Prior Analytics - Book II   

the impossible conclusion reached. But this is the middle figure, if C

belongs to all A and to no B. And it is clear from these premisses

that A belongs to no B. Similarly if has been proved not to belong

to all B. For the hypothesis is that A belongs to all B; and the

original premisses are that C belongs to all A but not to all B.

Similarly too, if the premiss CA should be negative: for thus also

we have the middle figure. Again suppose it has been proved that A

belongs to some B. The hypothesis here is that is that A belongs to no

B; and the original premisses that B belongs to all C, and A either to

all or to some C: for in this way we shall get what is impossible. But

if A and B belong to all C, we have the last figure. And it is clear

from these premisses that A must belong to some B. Similarly if B or A

should be assumed to belong to some C.

Again suppose it has been proved in the middle figure that A belongs

to all B. Then the hypothesis must have been that A belongs not to all

B, and the original premisses that A belongs to all C, and C to all B:

for thus we shall get what is impossible. But if A belongs to all C,

and C to all B, we have the first figure. Similarly if it has been

proved that A belongs to some B: for the hypothesis then must have

been that A belongs to no B, and the original premisses that A belongs

to all C, and C to some B. If the syllogism is negative, the

hypothesis must have been that A belongs to some B, and the original

premisses that A belongs to no C, and C to all B, so that the first

figure results. If the syllogism is not universal, but proof has

been given that A does not belong to some B, we may infer in the

same way. The hypothesis is that A belongs to all B, the original

premisses that A belongs to no C, and C belongs to some B: for thus we

get the first figure.

Again suppose it has been proved in the third figure that A

belongs to all B. Then the hypothesis must have been that A belongs

not to all B, and the original premisses that C belongs to all B,

and A belongs to all C; for thus we shall get what is impossible.