Now take the square AFHG, which is larger than the square on AB. It contains 25 points.
| 16 inside | 16 |
| 16 on the sides, counting as | 8 |
| 4 on the corners | 1 |
making 25 altogether.
If two squares are equal we conclude the sides are equal. Hence, the line AF turning round A would move so that it would after a certain turning coincide with AC.
This is preliminary, but it involves all the mathematical difficulties that will present themselves.
There are two alterations of a body by which its volume is not changed.
One is the one we have just considered, rotation, the other is what is called shear.
Consider a book, or heap of loose pages. They can be slid so that each one slips over the preceding one, and the whole assumes the shape b in [fig. 24].
Fig. 24.