Mycerinus and Cephren, born, as one may say, of those two noble triangles 3, 4, 5, and 20, 21, 29, exhibit in their lineal developments ratios so nearly perfect that, for all practical purposes, they may be called correct.
| Thus—Mycerinus, | [3]20² | + | 25² | = | 1025, | and | 32² | = | 1024. |
| and Cephren, | [4]80² | + | 105² | = | 17425, | and | 132² | = | 17424. |
| or | [5]400² | + | 431² | = | 345761, | and | 588² | = | 345744. |
See diagrams, Figures 11 to 14 inclusive.
In the Pyramid Cheops, altitude is very nearly a mean proportional between apothem and half base. Apothem being 34, and half base 21, then altitude would be √(34²-21²) = √715 = 26·7394839, and—
21 : 26·7394839 :: 26·7394839 : 34, nearly.
Here, of course, the same difference comes in as occurred in considering the assumption of Herodotus, viz., the difference between √715 and √714; because if the altitude were √714, then would it be exactly a mean proportional between the half base and the apothem; (thus, 21 : 26·72077 :: 26·72077 :: 34.)
[3] Half base to altitude.
[4] Half base to altitude.
[5] Half diagonal of base to altitude.