14. Also, any two universal propositions, of which the terms of the one (that is, the subject and predicate) are to the terms of the other, and their order inverted, as these, every man is a living creature, and every thing that is not a living-creature is not a man, are equipollent. For seeing every man is a living creature is a true proposition, the name living creature contains the name man; but they are both positive names, and therefore (by the last article of the precedent chapter) the negative name not man, contains the negative name not living-creature; wherefore every thing that is not a living-creature, is not a man, is a true proposition. Likewise these, no man is a tree, no tree is a man, are equipollent. For if it be true that tree is not the name of any man, then no one thing can be signified by the two names man and tree, wherefore no tree is a man is a true proposition. Also to this, whatsoever is not a living-creature is not a man, where both the terms are negative, this other proposition is equipollent, only a living creature is a man.
Negative propositions are the same, whether the negation be before or after the copula.
15. Fourthly, negative propositions, whether the particle of negation be set after the copula as some nations do, or before it, as it is in Latin and Greek, if the terms be the same, are equipollent: as, for example, man is not a tree, and, man is not-a-tree, are equipollent, though Aristotle deny it. Also these, every man is not a tree, and no man is a tree, are equipollent, and that so manifestly, as it needs not be demonstrated.
Particular propositions simply converted, are equipollent.
16. Lastly, all particular propositions that have their terms inverted, as these, some man is blind, some blind thing is a man, are equipollent; for either of the two names, is the name of some one and the same man; and therefore in which soever of the two orders they be connected, they signify the same truth.
What are subaltern, contrary, subcontrary, and contradictory propositions.
17. Of propositions that have the same terms, and are placed in the same order, but varied either by quantity or quality, some are called subaltern, others contrary, others subcontrary, and others contradictory.
Subaltern, are universal and particular propositions of the same quality; as, every man is a living creature, some man is a living creature; or, no man is wise, some man is not wise. Of these, if the universal be true, the particular will be true also.
Contrary, are universal propositions of different quality; as, every man is happy, no man is happy. And of these, if one be true, the other is false: also, they may both be false, as in the example given.
Subcontrary, are particular propositions of different quality; as, some man is learned, some man is not learned; which cannot be both false, but they may be both true.