Another interesting mathematical discovery due to Archytas is that there can be no number which is a geometric mean between two numbers in the ratio (n+1) : n. The most interesting thing about his proof is that it is close to that given by Euclid many years later, and also that it quotes known theorems which would later appear in Euclid 's Elements Book VII.
Teine huvitav matemaatiline avastus tõttu Archytas on, et ei saa olla number, mis on geomeetriline keskmine kahe arvuga suhe (n +1): N. Kõige huvitavam asi tema tõendit, et see on selle lähedal, et antud Euclid aastaid hiljem, ja samuti, et ta tsiteerib tuntud teoreemid, mis hiljem ilmuvad Euclid 's Elements Book VII.