Among us, one cannot find by experiment the true centre of natural gravity, since one would have to make that experiment with the centre of the world; but the centre of accidental gravity is readily found. Pyramidal bodies resolve into pyramids equal among themselves and similar to the largest. Proceed thus: multiply the side a L cubically by itself, and you will have resolved the whole pyramid a K L m. Now, to find in what way the centre of its gravity divides it, which lies at the quarter of its axis toward the base, do thus: multiply cubically three quarters of the pyramid and subtract the resulting sum from the first sum of the whole. The remainder will be the whole sum of the quarter toward the base. Say first, for the whole of the pyramid on the side a L: 4 times 4 makes 16, and you have the surface a L K, which is 16 surface triangles. Then carry out the second cubic multiplication and say: 4 times 16 makes 64, and thus you have resolved the whole great pyramid into small pyramids similar to it, which are 64. Then multiply the three quarters by the line a h, which is 3, and say: 3 times 3 makes 9, and thus you have 9 surface pyramids in a h g. Then say once more: 3 times 9 makes 27, and thus you have resolved the three quarters of the greater pyramid a g h i, which are 27 small pyramidal bodies equal among themselves. Now subtract 27 from 64, that is from the whole greater pyramid, and 37 remains. Now you have 37 equal parts from the centre of gravity toward the base, and 27 from that centre toward the apex of the pyramid. So you can recognize how the centre of accidental gravity lies between 27 and 37, while the centre of natural gravity lies between 32 and 32, so you see how badly they meet together.

1, 16

a, b c S, d e f, g h i, K l m

27, 37

4, 5