In mathematics, the following phrase is common:

By Theorem 5.6, the function is differentiable.

How do I say 'by' in Latin? I don't think 'ab' is appropriate to use here. One way is to put 'Theorem' into ablative case:

Theoremate 5.6, functio est differentiabilis.

1 Answer 1


I suggest using propter with accusative. With your example:

Propter theorema 5.6 functio est differentiabilis.

This Latin mathematical text by Gauss has several instances of propter, for example:

propter [...] seriei convergentiam — by convergence of the [...] series
propter has rationes — for these reasons
propter [1] — by equation [1]

The word theorema appears several times, but never in the sense of "by theorem", and lemma only appears as a title for two auxiliary results. However, based on modern mathematical language and these examples from Gauss, it makes sense to me say propter lemma/theorema.

It might also be worthwhile to take a look at propter in L&S, especially II.B.1.

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