apôÙproxôÙiôÙmateôÙly, 1ã₤:ã₤0ôñ618. The gnomon to this figure is a square ( B ) erected on its longer side, and so on successively (Fig. 252).
Fig. 253. Fig. 254.
In any triangle, as Aristotle tells us, one part is always a gnomon to the other part. For instance, in the triangle ABC (Fig. 253), let us draw CD, so as to make the angle BCD equal to the angle A. Then the part BCD is a triangle similar to the whole triangle ABC, and ADC is a gnomon to BCD. A very elegant case is when the original triangle ABC is an isosceles triangle having one angle of 36ô¯, and the other two angles, therefore, each equal to 72ô¯ (Fig. 254). Then, by bisecting one of the angles of the base, we subdivide the large isosceles triangle into two isosceles triangles, of which one is similar to the whole figure and the other is