Archimedes' solution of compound ratios of the sides of the square was not as efficient as Archytas' method, which added another dimension to the square in order to better increase its area.
The first recorded attempt at solving this problem was done by Hippocrates, who reduced it to the idea of finding two mean proportionals between two lines. Book VI of Euclid's Elements addresses the problem, as well, relating the squares of the length of the sides of a square. Archimedes' solution of compound ratios of the sides of the square was not as efficient as Archytas' method, which added another dimension to the square in order to better increase its area. FTP, identify this classic problem of mathematics that attempts to find a cube whose ratio to a given cube equals the ratio of two given lines.
The first recorded attempt at solving this problem was done by Hippocrates, who reduced it to the idea of finding two mean proportionals between two lines.
{doubling the cube} (accept equivalents)