I've only been learning Latin for a month or so, but I'm specifically learning so that I can read scientific and mathematical texts from the 17th-19th centuries. It's slow going, of course- I'm only about 10 chapters into Wheelocks (among other things I'm practicing with like LLpsI) but I wanted to find some simple sentences that had manageable vocabulary. This sentence is one I've found, from Euler's Institutionum Calculi Integralis volume 1:

Calculus integralis dividitur in duas partes, quarum prior tradit methodum functionem unius variabilis inveniendi ex data quadam relatione inter eius differentialia tam primi quam altiorum ordinum.

I helped myself out by looking up some of the more (for me..) advanced forms (3rd decl adjectives, quarum and quadam, things I haven't learned properly yet) but one part is giving me issues:

..., quarum prior tradit methodum functionem unius variabilis...

Here, both methodum (methodus, methodi, fem. 2nd decl) and functionem (functio, functionis) are in the accusative. At first I didn't know what to make of this, but looking it up I came across hyperbaton, and double accusatives, and because tradere (3rd conj) has a sense of 'to teach' I thought double accusatives would make some kind of sense. But I'm out of my depth here! What is grammatically happening at that point in the sentence?

P.S. my translation for this sentence is:

Integral calculus is divided in two parts, of which the former (part's) method relates to functions of one variable found from some given relationship between its differentials both of first as well as of higher orders.

I cleaned up the translation, after first writing a couple more literal versions.

  • 2
    Welcome to the site! I'm always glad to see more people with interest in both mathematics and Latin. I look forward to seeing more questions from you.
    – Joonas Ilmavirta
    Commented Dec 11, 2020 at 12:17
  • You'll have a better understanding of tradit when you get to Cap. XXIII of LLPSI.
    – Ben Kovitz
    Commented Dec 11, 2020 at 18:57
  • 1
    Just as a comment, hyperbaton means separating words that go together grammatically (e.g. Magnum vidi puerum), so it's not a relevant term in this case.
    – TKR
    Commented Dec 11, 2020 at 23:51

1 Answer 1


Congratulations on your, for one month (!), very impressive progress. You have chosen a highly unusual but excellent reason for learning the language.

I would not translate tradit as “relates to” but as “yields” or “gives us” etc. Tradere does not have double accusative objects, it has an accusative and a dative (like in English: what is yielded/delivered/taught... to whom; the latter not used here, the former is methodum).

What kind of method? A methodus functionem inveniendi – a method of finding a function. Functionem is the object of invenire. (You may have learnt that gerunds with objects are replaced with gerundives, like so: methodus functionis inveniendae. That is true but not obligatory for genetive gerunds, for whatever reason. My guess is that Euler did not do it here.)

Thus my interpretation would be: “… two parts, of which the former provides a method of finding a function with one variable from a certain given relation …”

  • It occurs to me that English "teach" is typically used with a double direct object ("teach him that" etc). So is docere, the usual Latin word for "teach" (double accusative). But not tradere. Commented Dec 11, 2020 at 9:12

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