# What does "Solutiones in medium affere visum est praeparatio ad solutionem." mean?

I am reading an article by Euler (Solutio problematis difficillimi a Fermatio propositi, Enestrom number 167) and I have trouble understanding the following sentence (§ 2, p. 50):

Huius ergo problematis sequentes, quas mihi quidem elicere contigit, solutiones in medium afferre visum est, Praeparatio ad solutionem.

I came up with

The following solutions to this problem that I had the pleasure of obtaining [] preparation to the solution.

But "in medium affere visum est" really confuses me.

• Praeparatio ad solutionem is the heading of the next paragraph and not a part of this sentence. For visum est, see the very end of the L & S entry. Oct 15, 2022 at 11:26
• I thought like you at first, but the fact that it was placed after a comma confused me. I will look at your link, thanks
– user11281
Oct 15, 2022 at 11:29
• @SebastianKoppehel Any idea why there is a comma after "visum est"? Your reading is the only one that makes sense, but I don't see how the punctuation supports it. Oct 16, 2022 at 20:42
• @brianpck I do not know why the comma is there, but I gather it must be a typographical mistake. There is no comma, but the expected full stop instead, in the Opera Omnia, see here (published Lipsiae & Berolini by Latin's own B. G. Teubner, go figure!). Oct 17, 2022 at 20:03
• @SebastianKoppehel Good catch!
– user11281
Oct 17, 2022 at 20:06

## 3 Answers

As Sebastian noted in a comment, praeparatio ad solutionem doesn't fit syntactically with what precedes and should be read separately. (It's an open question for me, though, why it is only separated by a comma.)

Here's a literal translation of the Latin:

Therefore, it seemed right to publish the following solutions, which I happened to ascertain, of this problem. Preparation for the solution:

• Tyler's answer has a good explanation of in medium afferre and visum est (cf. Greek δοκεῖ). You'll often see in medium proferre used to mean "make known to the public," as for instance in Cicero, In Verrem:

Vnius etiam urbis omnium pulcherrimae atque ornatissimae, Syracusarum, direptionem commemorabo et in medium proferam, iudices, ut aliquando totam huius generis orationem concludam atque definiam.

• I have opted not to translate quidem: it often means "indeed," but that's a bit too heavy-handed as a translation here. It just gives some color to the relative clause, but I don't read it as having any implication about "solving further problems."

Two corrections on the other offered translation:

• The genitive huius problematis goes with solutiones, not ergo. Though there is an archaic usage of ergo + gen., the meaning is more like "because of" or "on account of," which wouldn't be appropriate here. I wrote "of this problem" to make this obvious, but a more natural way to say this in English would be "to this problem."
• elicio means to "draw out" or "entice" or (in this case) "ascertain." The antecedent of quas (and thus the object of elicere) is solutiones, not problematis.
• Thanks for this answer, I am rather convinced but I will wait if there are other objections
– user11281
Oct 16, 2022 at 21:38
• Obviously I disagree with this translation. For one thing, ergo does not mean "therefore" and that is clear from the context even disregarding the grammar. The context is that Euler writes (paraphrasing) "Fermat posed the following difficult problem: the triangle etc etc" then he says: "Huius ergo problematis" which means "Concerning this problem..." It makes no sense in the context to render ergo as "Therefore". Oct 17, 2022 at 14:14
• @TylerDurden You're missing the context of the intro. Euler just finished saying that a certain class of problems (Diophantine equations, as far as I can tell from my limited mathematical knowledge) has been neglected by analysis, despite enormous progress in other areas. "Therefore I thought it would be good to publish my solutions" to those problems. Oct 17, 2022 at 15:32
• I'm curious what else you disagree with: the only other substantial difference in my translation is the object of elicere, which is just an obvious (pardon me--but the context of our earlier interactions forces me to be blunt) point of syntax. Oct 17, 2022 at 15:34
• Ok, I will accept that as a reasonable interpretation. Oct 17, 2022 at 15:59

The sentence ought to be:

Huius ergo problematis sequentes, quas mihi quidem elicere contigit, solutiones in medium afferre visum est.

And the comma is likely a typographical error (although having a heading follow as part of a sentence does happen in Euler's writing, if it doesn't make grammatical sense then I'd ignore it).

Rearranging slightly (Euler tends to separate words that go together, e.g. with a clause in between, or an adverb, etc):

Huius ergo problematis sequentes solutiones, quas mihi quidem elicere contigit, in medium afferre visum est.

Some notes about usage here:

• contingere = accidere, fieri, evenire
• elicere = educere, extrahere
• visum est = convenit, oportet
• in medium = pro omnes

Thus:

Therefore, the following solutions of this problem, which it happened upon me to elicit/obtain/ascertain, seemed appropriate to share.

Or more idiomatically,

It therefore seemed appropriate to share the following solutions of this problem, which happened to occur to me.

It means: "Concerning this problem, which it perforce fell to me to unravel, it is appropriate to report the following solutions publicly; Preparation for the solution."

Comments:

(1) I bolded the part of the Latin that you are asking about in particular.

(2) Sequentes does not modify problematis. It is either nominative or accusative and in this context either just means "the next things", but in English we can render it like an adverb, "Next". Euler is using this word to introduce what is coming next, the next things he will be discussing. Or, as Kingshorsey comments below, it might modify solutiones, "the following solutions".

(3) Ergo can act as a conjunction or a preposition. In this context, when it is used with the genitive, it is more like a preposition.

(4) Quidem has a context-sensitive meaning that generally intensifies whatever is being discussed so it is often translated as "indeed". Here, in a mathematical context, the implication is that he was required for some reason to solve these particular problems I guess as a precondition for solving some other problems.

(5) in medium refers to what is in the community or what is public; visum est means what is seemly or right or appropriate

(6) I am not exactly sure why solutiones is plural. The full context involves I believe a single solution to the problem, so why Fermat is using the plural is not clear to me.

• Sequentes is accusative, modifying solutiones. [sequentes … solutiones affere] visum est. Oct 16, 2022 at 19:58
• @Kingshorsey I would be surprised if that were true for two reasons. First of all, saying "Concerning these problems, the next solutions" does not make sense. Secondly, if sequentes was intended to modify solutiones, it would be normal to put it in the same clause with solutiones. If you have a different translation where you can make your idea work, I suggest you create an answer showing how that could make sense. Oct 16, 2022 at 20:00
• @Kingshorsey I suppose you could have "to report the following solutions publicly", but in that case, as I said, I would expect sequentes to be in the same clause with solutiones. There is a certain amount of ambiguity because sequentes can be either nominative or accusative. We could probably figure out the intent if looked at how Euler used the word elsewhere. Oct 16, 2022 at 20:06
• @TylerDurden it’s not that uncommon in neo-Latin (nor impossible in classical) to have a relative clause between a modifier and noun. Petrarch, for one, preferred that ordering. Oct 16, 2022 at 20:36
• @TylerDurden Re your last edit: a cursory glance at the headings in the text shows multiple solutions: solutio prima/secunda/tertia and finally generalis. Oct 16, 2022 at 20:44