The Book of Mechanics

...turned.

ANOTHER DEFINITION OF THE SAME.

The center of gravity of every solid figure is that point placed within, around which the parts of equal moments consist on every side. For if a plane is drawn through such a center, cutting the figure in any way, it will always divide it into parts of equal weight.

Federico Commandino handed down this last definition, or rather description, in his book on the center of gravity of solids. From these definitions, indeed, the nature and power of the center of gravity shine forth.

A perspective diagram of a rectangular prism. A central point within the volume is labeled 'A'. The prism itself is labeled with 'B' and 'C' at opposite corners.

So that if point A were the center of gravity of the body BC, then according to the opinion of Pappus, if BC were suspended from A, the magnitude BC would remain located in the same arrangement in which it is found; and neither would any parts of that body, as those that are toward BC, be seen to turn about, nor to change their position at all. But if, as it pleased Commandino, A were the center of gravity of the magnitude BCD, and the same were cut through point A in any way along a straight line, as for example through EAF, then the part EBF would be of equal weight to ECDF, even though EBF and ED are unequal magnitudes. For it often happens that in the division of a figure through its center of gravity, it is sometimes divided into equal parts, sometimes into unequal parts: as we shall show in its proper place:

A geometric diagram of a triangle with vertices B, C, and D. A line segment EAF cuts through the triangle, passing through a point 'A' in the interior. The line intersects the triangle's sides at points E and F.

at the end of this first book.

it is always, however, divided into parts of equal weight on either side; yet not established separately and disjointed from one another, and examined as if for equilibrium; as if, for example, if EBF weighed ten pounds, it would be necessary that ED also weighed the same. Indeed, the matter does not stand so, but that they are of equal weight in that position in which they are found; so that neither...