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The phrase "it remains to" is pretty common in mathematics. It can be used in other contexts as well, but let me restrict my question to the abstract realm for concreteness. For example, this would not be an unusual phrasing of a proof:

To show that f is a continuous linear operator A → B, we need to show that f(a)∈B for every a∈A, that f is linear, and that ||f(a)||≤C||a|| for some C.

Take any a∈A. Now f(a)∈B because…

Linearity is an elementary observation.

It now remains to show the continuity estimate. To this end, let…

How should I phrase "It now remains to show" in Latin? The best thing I could come up with is Nunc remanet, ut demonstremus with an object noun or with an accusativus cum infinitivo. Is this the best way to go? Are there other options I should have in mind?

Bonus question: How did those the mathematicians who wrote in Latin express this?

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The impersonal verb superest is regularly used for 'it remains (to)'/'all that remains is (to)': either superest ut + subjunctive, or quod superest.

superest ut ad extremas partes corporis ueniam, quae articulis inter se conseruntur (Celsus, De medicina 4.29.1)

superest ut promissis deus adnuat tandemque me hac sollicitudine exsoluat. (Pliny the Younger 1.22.11)

quod superest, scribe, quaeso, quam accuratissime (iam enim extrema sunt) quid placeat, quid censeas. (Cicero, Ad Atticum 9.19.4)

So you could say something like:

Superest ut demonstrem...

Quod superest, demonstretur...

  • Thanks! I have to remark that I would never use first person singular in mathematics in any language. Either passive demonstretur or first person plural demonstremus, even if I'm the sole author. But that's just a quirk of mathematical writing. – Joonas Ilmavirta Feb 20 '17 at 7:40
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Why not simply say restat demonstrare, or restat ut demonstremus? It was good enough for Cicero, e.g. restat ut summa negligentia tibi obstiterit. (Quint. XII, end).

In more recent Latin, you might be further reassured by finding yourself in the company of Newton, (e.g. in Princ. Prop. III): Restat igitur ut vis illa, quæ ad Terram spectat, sit reciprocè ut D2; id quod etiam plenius constabit, conferendo hanc vim cum vi gravitatis, ut fit in Propositione sequente.

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