Now, such a square can be found in the one whose side is five units in length.
Fig. 23.
In [fig. 23], in the square on AB, there are—
| 9 points interior | 9 |
| 4 at the corners | 1 |
| 4 sides with 3 on each side, considered as 1½ on each side, because belonging equally to two squares | 6 |
The total is 16. There are 9 points in the square on BC.
In the square on AC there are—
| 24 points inside | 24 |
| 4 at the corners | 1 |
or 25 altogether.
Hence we see again that the square on the hypothenuse is equal to the squares on the sides.