Fig. 27 represents a square unsheared. Fig. 28 represents a square sheared. It is not the figure into which the square in [fig. 27] would turn, but the result of shear on some square not drawn. It is a simple slanting placed figure, taken now as we took a simple slanting placed square before. Now, since bodies in this world of shear offer no internal resistance to shearing, and keep their volume when sheared, an inhabitant accustomed to them would not consider that they altered their shape under shear. He would call ACDE as much a square as the square in [fig. 27]. We will call such figures shear squares. Counting the dots in ACDE, we find—
| 2 inside | = | 2 |
| 4 at corners | = | 1 |
or a total of 3.
Now, the square on the side AB has 4 points, that on BC has 1 point. Here the shear square on the hypothenuse has not 5 points but 3; it is not the sum of the squares on the sides, but the difference.
Fig. 29.
This relation always holds. Look at [fig. 29].
Shear square on hypothenuse—
| 7 internal | 7 |
| 4 at corners | 1 |
| 8 |
