I understand that before Hippasus of Metapontum proved that the square root of 2 is an irrational number, it was commonly assumed that, given two line segments, it would be possible to find a third line segment whose length divides evenly into the two, i.e. commensurability.
However why did the Greeks assume commensurability? What was the proof, reasonsing or evidence that made them think in this way? Or was it only an assumption without any proper justification?
Also what made Hippasus doubt this assumption? What motivated him to prove this assumption was wrong?