In this sentence from Euler's De Serie Lambertina, I'm having trouble deciphering the meaning (§ 20, p. 40):

At vero quomodo vicissim series Lambertina ad aequationem trinomialem perduci queat, quaestio multo magis ardua videtur; unde operae pretium erit talem analysin exposuisse, quod opus quo facilius succedat, sequens problem praemittam.

The translation I have, as a start, is as follows:

But again in whatever way the Lambert series is able to be followed to the trinomial equation, a far more difficult problem is found; from those efforts it will be valuable to have set forth such an analysis, because the work by which it follows more easily, I may set out in advance the following problem.

This doesn't really work and I've gone through it very carefully but I'm stuck. For example, the use of perduco, which might more accurately mean leads through, I've interpreted as is followed, because saying it is able to be led to the trinomial equation doesn't make much sense. Then there's the second half, and I've experimented with it a lot, but I'm sure it's still off base. It seems like there's an important connection between clauses I'm missing, which makes me wonder if quod is a pronoun instead, but I didn't think that worked.

How could this be better translated?


Note that queat is subjunctive: This is an indirect question, and the governing clause is quaestio multo magis ardua videtur. The context is that Euler previously talked about deriving the Lambert series from the trinomial equation, now – vicissim means “on the other hand, then again, etc.” – he turns to the return journey. I'm not entirely sure how to express perducere in English either; my understanding is that he wants to derive the equation from the series. Let's say:

But how, on the other hand, the Lambert series may be developed into the trinomial equation, seems to be a much more difficult question.

Operae pretium est + infinitive is a standing expression meaning “it is worth it, it is worth the effort.” Quod is indeed a pronoun here modifying opus, “which work.” This is a relative continuation. (1) Quo [hoc opus] facilius succedat – “so that [that work] may succeed the more easily.”

Hence it will be worth the effort to have set forth such an analysis; and in order so that that work will succeed more easily, I would first set out the following problem.

“First set out” is somewhat free for praemittere, you cannot really say “send ahead” in English here (in German you could!).

(1) A relative continuation is that thing in Latin where you don't say: Id cum videret Caesar etc. but rather: Quod cum videret Caesar etc. Romans loved them.

  • I had a feeling an indirect question might be involved here, thanks so much for the helpful answer! – Sam Gallagher Mar 17 at 22:45
  • @Sebastian Koppehel: In "quaestio multo magis ardua videtur", "multo (adjective) magis (adverb)" = "much more(ly)". Is "multo" dative or ablative? Would the double-adverb, "multum magis" = "much(ly) more(ly)" be equally correct? – tony Mar 21 at 11:50
  • @tony Multo is also an adverb, and with comparatives (like here) identical to multum, which would be equally correct. I would guess it was originally the neuter ablative of the substantivized adjective multus (cf. English "by a lot"), but I don't know if that's true. – Sebastian Koppehel Mar 21 at 17:01

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