristotle (eng.)

substance, animal, man; a negative relation,
substance, animal, number-substance being the middle term.
    Nor is a syllogism possible when M is predicated neither of any
N nor of any O. Terms to illustrate a positive relation are line,
animal, man: a negative relation, line, animal, stone.
    It is clear then that if a syllogism is formed when the terms
are universally related, the terms must be related as we stated at
the outset: for if they are otherwise related no necessary
consequence follows.
    If the middle term is related universally to one of the
extremes, a particular negative syllogism must result whenever the
middle term is related universally to the major whether positively
or negatively, and particularly to the minor and in a manner
opposite to that of the universal statement: by ‘an opposite
manner’ I mean, if the universal statement is negative, the
particular is affirmative: if the universal is affirmative, the
particular is negative. For if M belongs to no N, but to some O, it
is necessary that N does not belong to some O. For since the
negative statement is convertible, N will belong to no M: but M was
admitted to belong to some O: therefore N will not belong to some
O: for the result is reached by means of the first figure. Again if
M belongs to all N, but not to some O, it is necessary that N does
not belong to some O: for if N belongs to all O, and M is
predicated also of all N, M must belong to all O: but we assumed
that M does not belong to some O. And if M belongs to all N but not
to all O, we shall conclude that N does not belong to all O: the
proof is the same as the above. But if M is predicated of all O,
but not of all N, there will be no syllogism. Take the terms
animal, substance, raven; animal, white, raven. Nor will there be a
conclusion when M is predicated of no O, but of some N. Terms to
illustrate a positive relation between the extremes are animal,
substance, unit: a negative relation, animal, substance,
science.
    If then the universal statement is opposed to the particular, we
have stated when a syllogism will be possible and when not: but if
the premisses are similar in form, I mean both negative or both
affirmative, a syllogism will not be possible anyhow. First let
them be negative, and let the major premiss be universal, e.g. let
M belong to no N, and not to some O. It is possible then for N to
belong either to all O or to no O. Terms to illustrate the negative
relation are black, snow, animal. But it is not possible to find
terms of which the extremes are related positively and universally,
if M belongs to some O, and does not belong to some O. For if N
belonged to all O, but M to no N, then M would belong to no O: but
we assumed that it belongs to some O. In this way then it is not
admissible to take terms: our point must be proved from the
indefinite nature of the particular statement. For since it is true
that M does not belong to some O, even if it belongs to no O, and
since if it belongs to no O a syllogism is (as we have seen) not
possible, clearly it will not be possible now either.
    Again let the premisses be affirmative, and let the major
premiss as before be universal, e.g. let M belong to all N and to
some O. It is possible then for N to belong to all O or to no O.
Terms to illustrate the negative relation are white, swan, stone.
But it is not possible to take terms to illustrate the universal
affirmative relation, for the reason already stated: the point must
be proved from the indefinite nature of the particular statement.
But if the minor premiss is universal, and M belongs to no O, and
not to some N, it is possible for N to belong either to all O or to
no O. Terms for the positive relation are white, animal, raven: for
the negative relation, white, stone, raven. If the premisses are
affirmative, terms for the negative relation are white, animal,
snow; for the positive relation, white, animal, swan. Evidently
then, whenever the premisses are similar in form, and one is
universal, the other particular, a syllogism can, not be formed
anyhow. Nor is one possible if the middle term belongs to some of
each of the extremes, or does not belong to some of either, or
belongs to some of the one, not to some of the other, or belongs to
neither universally, or is related to them indefinitely. Common
terms for all the above are white, animal, man: white, animal,
inanimate. It is clear then from what has been said that if the
terms are related to one another in the way