where the minor premise, All B is A, conformably to what was laid down in the last chapter respecting universal affirmatives, does not admit of simple conversion, but may be converted per accidens, thus, Some A is B; which, though it does not express the whole of what is asserted in the proposition All B is A, expresses, as was formerly shown, part of it, and must therefore be true if the whole is true. We have, then, as the result of the reduction, the following syllogism in the third mood of the first figure:
All B is C
Some A is B,
from which it obviously follows, that
Some A is C.
In the same manner, or in a manner on which after these examples it is not necessary to enlarge, every mood of the second, third, and fourth figures may be reduced to some one of the four moods of the first. In other words, every conclusion which can be proved in any of the last three figures, may be proved in the first figure from the same premises, with a slight alteration in the mere manner of expressing them. Every valid ratiocination, therefore, may be stated in the first figure, that is, in one of the following forms:
| Every B is C | No B is C |
| All A is B, | All A is B, |
| Some A is B, | Some A is B, |
| therefore | therefore |
| All A is C. | No A is C. |
| Some A is C. | Some A is not C. |
Or, if more significant symbols are preferred:
To prove an affirmative, the argument must admit of being stated in this form:
All animals are mortal;
All men/Some men/Socrates are animals;
therefore
All men/Some men/Socrates are mortal.
To prove a negative, the argument must be capable of being expressed in this form: