The Complete Aristotle (eng.)

and
coordinates and opposites. For if justice be the same as courage,
then too the just man is the same as the brave man, and ‘justly’ is
the same as ‘bravely’. Likewise, too, in the case of their
opposites: for if two things be the same, their opposites also will
be the same, in any of the recognized forms of opposition. For it
is the same thing to take the opposite of the one or that of the
other, seeing that they are the same. Again it may be examined in
the light of those things which tend to produce or to destroy the
things in question of their formation and destruction, and in
general of any thing that is related in like manner to each. For
where things are absolutely the same, their formations and
destructions also are the same, and so are the things that tend to
produce or to destroy them. Look and see also, in a case where one
of two things is said to be something or other in a superlative
degree, if the other of these alleged identical things can also be
described by a superlative in the same respect. Thus Xenocrates
argues that the happy life and the good life are the same, seeing
that of all forms of life the good life is the most desirable and
so also is the happy life: for ‘the most desirable’ and the
greatest’ apply but to one thing.’ Likewise also in other cases of
the kind. Each, however, of the two things termed ‘greatest’ or
most desirable’ must be numerically one: otherwise no proof will
have been given that they are the same; for it does not follow
because Peloponnesians and Spartans are the bravest of the Greeks,
that Peloponnesians are the same as Spartans, seeing that
‘Peloponnesian’ is not any one person nor yet ‘Spartan’; it only
follows that the one must be included under the other as ‘Spartans’
are under ‘Peloponnesians’: for otherwise, if the one class be not
included under the other, each will be better than the other. For
then the Peloponnesians are bound to be better than the Spartans,
seeing that the one class is not included under the other; for they
are better than anybody else. Likewise also the Spartans must
perforce be better than the Peloponnesians; for they too are better
than anybody else; each then is better than the other! Clearly
therefore what is styled ‘best’ and ‘greatest’ must be a single
thing, if it is to be proved to be ‘the same’ as another. This also
is why Xenocrates fails to prove his case: for the happy life is
not numerically single, nor yet the good life, so that it does not
follow that, because they are both the most desirable, they are
therefore the same, but only that the one falls under the
other.
    Again, look and see if, supposing the one to be the same as
something, the other also is the same as it: for if they be not
both the same as the same thing, clearly neither are they the same
as one another.
    Moreover, examine them in the light of their accidents or of the
things of which they are accidents: for any accident belonging to
the one must belong also to the other, and if the one belong to
anything as an accident, so must the other also. If in any of these
respects there is a discrepancy, clearly they are not the same.
    See further whether, instead of both being found in one class of
predicates, the one signifies a quality and the other a quantity or
relation. Again, see if the genus of each be not the same, the one
being ‘good’ and the other evil’, or the one being ‘virtue’ and the
other ‘knowledge’: or see if, though the genus is the same, the
differentiae predicted of either be not the same, the one (e.g.)
being distinguished as a ‘speculative’ science, the other as a
‘practical’ science. Likewise also in other cases.
    Moreover, from the point of view of ‘degrees’, see if the one
admits an increase of degree but not the other, or if though both
admit it, they do not admit it at the same time; just as it is not
the case that a man desires intercourse more intensely, the more
intensely he is in love, so that love and the desire for
intercourse are not the same.
    Moreover, examine them by means of an addition, and see whether
the addition of each to the same thing fails to make the same
whole; or if the subtraction of the same thing from each leaves a
different remainder. Suppose (e.g.) that he has declared ‘double a
half’ to be the same as ‘a multiple of a half’: then, subtracting
the words ‘a half’ from each, the remainders ought to have
signified the same thing: