Swannies Fifth Theorem: A theorem for the **volumes of Cuboids** on a trirectangular tetrahedron. A Cube and three cuboids - a la Swannie. (cuboid, in this case: "like a high box with a square base") On the original square of Swannies Fourth Theorem place a cube and on each of the other squares cuboids with height equal to the length of the side of the cube. Result: The volume of the cuboids add up to that of the cube.

*Definition:* **Proceeding from Swannies Fourth Theorem for squares, the sum of the volumes of cuboids fitted onto the squares on the rectangularfaces of the trirectangular tetrahedron equals the volume of a cube fitted onto the square on the base, provided the cuboids have a height equal in length to**

**the side of the cube.** (Sorry no model yet. Also wish to turn them all into cubes without my calculation trick - but no dice!)

**Below on the left:** Extension of Theorem VI (next page) to a model. At the centre of the model is a trirectangular tetrahedron with an equilateral base. Stuck on the rectangular faces are three regular tetrahedrons/pyramids and below a tetrahedrom/pyramid with the same altitude. The volumes of the smaller pyramids add up to that of the one below.

**Below on the righ:** Just to fill the space. A 'which is more' - red or black?