Book, Paragraph

 1      I,  1 |      of any subject, and that "triangle" means so and so; as regards "
 2      I,  1 |       that the angles of every triangle are equal to two right angles;
 3      I,  1 |        the semicircle" to be a triangle. For some things (viz. the
 4      I,  1 |     know the existence of this triangle, how could he know without
 5      I,  1 | premiss, viz. not merely every triangle or number which they know
 6      I,  1 |        any and every number or triangle without reservation. For
 7      I,  4 |      e.g. line thus belongs to triangle, point to line; for the
 8      I,  4 |        being or "substance" of triangle and line is composed of
 9      I,  4 |       in the formulae defining triangle and line): (2) such that,
10      I,  4 |    belong to line as such; and triangle as such has two right angles,
11      I,  4 |      other hand, any isosceles triangle has its angles equal to
12      I,  4 |    right angles, yet isosceles triangle is not the primary subject
13      I,  4 |  subject of this attribute but triangle is prior. So whatever can
14      I,  5 |        isosceles were the only triangle, it would be thought to
15      I,  5 |      one prove of each kind of triangle that its angles are equal
16      I,  5 |     except sophistically, that triangle has its angles equal to
17      I,  5 |     nor does one yet know that triangle has this property commensurately
18      I,  5 |   there is no other species of triangle but these. For one does
19      I,  5 |     For one does not know that triangle as such has this property,
20      I,  5 |      unqualified knowledge? If triangle be identical in essence
21      I,  5 |     belongs to equilateral qua triangle; then our knowledge fails
22      I,  5 |      has been demonstrated qua triangle or qua isosceles? What is
23      I,  5 |   angles of a brazen isosceles triangle are equal to two right angles:
24      I,  5 |        is the first?" If it is triangle, it will be in virtue of
25      I,  5 |        it will be in virtue of triangle that the attribute belongs
26      I,  5 |    which it is predicable, and triangle is the subject to which
27      I,  24|        isosceles but only that triangle is x—whereas particular
28      I,  24|         that, for instance, of triangle or of figure or number,
29      I,  24|      not qua isosceles but qua triangle, he who knows that isosceles
30      I,  24|  degree than he who knows that triangle has that attribute. To sum
31      I,  24|       is proved to possess qua triangle an attribute which it does
32      I,  24|        not in fact possess qua triangle, that is not demonstration:
33      I,  24|      if it does possess it qua triangle the rule applies that the
34      I,  24|       possess it. Since, then, triangle is the wider term, and there
35      I,  24| triangles, it is isosceles qua triangle and not triangle qua isosceles
36      I,  24| isosceles qua triangle and not triangle qua isosceles which has
37      I,  24|        answer "Because it is a triangle, and a triangle has it because
38      I,  24|        it is a triangle, and a triangle has it because a triangle
39      I,  24|      triangle has it because a triangle is a rectilinear figure."
40      I,  24|        that the isosceles is a triangle; but to grasp this posterior
41      I,  31|    possible to perceive that a triangle has its angles equal to
42     II,  2 |        moon or earth or sun or triangle; by that which a subject
43     II,  3 |     are definable, e.g. "every triangle has its angles equal to
44     II,  7 |        the meaning of the word triangle, but that it is possessed
45     II,  7 |     defining essential nature? Triangle? In that case a man will
46     II,  8 |        it make the angles of a triangle equal or not equal to two
47     II,  10|         When we are aware that triangle exists, we inquire the reason
48     II,  17|        an attribute wider than triangle or are), but it is coextensive