Book talk:Euclid/The Elements/Book X

I propose the following nomenclature:


 * If $x \in \Q$, $x$ is called rational (ῥητός).
 * If $x^2 \in \Q$, $x$ is called rationally expressible (ῥητός).
 * If $x \notin \Q$ but $x^2 \in \Q$, $x$ is called singly irrational (ῥητός).
 * If $x \notin \Q$ and $x^2 \notin \Q$, $x$ is called doubly irrational (ἄλογος).

Advantages:


 * 1) It matches with the modern-day definition of rational and irrational numbers.
 * 2) It clearly distinguishes every case.

Drawbacks:


 * 1) The last two names are not from literature.

The above. --kc_kennylau (talk) 10:17, 6 November 2016 (EST)


 * Some part of me likes "squarely irrational" for $x^2 \notin \Q$. &mdash; Lord_Farin (talk) 11:27, 6 November 2016 (EST)
 * What do you suggest for the third one then? --kc_kennylau (talk) 05:10, 7 November 2016 (EST)