The New Thoughts of Galileo

or to line M D, as four to three, point M will be the center of gravity of this figure. And in the curve, where the segments of the diameters are to each other as the squares of the squares of the ordinates, one must make B M to M D as five to four. In the following one, where these segments are as the sursolids original: "sur-solides", referring to the fifth power or higher of a variable of the ordinates, one must make B M to M D as six to five. And as seven to six in the one where these segments are as the squares of the cube of the ordinates. And as eight to seven in the following one, and so on for others to infinity, to find their centers of gravity. Certainly, those who take pleasure in relating to harmony all that is encountered in art and in nature have very beautiful remarks here, since the center of the squared parabola divides the axis into two parts, which are as three to two. The parts of that of the cubic are as four to three: of the square squared, as five to four, and those of the sursolid, as six to five, which give the ratios of all simple consonances.

Besides that, assuming that B D falls