> Euclid […] had nothing to say about what fills the gaps between the algebraically (geometrically!) constructible numbers Did he even know those gaps existed?

> Euclid […] had nothing to say about what fills the gaps between the algebraically (geometrically!) constructible numbers Did he even know those gaps existed? Euclid lived around 300BC. The problem of squaring the circle had been proposed around two centuries before that (https://en.wikipedia.org/wiki/Anaxagoras#Mathematics https://en.wikipedia.org/wiki/Anaxagoras#Mathematics), but I don’t think people even considered it to be impossible by that time.