The pyramid of triangular base has the center of its natural gravity on the line that extends from the middle of the base to the middle of the side opposite that base, placed equally distant from the junction of the base with the said side.

Every solid that has its opposite parts similar and equal to one another will have the center of its natural gravity concentric with the center of its magnitude.

Bodies uniformly non-uniform have in themselves three centers, of which one is the center of magnitude, another is the center of accidental gravity, and the third, least known, is the center of natural gravity.

The center of magnitude of bodies is set in the middle of the length and breadth and thickness of those bodies.

The center of accidental gravity of those bodies is set in the middle of those parts which resist one another while standing in equilibrium.

The center of natural gravity is that which divides a body into two parts equal in weight and in quantity.

With the centers of the accidental gravity of the whole and of the part of a body, the center of the natural gravity of that body will not be found.

The line b c multiplied cubically upon itself makes a cube double the cube of the line f g multiplied cubically upon itself.

Of the wedge a b c the center of its magnitude is the line d e, the center of its accidental gravity is on the line n o, the center of its natural gravity is on the line f g.

The center of the magnitude of the largest pyramid that can be found in that wedge is on the line d e; the center of the accidental gravity of that pyramid is on the line r t; the center of the gravity of such pyramid is on the line h i.

With the knowledge of the center of the natural gravity of the wedge and with the knowledge of the center of the natural gravity of the remainder of the largest pyramid that can be imagined within that wedge, I wish to find the center of the natural gravity of the aforesaid pyramid.

c d e is a pyramid divided from the wedge c d e f; the center of its natural gravity is at a b, and such pyramid c d e is one third of the whole wedge c d e f; g h is the center of the natural gravity of the whole wedge. Therefore, having certainty of that center of the natural gravity of the pyramid d c e and likewise of the center of the natural gravity of the wedge, and knowing that the pyramid is one third of the gravity of the wedge, we shall make the converse proportion of 2 of space against 2 of weight, and divide the space a g into two equal parts, and place one of those spaces at i k, and there we shall have the center of the natural gravity of the pyramid d e f.