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In mathematics people say that

Evaluate f at x

What word in Latin means "evaluate"? The construction ex-valor-are -> evaloro, -are, -avi, -atum seems to be an analogue but I am not sure if this makes sense, and I don't see it used anywhere.

Evalora f in x

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Good question! First, valor seems to be indeed a good word for "value" in the sense of mathematics and computer science. It appears in Newton's Philosophiae naturalis principia mathematica and is also used by Gauss.

However, I found no hits for a verb containing -valor-. We may need to coin a new verb; I will discuss the reasons for this at the end. The easiest way out is to borrow the English word, since evaluare fits Latin very well. But this doesn't feel quite right to me, as the originally Latin word valor has been changed after borrowing to French. A similar verb can be derived within Latin.

No Romance language seems to use anything with valor for this verb, but the verbs are related. Italian seems to be valutare, Spanish evaluar, and French évaluer, for example. The simplest Latin verb seems to be valorare, and this is my first suggestion. (The word valor itself comes from valere, but for this purpose I think it is best to derive from valor instead of the underlying verb. The noun valor in this use is abstracted from the meaning of valere.)

It is possible to and a prefix. Since the verb starts with V, it should be e- instead of ex-. This prefix can be used to emphasize that the action is carried out completely (cf. efficere or ebibere), and this sense is appropriate — although not strictly necessary. As the Romance examples above show, the prefix may or may not be present in daughter languages. If such a prefix is used, then the natural choice is evalorare.

The different options have different pros and cons. For anyone who has studied mathematics or programming in English, evaluare is easy to understand without much thought. However, it does sound somewhat non-Latin. The most Latin option to my ear is valorare, but it is further away from other languages. The middle ground between these is evalorare. My suggestion is valorare, but there is no canonical correct choice as far as I know. Your suggestion of evalorare sounds legitimate, too.

I have found no attestations for these three options. But this is not really surprising; the abstraction level of evaluation (as opposed to using simply the word "value" in some way) seems to have arisen only after Latin fell out of fashion in science. I would be thrilled to see examples, but there might not be any. When it comes to contemporary use, there is no council to decide on the correct terminology, and if there is too little precedent to establish a rule, you are free to choose anything reasonable.

Lastly, let me point out that my purpose was to find a verb that would be comfortable to use for a modern scientist who happens to know Latin. If I were to write lecture notes on functional analysis and distribution theory in Latin and wanted to define an evaluation functional, I would pick one of these three verbs to evaluate with. Any kind of elegance or classical precedent, while great, is secondary. For a different perspective, you'll have to ask someone else.

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  • Non sure, but I suspect you need a workaround to say both evaluate and function in proper scientific Latin. A quick lookup in the principia gave lots of equatio, inveniri, computatio, etc. in places evaluate and function would have fitted. – Rafael Feb 27 '18 at 12:46
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    @Rafael That would depend on your definition of proper scientific Latin. Perhaps I should have made it clearer in the answer (I'll edit), but I'm aiming for something that would feel natural to a modern scientist who happens to know Latin, leaving classical or otherwise high style as a secondary goal. Newton's language might feel a little awkward in today's use. Gauss doesn't seem to shy away from functio, so I wouldn't either. – Joonas Ilmavirta Feb 27 '18 at 12:58
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    Allright. By scientific Latin I meant broadly which was used in science at the time it was the language of science. I'm no expert in it at all, and spoke out of intuition only. I'm actually relieved to know Gauss used functio! – Rafael Feb 27 '18 at 13:37
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    @Joonas Ilmavirta Looking at it slightly differently, I would use something like vim or significationem with subducere, 'drawing out the force / significance'. Might not this better represent the meaning — and in classical Latin? – Tom Cotton Feb 27 '18 at 15:36
  • @TomCotton Vim subducere sounds like a good classical way to put it. However, I would not use such a phrase in technical use when a derivative like valorare is available. The problem is partly the ambiguity of terms, since vis and subducere could mean so many other things. It might have the correct meaning, but perhaps not the convenience of use. The best translation of "evaluate" depends very heavily on the exact goal, much more than with everyday language. Cicero might indeed translate "value" as vis, but I would not. I admit to being strongly biased as a modern mathematician. – Joonas Ilmavirta Feb 27 '18 at 15:47

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