APPENDIX H.
Sections of Cube and Tessaract.
There are three kinds of sections of a cube.
1. The sectional plane, which is in all cases supposed to be infinite, can be taken parallel to two of the opposite faces of the cube; that is, parallel to two of the lines meeting in Corvus, and cutting the third.
2. The sectional plane can be taken parallel to one of the lines meeting in Corvus and cutting the other two, or one or both of them produced.
3. The sectional plane can be taken cutting all three lines, or any or all of them produced.
Take the first case, and suppose the plane cuts Dos half-way between Corvus and Cista. Since it does not cut Arctos or Cuspis, or either of them produced, it will cut Via, Iter, and Bolus at the middle point of each; and the figure, determined by the intersection of the Plane and Mala, is a square. If the length of the edge of the cube be taken as the unit, this figure may be expressed thus: Z0 . X0 . Y1⁄2 showing that the Z and X lines from Corvus are not cut at all, and that the Y line is cut at half-a-unit from Corvus.
Sections taken Z0 . X0 . Y1⁄4 and Z0 . X0 . Y1 would also be squares.
Take the second case.