
Prior Analytics  Book II
is necessary then that C should not belong to some B. But originally
it belonged to all B, consequently the hypothesis is false: A then
will belong to no B.
When A does not belong to an B, suppose it does belong to all B, and
to no C. It is necessary then that C should belong to no B. But this
is impossible: so that it is true that A does not belong to all B.
It is clear then that all the syllogisms can be formed in the middle
figure.
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Similarly they can all be formed in the last figure. Suppose that
A does not belong to some B, but C belongs to all B: then A does not
belong to some C. If then this is impossible, it is false that A
does not belong to some B; so that it is true that A belongs to all B.
But if it is supposed that A belongs to no B, we shall have a
syllogism and a conclusion which is impossible: but the problem in
hand is not proved: for if the contrary is supposed, we shall have the
same results as before.
But to prove that A belongs to some B, this hypothesis must be made.
If A belongs to no B, and C to some B, A will belong not to all C.
If then this is false, it is true that A belongs to some B.
When A belongs to no B, suppose A belongs to some B, and let it have
been assumed that C belongs to all B. Then it is necessary that A
should belong to some C. But ex hypothesi it belongs to no C, so
that it is false that A belongs to some B. But if it is supposed
that A belongs to all B, the problem is not proved.
But this hypothesis must be made if we are prove that A belongs
not to all B. For if A belongs to all B and C to some B, then A
belongs to some C. But this we assumed not to be so, so it is false
that A belongs to all B. But in that case it is true that A belongs
not to all B. If however it is assumed that A belongs to some B, we
