The Complete Aristotle (eng.)

to some C,
e.g. a genus to its species and difference: for animal belongs to
every man and to every footed thing, and man to some footed things
though not to all. If then it is assumed that A belongs to all B,
and B to all C, A will belong to all C: and this ex hypothesi is
true. Similarly if the premiss AB is negative. For it is possible
that A should neither belong to any B nor to any C, though B
belongs to some C, e.g. a genus to the species of another genus and
its difference: for animal neither belongs to any wisdom nor to any
instance of ‘speculative’, but wisdom belongs to some instance of
‘speculative’. If then it should be assumed that A belongs to no B,
and B to all C, will belong to no C: and this ex hypothesi is
true.
    In particular syllogisms it is possible when the first premiss
is wholly false, and the other true, that the conclusion should be
true; also when the first premiss is false in part, and the other
true; and when the first is true, and the particular is false; and
when both are false. (7) For nothing prevents A belonging to no B,
but to some C, and B to some C, e.g. animal belongs to no snow, but
to some white thing, and snow to some white thing. If then snow is
taken as middle, and animal as first term, and it is assumed that A
belongs to the whole of B, and B to some C, then the premiss BC is
wholly false, the premiss BC true, and the conclusion true.
Similarly if the premiss AB is negative: for it is possible that A
should belong to the whole of B, but not to some C, although B
belongs to some C, e.g. animal belongs to every man, but does not
follow some white, but man belongs to some white; consequently if
man be taken as middle term and it is assumed that A belongs to no
B but B belongs to some C, the conclusion will be true although the
premiss AB is wholly false. (If the premiss AB is false in part,
the conclusion may be true. For nothing prevents A belonging both
to B and to some C, and B belonging to some C, e.g. animal to
something beautiful and to something great, and beautiful belonging
to something great. If then A is assumed to belong to all B, and B
to some C, the a premiss AB will be partially false, the premiss BC
will be true, and the conclusion true. Similarly if the premiss AB
is negative. For the same terms will serve, and in the same
positions, to prove the point.
    (9) Again if the premiss AB is true, and the premiss BC is
false, the conclusion may be true. For nothing prevents A belonging
to the whole of B and to some C, while B belongs to no C, e.g.
animal to every swan and to some black things, though swan belongs
to no black thing. Consequently if it should be assumed that A
belongs to all B, and B to some C, the conclusion will be true,
although the statement BC is false. Similarly if the premiss AB is
negative. For it is possible that A should belong to no B, and not
to some C, while B belongs to no C, e.g. a genus to the species of
another genus and to the accident of its own species: for animal
belongs to no number and not to some white things, and number
belongs to nothing white. If then number is taken as middle, and it
is assumed that A belongs to no B, and B to some C, then A will not
belong to some C, which ex hypothesi is true. And the premiss AB is
true, the premiss BC false.
    (10) Also if the premiss AB is partially false, and the premiss
BC is false too, the conclusion may be true. For nothing prevents A
belonging to some B and to some C, though B belongs to no C, e.g.
if B is the contrary of C, and both are accidents of the same
genus: for animal belongs to some white things and to some black
things, but white belongs to no black thing. If then it is assumed
that A belongs to all B, and B to some C, the conclusion will be
true. Similarly if the premiss AB is negative: for the same terms
arranged in the same way will serve for the proof.
    (11) Also though both premisses are false the conclusion may be
true. For it is possible that A may belong to no B and to some C,
while B belongs to no C, e.g. a genus in relation to the species of
another genus, and to the accident of its own species: for animal
belongs to no number, but to some white things, and number to
nothing white. If then it is assumed that A belongs to all B and B
to some C, the conclusion will be true, though both premisses are
false. Similarly also if the premiss AB is negative. For nothing
prevents A belonging to the whole of B, and not to some C, while B
belongs to no C, e.g. animal