a

b

c

d

n - e - m

o - f

The pyramid turns less than the cube. It happens that the cube gives its turn onto the ground with one and the same impetus along one and the same line, and the pyramid does not, as is seen.

On the 5 regular solids.

Against certain commentators who disparage the ancient inventors, from whom grammar and the sciences were born, and who make themselves champions against those dead inventors; and who, through laziness, have found nothing to make themselves inventors; and how, out of so many books, they continually apply themselves with false arguments to rebuke their own masters.

They say that the earth is tetrahedral, that is cubic, that is a body of 6 faces, and they prove this by saying that among the regular bodies there is no body of less movement nor more stable than the cube. And to fire they attributed the tetrahedron, that is the pyramidal body, which is more mobile (according to these philosophers) than the earth is; therefore they attributed the pyramid to fire and the cube to earth. But if one were to investigate the stability of the pyramidal body and compare it with the cubic body, the cube is beyond comparison more mobile than the pyramid, and this is proved thus. The cube has 6 sides and the regular pyramid has 4, which are set here in the margin at a, b: a is the cube, b is the pyramid. And to settle this proof I shall take one side of the cube and one side of the pyramid, and they will be c, d. I say that the cube c will be more apt to rolling movement than the pyramid d; and let the beginning of such movement be e, f below. I say in effect that, with the base of the cube and the base of the pyramid set upon one and the same plane, the pyramid will turn a third of its quantity to fall upon its next side, and the cube will turn a quarter of its circuit to change onto the next side to make it its base. It follows from these 2 demonstrations that the cube makes a whole turn by changing onto 4 of its sides upon one and the same plane, whereas the triangle, or pyramid, will make its whole turn with three of its sides upon that same plane. The pentagon will rest on all its 5 sides, and thus the more sides it has, the easier is its movement, because it comes closer to the sphere. Therefore I wish to infer that the triangle is of slower motion than the cube, and consequently it was the pyramid, and not the cube, that should have been assigned to earth.