TITLE: Reproving a known theorem in an article
QUESTION [19 upvotes]: Suppose one wants to use a theorem that was published quite a long time ago (+80 years) in a paper that is using a terminology and notations that are very much out-dated (making the paper very hard to read). Is it okay if we want to reformulate the result as well as the proof in an article using a more modern language (of course giving credit to the original paper)?
Or, on the other hand, is it something one shouldn't put in a research paper, since it's not a new result ? What is the general policy for this kind of things ?

REPLY [4 votes]: Littlewood's Miscellany includes a quote from somebody's paper saying 

Part 2 [of the theorem], which is trivial, is due to Hardy and Littlewood

which met the requirements of both completeness and acknowledging prior publication of something H&L had earlier also included for completeness, while coming across as vaguely demeaning  
Your aim should be for usefulness and prior attribution of the result without sounding negative