[54e]
and the short sides together as to a center, there is produced from those triangles, six in number, one equilateral triangle.1 And when four equilateral triangles are combined so that three plane angles
1 As in the figure the equilateral triangle ABC is divided into 6 triangles of unequal sides by joining the vertical points A, B, C to the points of bisection of the opposite sides, viz. D, E, F. Then the hypotenuse in each such triangle is double the shortest side (e.g. AO = 2FO). And FAO = 1/3 right angle; while FOA = 2/3 right angle. The “three plane edges” are thus of 60degrees each = 180degrees = “the most obtuse” plane angle; so that the solid angle is one degree less, i.e., 179degrees.
Plato. Plato in Twelve Volumes, Vol. 9 translated by W.R.M. Lamb. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1925.
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