Book, Paragraph

 1      I, 8 |           the particular negative proposition, to which the predicate
 2      I, 11|       however necessarily. If the proposition BC is converted the first
 3      I, 11|           can be made, should the proposition AC be both particular and
 4      I, 11|          whenever the affirmative proposition is necessary, whether universal
 5      I, 11|     animal. But when the negative proposition being particular is necessary,
 6      I, 15|           one premiss is a simple proposition, the other a problematic,
 7      I, 15|   necessarily follows: but if the proposition BC is converted and it is
 8      I, 16|         to the necessary negative proposition: for "not necessarily to
 9      I, 16|           Since then the negative proposition is convertible, B is not
10      I, 16| syllogisms. Whenever the negative proposition is necessary, the conclusion
11      I, 16|         premiss, or the universal proposition in the affirmative syllogism,
12      I, 17|          the negative problematic proposition is not convertible, e.g.
13      I, 17|         consequently the negative proposition is not convertible. Further,
14      I, 17|        some B" are opposed to the proposition "A belongs to all B". Similarly
15      I, 17|           they are opposed to the proposition "A may belong to no B".
16      I, 17|       been said that the negative proposition is not convertible.~This
17      I, 18|         to all C. If the negative proposition is converted, B will belong
18      I, 18|          Whenever the affirmative proposition is assertoric, whether universal
19      I, 18|             but when the negative proposition is assertoric, a conclusion
20      I, 18|      negative, and the assertoric proposition is universal, although no
21      I, 18|       before. But if the negative proposition is assertoric, but particular,
22      I, 19|         Again let the affirmative proposition be necessary, and the other
23      I, 19|           or a negative necessary proposition because no negative premiss
24      I, 19|         be a problematic negative proposition. For if the terms are so
25      I, 19|         For whenever the negative proposition is universal and necessary,
26      I, 19|         and a negative assertoric proposition (the proof proceeds by conversion);
27      I, 19|          but when the affirmative proposition is universal and necessary,
28      I, 19|        also a negative assertoric proposition; but if the affirmative
29      I, 20|          in a negative assertoric proposition, as above. In these also
30      I, 20|        Since then the affirmative proposition is convertible into a particular,
31      I, 20|          the Bs. Similarly if the proposition BC is universal. Likewise
32      I, 20|   universal. Likewise also if the proposition AC is negative, and the
33      I, 20|           AC is negative, and the proposition BC affirmative: for we shall
34      I, 21|           belong to all C. If the proposition BC is converted, we shall
35      I, 21|     problematic. Similarly if the proposition BC is pure, AC problematic;
36      I, 22|         always be drawn; when one proposition is affirmative, the other
37      I, 22|     inferred; but if the negative proposition is necessary both a problematic
38      I, 22|         proof may be given if the proposition BC is necessary, and AC
39      I, 22|    problematic. Again suppose one proposition is affirmative, the other
40      I, 22|         all C. If the affirmative proposition BC is converted, we shall
41      I, 22|           will be a pure negative proposition; for the same kind of proof
42      I, 23|      should be asserted of B, the proposition originally in question will
43      I, 23|         syllogism leads up to the proposition that is substituted for
44      I, 25|           and B. Suppose that the proposition E is inferred from the premisses
45      I, 25|       does not prove the original proposition.~So it is clear that every
46      I, 25| continuous middle terms, e.g. the proposition AB by means of the middle
47      I, 27|           indeed we state it in a proposition: for the other statement
48      I, 28|        universal but a particular proposition, they must look for the
49      I, 28|   establish a particular negative proposition, we must find antecedents
50      I, 28|            for since the negative proposition is convertible, and F is
51      I, 28|          clear then that in every proposition which requires proof we
52      I, 28|    possible at all to establish a proposition from consequents, and it
53      I, 29|      whether a possible or a pure proposition is proved. We must find
54      I, 35|         be no middle term for the proposition AB, although it is demonstrable.
55     II, 5 |          one another. Suppose the proposition AC has been demonstrated
56     II, 5 |        middle term, and again the proposition AB through the conclusion
57     II, 5 |      converted, and similarly the proposition BC through the conclusion
58     II, 5 |          that B belongs to C, the proposition AB must no longer be converted
59     II, 5 |        particular premiss, if the proposition AB is converted as in the
60     II, 6 |           to prove an affirmative proposition in this way, but a negative
61     II, 6 |          this way, but a negative proposition may be proved. An affirmative
62     II, 6 |         be proved. An affirmative proposition is not proved because both
63     II, 6 |      negative) but an affirmative proposition is (as we saw) proved from
64     II, 7 |          be possible to prove the proposition AC, when it is assumed that
65     II, 9 |         belongs to all C, and the proposition AB stands, A will belong
66     II, 9 |       universal. Consequently the proposition AB is not refuted. But if
67     II, 11|    proceed in the same way if the proposition CA has been taken as negative.
68     II, 11|           results if the original proposition CA was negative: for thus
69     II, 11|    syllogism. But if the negative proposition concerns B, nothing is proved.
70     II, 14|          establishes a particular proposition: the hypothesis then must
71     II, 17|         impossibile, to rebut the proposition which was being proved by
72     II, 17|         man has contradicted this proposition he will not say, "False
73     II, 20|   affirmative propositions or one proposition is affirmative, the other
74     II, 27|           is a generally approved proposition: what men know to happen
75     II, 27|        sign means a demonstrative proposition necessary or generally approved:
76     II, 27|         for woman. Now if the one proposition is stated, we have only