Book, Paragraph

 1      I, 23|       because odd numbers are equal to evens if it is supposed
 2      I, 23|     that odd numbers come out equal to evens, and one proves
 3      I, 24|     an isosceles triangle are equal. Suppose the lines A and
 4      I, 24|   assume that the angle AC is equal to the angle BD, without
 5      I, 24|     angles of semicircles are equal; and again if one should
 6      I, 24|    assume that the angle C is equal to the angle D, without
 7      I, 24|   every angle of a segment is equal to every other angle of
 8      I, 24|       should assume that when equal angles are taken from the
 9      I, 24|  angles, which are themselves equal, the remainders E and F
10      I, 24|    the remainders E and F are equal, he will beg the thing to
11      I, 24|     equals the remainders are equal.~It is clear then that in
12      I, 25|     and the premisses will be equal in number to the relations
13      I, 36| term-either the dative, e.g. "equal to this", or the genitive,
14      I, 44|     that then odd numbers are equal to evens.~Many other arguments
15      I, 46|        the same as "not to be equal": for there is something
16      I, 46|      not everything is either equal or unequal, but everything
17      I, 46|    unequal, but everything is equal or is not equal. Further
18      I, 46| everything is equal or is not equal. Further the expressions "
19      I, 46| arrangement. Let A stand for "equal", B for "not equal", C for "
20      I, 46|       for "equal", B for "not equal", C for "unequal", D for "
21     II, 21|       triangle has its angles equal to two right angles" is
22     II, 21|      e.g. that the angles are equal to two right angles, if
23     II, 25|       that the circle is made equal to a rectilinear figure