The Static surface of the Chess-board being a square, its least division is into two great right angled triangles having a common hypothenuse.
The Dynamic surface being the quadrant of a circle, its least division also is into two great sections, one of which is a right angled triangle and the other a semi-circle.
Comparing the two surfaces of the Chess-board thus divided, it will be seen that these three great right angled triangles are equal, each containing thirty-six points; and having for their common vertices, the points KR1, QR1 and R8.
Furthermore, it will be seen that the hypothenuse common to these triangles, also is the chord of that semi-circle which appertains to the Dynamic surface.
Again, it will be perceived that this semi-circle, like the three right angled triangles, is composed of thirty-six points, and consequently that all of the four sub-divisions of the Static and Dynamic surfaces of the Chess-board are equal.
Thus it obviously follows, that:
- 1. The great central diagonal, always is one side of each of the four chief geometric figures into which the Chess board is divided; that:
- 2. It mathematically perfects each of these figures and harmonizes each to all, and that:
- 3. By means of it each figure becomes possessed of eight more points than it otherwise would contain.
Hence, the following is self-evident:
PRINCIPLE
That Chessic army which can possess itself of the great central diagonal, thereby acquires the larger number of points upon which to act and consequently greater facilities for movement; and conversely: