, 6
, etc., being represented by the formula
(Liddel and Scott’s Lexicon). Each side of the triangle of course contains an equal number of units, the sum of which amounts to the number.
[1040] This number is called equality, because it is composed of eight numbers, an even number; as fifty-six is called inequality, because it is composed of seven numbers, an odd number.
[1041] The clause within brackets has been suggested by Hervetus to complete the sense.
[1042] That is, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 120; and 1 + 3 = 4 + 5 = 9 + 7 = 16 + 9 = 25 + 11 = 36 + 13 = 49 + 15 = 64, giving us the numbers 4, 9, 16, 25, 36, 49, 64, the squares of 2, 3, 4, 5, 6, 7, 8.
[1043] ἑτερομήκεις, the product of two unequal factors, i.e. 2 + 4 + 6 + 8 + 10 + 12 + 14 = 56; and 2 + 4 = 6 = 3 × 2, 6 + 4 = 10 = 5 × 2, and so on.