(κύβου διπλασιασμός/kýbou diplasiasmós according to Eratosthenes, in [1. 88,16]).
I. General
The duplication of the cube ─ besides the division of angles and circles and the squaring of the circle ─ belongs to the three classic problems in Greek mathematics. The challenge is such: to find ─ through the use of geometry ─ for a given cube with a side-length of a (and thus the volume of a 3) the side x of another cube whose volume is twice as big as that of the given cube…