Book, Paragraph

 1      I, 7 |      impossibile, because on the assumption of the false statement the
 2      I, 15|         false and not impossible assumption is made, the consequence
 3      I, 15|           the consequence of the assumption will also be false and not
 4      I, 15|        for all C. For though the assumption we made is false and not
 5      I, 15|      possible for all C. But the assumption was made that A is not possible
 6      I, 15|         the contradictory of the assumption which was made: for it was
 7      I, 17|         D, he would make a false assumption: for it does belong to all
 8      I, 23|      impossible results from the assumption of its contradictory; e.g.
 9      I, 24|           without the additional assumption that every angle of a segment
10      I, 44|         of what follows from the assumption that the diagonal is commensurate,
11     II, 8 |          are refuted: but if the assumption is that A belongs to some
12     II, 15|   contradiction by an additional assumption, assuming, e.g., that every
13     II, 17| syllogism does not depend on the assumption laid down. For we use the
14     II, 17|    ostensive proofs: since if an assumption is refuted, a syllogism
15     II, 17|         of the irrelevance of an assumption to a conclusion which is
16     II, 17|         at all with the original assumption. Another case is where the
17     II, 17|         result on account of the assumption. Or perhaps even so it may
18     II, 17|        results whether the first assumption is suppressed or not, it
19     II, 17|        to be independent of that assumption. Or perhaps we ought not
20     II, 17|     results independently of the assumption, in the sense that if something
21     II, 17|         mean that when the first assumption is eliminated, the same
22     II, 17|      parallels meet, both on the assumption that the interior angle
23     II, 17|          the exterior and on the assumption that a triangle contains