E No X is B E No X is B A Every A is X I Some A is X ———————————— ———————————————— E No A is B O Some A is not B _Second Figure._ E No B is X (Co) E No B is X (Co) A Every A is X I Some A is X ———————————— ————————————————— E No A is B O Some A is not B A Every B is X A Every B is X E No A is X (Co) O Some A is not X ———————————— ———————————————— E No A is B O Some A is not B _Third Figure._ A Every X is B E No X is B A Every X is A (Co+) A Every X is A (Co+) ———————————— —————————————————— I Some A is B O Some A is not B I Some X is B (Co) O Some X is not B A Every X is A A Every X is A ———————————— ———————————————— I Some A is B O Some A is not B A Every X is B E No X is B I Some X is A (Co) I Some X is A (Co) ———————————— ————————————————— I Some A is B O Some A is not B _Fourth Figure._ A Every B is X (+) I Some B is X A Every X is A A Every X is A ———————————— ———————————— I Some A is B I Some B is A A Every B is X E No B is X (Co) E No X is A A Every X is A (Co+) ———————————— —————————————————— E No A is B O Some A is not B E No B is X (Co) I Some X is A (Co) ———————————————— O Some A is not B The above is the ancient method of dividing syllogisms; but, for the present purpose, it will be sufficient to consider the six from which the rest can be obtained. And since some of the six have A in the predicate of the conclusion, and not B, we shall join to them the six other syllogisms which are found by transposing B and A. The complete list, therefore, of syllogisms with the weakest premises and the strongest conclusions, in which a comparison of A and B is obtained by comparison of both with X, is as follows: