The New Thoughts of Galileo

of gravity at the end of his Book: but there is, it seems to me, little to say on this subject, after what Archimedes, Commandino, Luca Valerio, Stevin, and a few others have demonstrated about it. This is why I only put here what an excellent Geometer has remarked upon it.

Let A B C therefore be a curved line, of
A geometric diagram showing a curve A B C inscribed within a larger triangle E A C. A vertical line B D serves as the axis of symmetry, extending from the curve's peak B down to its base D on line A C. Two horizontal dashed lines, I F and H G, connect points on the curve to the central axis. A point M is marked on the lower part of the axis B D.
such a nature that the segments of its diameter, for example, B F and F G, have between them the same proportion as the cubes of the lines applied in order to these segments, namely I F and H G, and that B D be the axis, or the diameter of the figure comprised by this curved line A B C and the straight line A C.

If one divides this diameter B D by the point M, in such a way that the line B M