11 The Diagony of an octaedrum is of double power to the side.
As is manifest by the [9 e xij].
And
12 If the quadrate of the side of an octaedrum, be
doubled, the side of the double shall be the diagony.
As in the figure following, the side is 6. The quadrate is 36. the double is 72. whose side 8.8/17, is the diagony.
And from hence doth arise the geodesy of the octaedrum. For the semidiagony is 4.4/17. whose quadrate is 17.171/289. And the quadrate of 6, the side of the equilater triangle, being of treble power to the ray, by the [12 e, xviij]. is 36. And the side of 12. the third part 3.3/7 is the ray of the circle. Wherefore 8.8/17. that is 5.21/289. is the quadrate of the perpendicular, whose side 2.1/5 is the height of the same perpendicular: whose third part againe 11/25. multiplied by 15.18/31. the triangular base doe make 11.66/155 for one of the eight pyramides: Therefore the same 11.66/155 multiplied by eight, shall make 91.63/155 for the whole octoedrum.
13 An Icosaedrum is an ordinate polyedrum comprehended of 20 triangles 29 d xj.
