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)

If there is no objection, I shall name it linearly irrational. --kc_kennylau (talk) 05:05, 10 November 2016 (EST)


 * as long as we make it blindingly clear that we have made up this bodgey nomenclature off the top of our heads. --prime mover (talk) 07:31, 10 November 2016 (EST)


 * Can I make a template such as  to state in every page using this nomenclature that this bodgey nomenclature is made off the top of our heads? --kc_kennylau (talk) 07:38, 10 November 2016 (EST)


 * Actually, that's a brilliant idea. (Might just be the wine talking, coming to the end of a week-long business trip ending in the de rigueur knees-up.) feel free to craft one -- more than once have we found that the accepted terminology is lacking. --prime mover (talk) 16:21, 10 November 2016 (EST)

Next big question: can anyone think of a generic section title that such a template can be placed? I dislike "notes" for all sorts of reasons. --prime mover (talk) 15:01, 11 November 2016 (EST)


 * Disclaimer. --kc_kennylau (talk) 20:04, 11 November 2016 (EST)


 * Thinking of more like "origin of name", or "non-standard name", or something which in some way describes exactly what the section contains. --prime mover (talk) 03:14, 12 November 2016 (EST)


 * Neologism, just like the name of the template. --kc_kennylau (talk) 06:49, 12 November 2016 (EST)