The Complete Aristotle (eng.)

C as footless,
and D as man, he assumes in the same way that A inheres either in B
or in C (for every mortal animal is either footed or footless), and
he assumes A of D (for he assumed man, as we saw, to be a mortal
animal); consequently it is necessary that man should be either a
footed or a footless animal; but it is not necessary that man
should be footed: this he assumes: and it is just this again which
he ought to have demonstrated. Always dividing then in this way it
turns out that these logicians assume as middle the universal term,
and as extremes that which ought to have been the subject of
demonstration and the differentiae. In conclusion, they do not make
it clear, and show it to be necessary, that this is man or whatever
the subject of inquiry may be: for they pursue the other method
altogether, never even suspecting the presence of the rich supply
of evidence which might be used. It is clear that it is neither
possible to refute a statement by this method of division, nor to
draw a conclusion about an accident or property of a thing, nor
about its genus, nor in cases in which it is unknown whether it is
thus or thus, e.g. whether the diagonal is incommensurate. For if
he assumes that every length is either commensurate or
incommensurate, and the diagonal is a length, he has proved that
the diagonal is either incommensurate or commensurate. But if he
should assume that it is incommensurate, he will have assumed what
he ought to have proved. He cannot then prove it: for this is his
method, but proof is not possible by this method. Let A stand for
‘incommensurate or commensurate’, B for ‘length’, C for ‘diagonal’.
It is clear then that this method of investigation is not suitable
for every inquiry, nor is it useful in those cases in which it is
thought to be most suitable.
    From what has been said it is clear from what elements
demonstrations are formed and in what manner, and to what points we
must look in each problem.
32
    Our next business is to state how we can reduce syllogisms to
the aforementioned figures: for this part of the inquiry still
remains. If we should investigate the production of the syllogisms
and had the power of discovering them, and further if we could
resolve the syllogisms produced into the aforementioned figures,
our original problem would be brought to a conclusion. It will
happen at the same time that what has been already said will be
confirmed and its truth made clearer by what we are about to say.
For everything that is true must in every respect agree with itself
First then we must attempt to select the two premisses of the
syllogism (for it is easier to divide into large parts than into
small, and the composite parts are larger than the elements out of
which they are made); next we must inquire which are universal and
which particular, and if both premisses have not been stated, we
must ourselves assume the one which is missing. For sometimes men
put forward the universal premiss, but do not posit the premiss
which is contained in it, either in writing or in discussion: or
men put forward the premisses of the principal syllogism, but omit
those through which they are inferred, and invite the concession of
others to no purpose. We must inquire then whether anything
unnecessary has been assumed, or anything necessary has been
omitted, and we must posit the one and take away the other, until
we have reached the two premisses: for unless we have these, we
cannot reduce arguments put forward in the way described. In some
arguments it is easy to see what is wanting, but some escape us,
and appear to be syllogisms, because something necessary results
from what has been laid down, e.g. if the assumptions were made
that substance is not annihilated by the annihilation of what is
not substance, and that if the elements out of which a thing is
made are annihilated, then that which is made out of them is
destroyed: these propositions being laid down, it is necessary that
any part of substance is substance; this has not however been drawn
by syllogism from the propositions assumed, but premisses are
wanting. Again if it is necessary that animal should exist, if man
does, and that substance should exist, if animal does, it is
necessary that substance should exist if man does: but as yet the
conclusion has not been drawn syllogistically: for the premisses
are not in the shape we required. We are deceived in such cases
because something necessary results from what is assumed,