Book, Paragraph

 1      I,  5 |          though it could have been proved of them all by a single
 2      I,  5 |         another, this property was proved of each of them separately.
 3      I,  6 |        middle through which it was proved may yet quite easily be
 4      I,  7 |         demonstration: (1) what is proved, the conclusion-an attribute
 5      I,  7 |           That is why it cannot be proved by geometry that opposites
 6      I,  9 |      arithmetic. Such theorems are proved by the same middle terms
 7      I,  10|       existence of which cannot be proved. As regards both these primary
 8      I,  10|          assumed; but it has to be proved of the remainder, the attributes.
 9      I,  12|           e.g. one major A, may be proved of two minors, C and E.
10      I,  21|         negative conclusion can be proved in all three figures. In
11      I,  21|          In the first figure it is proved thus: no B is A, all C is
12      I,  21|             Next, since D is to be proved not to belong to C, then
13      I,  21|         premiss, i.e. C-B, will be proved either in the same figure
14      I,  21|         this premiss again will be proved by a similar prosyllogism.
15      I,  23|         Yet if the attribute to be proved common to two subjects is
16      I,  23|            A. Then if it has to be proved that no C is A, a middle
17      I,  24|            matter: if a subject is proved to possess qua triangle
18      I,  24|     superior. Thus, if A had to be proved to inhere in D, and the
19      I,  25|         first proof); since A-E is proved through A-D, and the ground
20      I,  25|          inferior.~(2) It has been proved that no conclusion follows
21      I,  25|           through which a truth is proved is a better known and more
22      I,  25|            negative proposition is proved through the affirmative
23      I,  28|        verified if the conclusions proved by means of them fall within
24      I,  31|         regard to connexions to be proved which are referred for their
25      I,  32|    premisses any conclusion may be proved, nor yet admitted that basic
26     II,  3 |            all triangles have been proved to possess angles equal
27     II,  3 |            this attribute has been proved to attach to isosceles;
28     II,  6 |      doubts whether the conclusion proved is the definable form that
29     II,  8 |          term, and, the conclusion proved being universal and affirmative,
30     II,  12| conclusions and premisses-has been proved in our early chapters, and
31     II,  15|        e.g. a whole group might be proved through "reciprocal replacement"-
32     II,  15|      rainbow: the connexions to be proved which these questions embody
33     II,  16|        that if the connexion to be proved is always universal and