STRATEGIES FOR CONCEPTUAL CHANGE - RATIO AND PROPORTION IN CLASSICAL-GREEK MATHEMATICS

...all men begin... by wondering that things are as they are...as they do about...the incommensurability of the diagonal of the square with the side; for it seems wonderful to all who have not yet seen the reas on, that there is a thing which cannot be measured even by the smalles t unit. But we must end in the contrary and, according to the proverb, the better state, as is the case in these instances too when men lear n the cause; for there is nothing which would surprise a geometer so m uch as if the diagonal turned out to be commensurable.