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