The Complete Aristotle (eng.)

same thing.
    Privative terms are similarly related positive ter terms respect
of this arrangement. Let A stand for ‘equal’, B for ‘not equal’, C
for ‘unequal’, D for ‘not unequal’.
    In many things also, to some of which something belongs which
does not belong to others, the negation may be true in a similar
way, viz. that all are not white or that each is not white, while
that each is not-white or all are not-white is false. Similarly
also ‘every animal is not-white’ is not the negation of ‘every
animal is white’ (for both are false): the proper negation is
‘every animal is not white’. Since it is clear that ‘it is
not-white’ and ‘it is not white’ mean different things, and one is
an affirmation, the other a denial, it is evident that the method
of proving each cannot be the same, e.g. that whatever is an animal
is not white or may not be white, and that it is true to call it
not-white; for this means that it is not-white. But we may prove
that it is true to call it white or not-white in the same way for
both are proved constructively by means of the first figure. For
the expression ‘it is true’ stands on a similar footing to ‘it is’.
For the negation of ‘it is true to call it white’ is not ‘it is
true to call it not-white’ but ‘it is not true to call it white’.
If then it is to be true to say that whatever is a man is musical
or is not-musical, we must assume that whatever is an animal either
is musical or is not-musical; and the proof has been made. That
whatever is a man is not musical is proved destructively in the
three ways mentioned.
    In general whenever A and B are such that they cannot belong at
the same time to the same thing, and one of the two necessarily
belongs to everything, and again C and D are related in the same
way, and A follows C but the relation cannot be reversed, then D
must follow B and the relation cannot be reversed. And A and D may
belong to the same thing, but B and C cannot. First it is clear
from the following consideration that D follows B. For since either
C or D necessarily belongs to everything; and since C cannot belong
to that to which B belongs, because it carries A along with it and
A and B cannot belong to the same thing; it is clear that D must
follow B. Again since C does not reciprocate with but A, but C or D
belongs to everything, it is possible that A and D should belong to
the same thing. But B and C cannot belong to the same thing,
because A follows C; and so something impossible results. It is
clear then that B does not reciprocate with D either, since it is
possible that D and A should belong at the same time to the same
thing.
    It results sometimes even in such an arrangement of terms that
one is deceived through not apprehending the opposites rightly, one
of which must belong to everything, e.g. we may reason that ‘if A
and B cannot belong at the same time to the same thing, but it is
necessary that one of them should belong to whatever the other does
not belong to: and again C and D are related in the same way, and
follows everything which C follows: it will result that B belongs
necessarily to everything to which D belongs’: but this is false.
‘Assume that F stands for the negation of A and B, and again that H
stands for the negation of C and D. It is necessary then that
either A or F should belong to everything: for either the
affirmation or the denial must belong. And again either C or H must
belong to everything: for they are related as affirmation and
denial. And ex hypothesi A belongs to everything ever thing to
which C belongs. Therefore H belongs to everything to which F
belongs. Again since either F or B belongs to everything, and
similarly either H or D, and since H follows F, B must follow D:
for we know this. If then A follows C, B must follow D’. But this
is false: for as we proved the sequence is reversed in terms so
constituted. The fallacy arises because perhaps it is not necessary
that A or F should belong to everything, or that F or B should
belong to everything: for F is not the denial of A. For not good is
the negation of good: and not-good is not identical with ‘neither
good nor not-good’. Similarly also with C and D. For two negations
have been assumed in respect to one term.

Prior Analytics, Book II
    Translated by A. J. Jenkinson
1
    We have already explained the number of the figures, the
character and number of the premisses, when and how a syllogism is
formed; further what