The supporters of democracy, headed by and , the former of whom is said to have been irritated by his exclusion from Pythagoras's brotherhood, roused the populace against them.
The construction of squares requires the immediately preceding theorems in Euclid, and depends upon the parallel postulate.
What proof known at this time showed that it was the right triangle? Of the two philosophers, Parmenides has a much stronger claim to having been the first and the attribution of these discoveries to Pythagoras seems to have possibly originated from a poem.