The sentence from Euler's De Serie Lambertina I'm working on now has the following form:

Praesenti autem forma hanc seriem exhibere est visum, ut litterae A et B inter se permutabiles evaderent, ita ut, quicquid de altera fuerit observatum, etiam de altera valeat.

I've translated this (to the best of my ability) as:

With the present form, however, this series is seen to show, as the letters A and B may come out interchangeable between themselves, in such a way that, whatever may be observed from one, may also be valid for the other.

Is "est visum" the perfect passive? Then, if that clause is correct, it seems like it's left dangling. Then, why "evaderent" (evado, to avoid, keep away from, come out/go out) and how should such a phrase as "inter se [adjective] evaderent" be translated?


Est visum is perfect passive but impersonal (the actual subject being the infinitive exhibere). It means something like 'it has seemed best' or 'it has seemed proper.' Hanc seriem is the direct object of exhibere.

When the verb evadere has a predicate noun or adjective, as here (permutabiles), it means 'To end up, emerge, turn out (as)' (definition 8a in Oxford Latin dictionary). Inter se shows reciprocity. With verbs, it means 'each other,' as in inter se amant, 'they love each other.' Here, it's dependent on the adjective permutabiles; the letters A and B are 'interchangeable with each other,' 'mutually interchangeable,' or simply 'interchangeable.'

In the original version of this answer, I though the first ut meant 'how'; but I now think ut...evaderent may be a purpose clause instead. More context would likely help pin this down. In any case, since evaderent is subjunctive, it doesn't mean 'as.'

So I'd translate as something like:

It seemed best to show this series in the present form so that the letters A and B might turn out to be interchangeable with each other in such a way that, whatever has been observed about one of the two, is also valid about the other.

  • Thanks much for this quick response. I think this would be a reasonable translation then (with some free rearranging): "It seemed proper however to provide this series with the present form, as the letters A and B may be interchanged, in such a way that whatever may be observed from one may also be valid for the other." Does that match up? From context I can say this is what Euler had in mind, but the specifics might be off. – Sam Gallagher Feb 8 at 19:05
  • @SamGallagher, See my updated answer for a rough translation and a correction about one point. – cnread Feb 8 at 19:19

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