Prior Analytics - Book II   

so related to one another, that if the one is, the other necessarily

is, then if the latter is not, the former will not be either, but if

the latter is, it is not necessary that the former should be. But it

is impossible that the same thing should be necessitated by the

being and by the not-being of the same thing. I mean, for example,

that it is impossible that B should necessarily be great since A is

white and that B should necessarily be great since A is not white. For

whenever since this, A, is white it is necessary that that, B,

should be great, and since B is great that C should not be white, then

it is necessary if is white that C should not be white. And whenever

it is necessary, since one of two things is, that the other should be,

it is necessary, if the latter is not, that the former (viz. A) should

not be. If then B is not great A cannot be white. But if, when A is

not white, it is necessary that B should be great, it necessarily

results that if B is not great, B itself is great. (But this is

impossible.) For if B is not great, A will necessarily not be white.

If then when this is not white B must be great, it results that if B

is not great, it is great, just as if it were proved through three

terms.



5



Circular and reciprocal proof means proof by means of the

conclusion, i.e. by converting one of the premisses simply and

inferring the premiss which was assumed in the original syllogism:

e.g. suppose it has been necessary to prove that A belongs to all C,

and it has been proved through B; suppose that A should now be

proved to belong to B by assuming that A belongs to C, and C to B-so A

belongs to B: but in the first syllogism the converse was assumed,

viz. that B belongs to C. Or suppose it is necessary to prove that B

belongs to C, and A is assumed to belong to C, which was the

conclusion of the first syllogism, and B to belong to A but the