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I would like to translate the following sentence into English, taken from a handwritten document produced in 1804 in Prague:

"Welche Beweise sind für den Satz über das Gleichgewicht am Hebel bekannt? und was hat jeder Vorzügliches für oder gegen sich?"

The sentence comes from a university competition in applied mathematics (mechanics). The first part poses no problems to me, however I find the meaning and grammatical function of the term "Vorzügliches" in the second part puzzling. In particular, would it be correct to translate "Vorzügliches" as an adverb? This would lead to the following literal translation: "and what each ["Beweis", i.e. proof] has eminently for or against itself?". As far as I can understand it, it is asked what particular pros and cons has each proof of the law of the lever ("Satz über das Gleichgewicht am Hebel"). Does my translation capture the meaning of "Vorzügliches" sufficiently well in this context? Are there different ways to understand it?

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    Interestingly, deepL can't handle this either. Aug 19 '21 at 13:48
  • you are also very welcome to ask your question in German. Aug 19 '21 at 13:49
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"vorzüglich" is used here in an obsolete meaning of mainly/primarily, see the DWDS entry.

So I would translate (in modern English) as:

Which proofs of the law of the lever are known? What are the main arguments for or against each of them?

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  • You would think that the language of mathematics wouldn't change that much over time, but nope. I find it difficult to read mathematics in English (my native language) written before about 1870. Mathematical language tends to be dense and full of jargon to start with, but when you throw in dated phrases and terminology it becomes nearly incomprehensible unless you have a lot of practice with it.
    – RDBury
    Aug 19 '21 at 19:08
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    @RDBury This is actually not language of mathematics. It's simply that vorzüglich has changed its meaning from literal "having advantages" to specialized "exquisite".
    – tofro
    Aug 20 '21 at 20:50
  • @tofro: Yes, it's more of a general change in language in this case. I'm just relating my own experience with English and I assume the same holds in German. Perhaps dated words and phrases are more difficult to interpret in mathematics because it's harder to get clues from context.
    – RDBury
    Aug 21 '21 at 14:49
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According to my understanding, your translation is fine.

Vorzüglich in this context establishes a priority scheme, and I guess, the asking person is just interested in the most important reasonings/counter-arguments (for the respective proof); today one would likely ask for a "managment summary" with a presentation slide having a most two bullet points on each side.

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There are two answers so far, both of which tacitly emend "Vorzügliches" to "vorzüglich". But this is not what the quotation says. If correct, "Vorzügliches" is a neuter adjective qualifying "was". The clause means "What eminent thing does each proof have for or against it?".

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