Galileo describes how to use these lines to find the corresponding side length in a similar solid where the solid has a given volume ratio to the original, how to determine the volume ratio of two similar solids given the lengths of a pair of corresponding sides, how to find the side lengths of a similar solid that has the combined volume of a set of other similar solids, how to find the cube root of a number, how to find the two values intermediate between two numbers p and q such that n_1 = r p, n_2 = r^2 p and q = r^3 p for a given scaling factor r, and how to find the side of a cube that has the same volume as a rectangular cuboid (square-cornered box).
