Book, Paragraph

 1      I, 5 |    results also by reductio ad impossibile.~It is clear then that a
 2      I, 5 |         i.e. when we prove per impossibile. And it is evident that
 3      I, 6 |      demonstrate this also per impossibile and by exposition. For if
 4      I, 6 |       might be proved also per impossibile, as in the former cases.
 5      I, 6 |        demonstrate it also per impossibile and by exposition, as in
 6      I, 6 |      also without reduction ad impossibile, if one of the Ss be taken
 7      I, 7 |      either ostensively or per impossibile. In both ways the first
 8      I, 7 |         if they are proved per impossibile, because on the assumption
 9      I, 7 |      syllogisms by reductio ad impossibile. In the first figure particular
10      I, 7 |       figure, reducing them ad impossibile, e.g. if A belongs to all
11      I, 15|   reversed, must be proved per impossibile. At the same time it will
12      I, 15|       C, but the syllogism per impossibile establishes the contradictory
13      I, 15|        them will be proved per impossibile, others by the conversion
14      I, 16|      assertoric conclusion per impossibile. For if it were supposed
15      I, 21|       proceed by a reductio ad impossibile. Suppose that B belongs
16      I, 23|       proof is the reductio ad impossibile. Let us speak first of ostensive
17      I, 23|     those which are proved per impossibile, and in general hypothetically.~
18      I, 23|     who effect an argument per impossibile infer syllogistically what
19      I, 23|      found to be reasoning per impossibile, viz. proving something
20      I, 23|   established in reductions ad impossibile by an ostensive syllogism,
21      I, 23|    evident that syllogisms per impossibile also will be made through
22      I, 29|  concluded syllogistically per impossibile by means of the same terms;
23      I, 29|         and what is proved per impossibile may also be proved ostensively,
24      I, 29| requiring proof. The proof per impossibile will always and in all cases
25      I, 29|      and it will be proved per impossibile to belong to no E. Similarly
26      I, 29|   differs from the reductio ad impossibile in this: in the ostensive
27      I, 29|      truth, in the reductio ad impossibile one of the premisses is
28      I, 44|    brought to a conclusion per impossibile. These cannot be analysed
29     II, 11|     results. The syllogism per impossibile is proved when the contradictory
30     II, 11|      also of the reduction per impossibile.~All the problems can be
31     II, 11|     problems can be proved per impossibile in all the figures, excepting
32     II, 11|        in the first figure per impossibile.~But the particular affirmative
33     II, 12|     affirmative are proved per impossibile. But in the middle and the
34     II, 13|   syllogisms which proceed per impossibile the contradictory must be
35     II, 14|           14~Demonstration per impossibile differs from ostensive proof
36     II, 14|  ostensively can be proved per impossibile, and that which is proved
37     II, 14|       that which is proved per impossibile can be proved ostensively,
38     II, 14|    ostensive to reduce them ad impossibile in the terms which have
39     II, 14|  proved in both ways, i.e. per impossibile and ostensively, and it
40     II, 17|      the case of a reductio ad impossibile, to rebut the proposition
41     II, 17|      the case of a reductio ad impossibile, and when the original hypothesis
42     II, 17|        establish a reductio ad impossibile: for Zeno’s false theorem