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I am reading this book "Traité du calcul différentiel et du calcul intégral" of Lacroix and came across this definition of a function. There are two terms I don't know how to translate:

Toute quantité dont la valeur dépend d'une ou de plusieurs autres quantités, est dite fonction de ces dernières, soit qu'on sache ou qu'on ignore par quelles opérations il faut passer pour remonter de celles-ci à la première.

My translation:

Any quantity of which the value is depend upon one or multiple other quantities is said to be the function of the latters, either we know or not know by which operations that have to be...

I don't understand the part "il faut passer" and "remonter" here. How to translate these parts in English?

Is my translation good as a whole or it is defective in some respects? My translation sounds kind of awkward even in English.

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    soit qu'on sache ou qu'on ignore par quelles opérations... should be translated as whether or not we know which operations... – Peter Shor Jan 19 at 21:47
  • I'm fairly sure that the meaning (in modern English mathematical language) is Any quantity of which the value depends on one or more other quantities, is said to be a function of the latter, whether or not we know how to explicitly calculate the first quantity from the others. I don't quite see why the verb remonter works here, though. – Peter Shor Jan 19 at 21:58
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    I'm voting to close this question as off-topic because OP asks for a translation from French to English. – Toto Jan 20 at 8:39
  • He is asking for help with a translation, but his specific problem is understanding the FR verbs passer (par) and remonter, so I think it's only the way the question is worded that makes it seem off-topic. – JD2000 Jan 20 at 8:52
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    To me passer par means go through and remonter literally means go back up but is often used just to mean go back e.g. ça remonte aux années xyz - so the structure is like whether or not we know what steps we have to go through in order to get back from those values to that quantity. What is odd about that (and I think this is what @PeterShor is getting at) is that it reverses the direction. At first the quantity is presented as a result obtained by applying the function to given values, but at the end the writer talks about getting back to the result from those values. – JD2000 Jan 20 at 8:56
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I think this passage is saying: you can define a function without defining explicitly the operations that map the input values to the output value.

Toute quantité dont la valeur dépend d'une ou de plusieurs autres quantités, est dite fonction de ces dernières, soit qu'on sache ou qu'on ignore par quelles opérations il faut passer pour remonter de celles-ci à la première.

All quantities whose value depends on one or more other quantities, is said to be a function of the latter, whether we know or ignore which operations must be executed (thus reassembling, or showing, the internal workings of the function).

Thanks to my sons who are both math majors.

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