The Complete Aristotle (eng.)

belongs to every swan, and not to some
black things, and swan belongs to nothing black. Consequently if it
is assumed that A belongs to no B, and B to some C, then A does not
belong to some C. The conclusion then is true, but the premisses
arc false.
3
    In the middle figure it is possible in every way to reach a true
conclusion through false premisses, whether the syllogisms are
universal or particular, viz. when both premisses are wholly false;
when each is partially false; when one is true, the other wholly
false (it does not matter which of the two premisses is false); if
both premisses are partially false; if one is quite true, the other
partially false; if one is wholly false, the other partially true.
For (1) if A belongs to no B and to all C, e.g. animal to no stone
and to every horse, then if the premisses are stated contrariwise
and it is assumed that A belongs to all B and to no C, though the
premisses are wholly false they will yield a true conclusion.
Similarly if A belongs to all B and to no C: for we shall have the
same syllogism.
    (2) Again if one premiss is wholly false, the other wholly true:
for nothing prevents A belonging to all B and to all C, though B
belongs to no C, e.g. a genus to its co-ordinate species. For
animal belongs to every horse and man, and no man is a horse. If
then it is assumed that animal belongs to all of the one, and none
of the other, the one premiss will be wholly false, the other
wholly true, and the conclusion will be true whichever term the
negative statement concerns.
    (3) Also if one premiss is partially false, the other wholly
true. For it is possible that A should belong to some B and to all
C, though B belongs to no C, e.g. animal to some white things and
to every raven, though white belongs to no raven. If then it is
assumed that A belongs to no B, but to the whole of C, the premiss
AB is partially false, the premiss AC wholly true, and the
conclusion true. Similarly if the negative statement is transposed:
the proof can be made by means of the same terms. Also if the
affirmative premiss is partially false, the negative wholly true, a
true conclusion is possible. For nothing prevents A belonging to
some B, but not to C as a whole, while B belongs to no C, e.g.
animal belongs to some white things, but to no pitch, and white
belongs to no pitch. Consequently if it is assumed that A belongs
to the whole of B, but to no C, the premiss AB is partially false,
the premiss AC is wholly true, and the conclusion is true.
    (4) And if both the premisses are partially false, the
conclusion may be true. For it is possible that A should belong to
some B and to some C, and B to no C, e.g. animal to some white
things and to some black things, though white belongs to nothing
black. If then it is assumed that A belongs to all B and to no C,
both premisses are partially false, but the conclusion is true.
Similarly, if the negative premiss is transposed, the proof can be
made by means of the same terms.
    It is clear also that our thesis holds in particular syllogisms.
For (5) nothing prevents A belonging to all B and to some C, though
B does not belong to some C, e.g. animal to every man and to some
white things, though man will not belong to some white things. If
then it is stated that A belongs to no B and to some C, the
universal premiss is wholly false, the particular premiss is true,
and the conclusion is true. Similarly if the premiss AB is
affirmative: for it is possible that A should belong to no B, and
not to some C, though B does not belong to some C, e.g. animal
belongs to nothing lifeless, and does not belong to some white
things, and lifeless will not belong to some white things. If then
it is stated that A belongs to all B and not to some C, the premiss
AB which is universal is wholly false, the premiss AC is true, and
the conclusion is true. Also a true conclusion is possible when the
universal premiss is true, and the particular is false. For nothing
prevents A following neither B nor C at all, while B does not
belong to some C, e.g. animal belongs to no number nor to anything
lifeless, and number does not follow some lifeless things. If then
it is stated that A belongs to no B and to some C, the conclusion
will be true, and the universal premiss true, but the particular
false. Similarly if the premiss which is stated universally is
affirmative. For it is possible that should A belong both to B and
to C as wholes, though B does not follow some C, e.g. a genus