Finding commensurate values of squares, cubes, triangles etc. or the sum of a given number of squares which is itself a square; or a certain number of squares etc. which are in arithmetical progression. The following examples will give some idea of the theory:
1. To find two whole numbers, the sum of whose squares is a square;
2. To find three square numbers which are in arithmetical progression;
3. To find a number from which two given squares being severally subtracted, each of the remainders is a square.
Diophantus was an Alexandrian Greek (5th cent. A.D.)