The Complete Aristotle (eng.)

of itself and of C, it is
clear that B will be said of everything of which A is said, except
A itself. Again when A and B belong to the whole of C, and C is
convertible with B, it is necessary that A should belong to all B:
for since A belongs to all C, and C to B by conversion, A will
belong to all B.
    When, of two opposites A and B, A is preferable to B, and
similarly D is preferable to C, then if A and C together are
preferable to B and D together, A must be preferable to D. For A is
an object of desire to the same extent as B is an object of
aversion, since they are opposites: and C is similarly related to
D, since they also are opposites. If then A is an object of desire
to the same extent as D, B is an object of aversion to the same
extent as C (since each is to the same extent as each-the one an
object of aversion, the other an object of desire). Therefore both
A and C together, and B and D together, will be equally objects of
desire or aversion. But since A and C are preferable to B and D, A
cannot be equally desirable with D; for then B along with D would
be equally desirable with A along with C. But if D is preferable to
A, then B must be less an object of aversion than C: for the less
is opposed to the less. But the greater good and lesser evil are
preferable to the lesser good and greater evil: the whole BD then
is preferable to the whole AC. But ex hypothesi this is not so. A
then is preferable to D, and C consequently is less an object of
aversion than B. If then every lover in virtue of his love would
prefer A, viz. that the beloved should be such as to grant a
favour, and yet should not grant it (for which C stands), to the
beloved’s granting the favour (represented by D) without being such
as to grant it (represented by B), it is clear that A (being of
such a nature) is preferable to granting the favour. To receive
affection then is preferable in love to sexual intercourse. Love
then is more dependent on friendship than on intercourse. And if it
is most dependent on receiving affection, then this is its end.
Intercourse then either is not an end at all or is an end relative
to the further end, the receiving of affection. And indeed the same
is true of the other desires and arts.
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    It is clear then how the terms are related in conversion, and in
respect of being in a higher degree objects of aversion or of
desire. We must now state that not only dialectical and
demonstrative syllogisms are formed by means of the aforesaid
figures, but also rhetorical syllogisms and in general any form of
persuasion, however it may be presented. For every belief comes
either through syllogism or from induction.
    Now induction, or rather the syllogism which springs out of
induction, consists in establishing syllogistically a relation
between one extreme and the middle by means of the other extreme,
e.g. if B is the middle term between A and C, it consists in
proving through C that A belongs to B. For this is the manner in
which we make inductions. For example let A stand for long-lived, B
for bileless, and C for the particular long-lived animals, e.g.
man, horse, mule. A then belongs to the whole of C: for whatever is
bileless is long-lived. But B also (’not possessing bile’) belongs
to all C. If then C is convertible with B, and the middle term is
not wider in extension, it is necessary that A should belong to B.
For it has already been proved that if two things belong to the
same thing, and the extreme is convertible with one of them, then
the other predicate will belong to the predicate that is converted.
But we must apprehend C as made up of all the particulars. For
induction proceeds through an enumeration of all the cases.
    Such is the syllogism which establishes the first and immediate
premiss: for where there is a middle term the syllogism proceeds
through the middle term; when there is no middle term, through
induction. And in a way induction is opposed to syllogism: for the
latter proves the major term to belong to the third term by means
of the middle, the former proves the major to belong to the middle
by means of the third. In the order of nature, syllogism through
the middle term is prior and better known, but syllogism through
induction is clearer to us.
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    We have an ‘example’ when the major term is proved to belong to
the middle by means of a term which resembles the third. It ought
to be known both that the middle belongs to the third term, and
that the first belongs to that which