Definitions of Duplication of the cube
The Delian problem, viz. to find by elementary geometry the edge of a cube whose volume is double that of a given cube. Under the conditions the problem is insoluble. It can be solved to any degree of nearness by extracting the cube root of 2. It is a particular case of the problem of inserting two mean proportionals between two given magnitudes ; i. e. given a and b find x and y such that a : x :: x : y and x : y :: y : b.