The Complete Aristotle (eng.)

we must look for when a refuting and
establishing propositions, and how we should investigate a given
problem in any branch of inquiry, also by what means we shall
obtain principles appropriate to each subject. Since some
syllogisms are universal, others particular, all the universal
syllogisms give more than one result, and of particular syllogisms
the affirmative yield more than one, the negative yield only the
stated conclusion. For all propositions are convertible save only
the particular negative: and the conclusion states one definite
thing about another definite thing. Consequently all syllogisms
save the particular negative yield more than one conclusion, e.g.
if A has been proved to to all or to some B, then B must belong to
some A: and if A has been proved to belong to no B, then B belongs
to no A. This is a different conclusion from the former. But if A
does not belong to some B, it is not necessary that B should not
belong to some A: for it may possibly belong to all A.
    This then is the reason common to all syllogisms whether
universal or particular. But it is possible to give another reason
concerning those which are universal. For all the things that are
subordinate to the middle term or to the conclusion may be proved
by the same syllogism, if the former are placed in the middle, the
latter in the conclusion; e.g. if the conclusion AB is proved
through C, whatever is subordinate to B or C must accept the
predicate A: for if D is included in B as in a whole, and B is
included in A, then D will be included in A. Again if E is included
in C as in a whole, and C is included in A, then E will be included
in A. Similarly if the syllogism is negative. In the second figure
it will be possible to infer only that which is subordinate to the
conclusion, e.g. if A belongs to no B and to all C; we conclude
that B belongs to no C. If then D is subordinate to C, clearly B
does not belong to it. But that B does not belong to what is
subordinate to A is not clear by means of the syllogism. And yet B
does not belong to E, if E is subordinate to A. But while it has
been proved through the syllogism that B belongs to no C, it has
been assumed without proof that B does not belong to A,
consequently it does not result through the syllogism that B does
not belong to E.
    But in particular syllogisms there will be no necessity of
inferring what is subordinate to the conclusion (for a syllogism
does not result when this premiss is particular), but whatever is
subordinate to the middle term may be inferred, not however through
the syllogism, e.g. if A belongs to all B and B to some C. Nothing
can be inferred about that which is subordinate to C; something can
be inferred about that which is subordinate to B, but not through
the preceding syllogism. Similarly in the other figures. That which
is subordinate to the conclusion cannot be proved; the other
subordinate can be proved, only not through the syllogism, just as
in the universal syllogisms what is subordinate to the middle term
is proved (as we saw) from a premiss which is not demonstrated:
consequently either a conclusion is not possible in the case of
universal syllogisms or else it is possible also in the case of
particular syllogisms.
2
    It is possible for the premisses of the syllogism to be true, or
to be false, or to be the one true, the other false. The conclusion
is either true or false necessarily. From true premisses it is not
possible to draw a false conclusion, but a true conclusion may be
drawn from false premisses, true however only in respect to the
fact, not to the reason. The reason cannot be established from
false premisses: why this is so will be explained in the
sequel.
    First then that it is not possible to draw a false conclusion
from true premisses, is made clear by this consideration. If it is
necessary that B should be when A is, it is necessary that A should
not be when B is not. If then A is true, B must be true: otherwise
it will turn out that the same thing both is and is not at the same
time. But this is impossible. Let it not, because A is laid down as
a single term, be supposed that it is possible, when a single fact
is given, that something should necessarily result. For that is not
possible. For what results necessarily is the conclusion, and the
means by which this comes about are at the least three terms, and
two relations of subject and predicate or premisses. If then it is
true that A belongs to all that to which B belongs, and that