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In this sentence:

In Fermat, Lagrange, Newton and Gauss studies [...].

Where should we put the apostrophe?

The complete sentence is here:

Besides Fermat, Lagrange, Newton and Gauss' studies is possible to observe in engineering, computing science and others knowledge areas not always the searcher disposes of the mathematical function.

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    In informal conversation you generally put it after the last item, and treat it as a singular ("Gauss's"). There is some clashing of opinions between style guides; some of them are so embarrassed by English's treatment of several different names, who are not co-authors, as one item for the purposes of the possessive that they insist on saying "studies by X, Y, and Z". But while that might be typographically more pleasing it does nothing to resolve the ambiguity anyway, so I would generally just say "Gauss's". – Luke Sawczak Jul 29 '17 at 17:09
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    In modern English we're becoming very free with invisibly bracketing such phrases for the purposes of the possessive. "The dog that Anna saw yesterday's right hind leg was missing." Style guides and grammars often reject this sort of thing, so steer clear if you're trying to write formally or professionally, but if your goal is to speak English as Anglophones do then have no fear. – Luke Sawczak Jul 29 '17 at 17:12
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    In the comment from @LukeSawczak for example, instead write "The right hind leg of the dog that Anna saw yesterday was missing." – user3169 Jul 29 '17 at 20:14
  • "it is possible" and "that the searcher does not always dispose of the mathematical function". If that's indeed what you mean. – gnasher729 Jul 30 '17 at 18:59
  • As per gnasher729: the question is still unclear even given the complete sentence. For example, exactly what is meant by “...knowledge areas not always the searcher disposes of the mathematical function”? Suggestion: write the sentence in Portuguese, use Google to translate it into English, and give us that. I actually tried it, going from your English into Portuguese and then back into English. It was clearer, but still not clear enough, since it ended with the still-cryptic “the researcher does not always have the mathematical function“ – tkp Jan 4 '18 at 2:51
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There is some ambiguity in this case; are the studies co-authored by the four, or are you referencing some studies from each? If the former, you would append an apostrophe and s to the last name (some style guides would recommend only an apostrophe, placed before the last s); this is the treatment for joint possession. In the second case, when each study belongs to only one of the authors, I believe it is correct to add an apostrophe to each name. I had trouble finding a source for this, however; this site concurs, but they do not themselves cite sources, and I could not find any other statements about it one way or the other. This could get really painful if different studies are co-authored by different members of the list, but assuming this is not the case, your final phrase should be one of these two, as described above:

In Fermat's, Lagrange's, Newton's and Gauss's studies,

or

In Fermat, Lagrange, Newton and Gauss's studies,

As I mentioned, the possessive of Gauss is a matter of debate, but I would strongly recommend the extra s.

The sentence as a whole also has significant unrelated errors; I am not sure what the intended meaning is, though, so I do not want to recommend specific corrections. As tkp suggested, it might be more clear if you had it translated by software and than asked for advice, corrections, or explanation of that version.

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