with every swan, black with no swan, and black with a certain animal. Hence if A and B are assumed present with every C, B C will be wholly true, but A C wholly false, and the conclusion will be true. Similarly, again, if A C is assumed true, for the demonstration will be through the same terms. Again, if one is wholly true, but the other partly false, since B may be with every C, but A with a certain C, also A with a certain B, as biped is with every man, but beauty not with every man, and beauty with a certain biped. If then A and B are assumed present with the whole of C, the proposition B C is wholly true, but A C partly false, the conclusion will also be true. Likewise, if A C is assumed true, and B C partly false, for by transposition of the same terms, there will be a demonstration. Again, if one is negative and the other affirmative, for since B may possibly be with the whole of C, but A with a certain C, when the terms are thus, A will not be with every B. If B is assumed present with the whole of C, but A with none, the negative is partly false, but the other wholly true, the conclusion will also be true. Moreover, since it has been shown that A being present with no C, but B with a certain C, it is possible that A may not be with a certain B, it is clear that when A C is wholly true, but B C partly false, the conclusion may be true, for if A is assumed present with no C, but B with every C, A C is wholly true, but B C partly false.
Nevertheless, it appears that there will be altogether a true conclusion by false premises, in the case also of particular syllogisms. For the same terms must be taken, as when the premises were universal, namely, in affirmative propositions, affirmative terms, but in negative propositions, negative terms, for there is no difference whether when a thing consists with no individual, we assume it present with every, or being present with a certain one, we assume it present uni-
