Should I rephase when quoting a theorem/definition?

Question

Actually I would like to ask two questions and the answers may not be the same.

1. When writing a paper and if one need to introduce a definition, is it alright to just copy-paste from wikipedia/a textbook/a paper, or should one at least rephrase it a little bit?
2. If I need to copy a theorem from an old paper, is it better just to copy exactly the theorem as it is, or should I rephrase it to make it in harmony with my notation/modern terminology, etc.?

Answer 1

Well, there is no law against using copy-paste from any document unless it has a copyright (in which case even rephrasing is a form of plagiarism). If you think the original is too unclear, you could rewrite using your own terms, as long as you don't change the meaning (even slightly). If it is clear enough, it's best to copy it as it is.

Answer 2

There are no rules that require you to rephrase anything. But you need to provide citations, at least for the results you quote (for the definitions, it can occasionally be appropriate with a citation, but not very often).

However, you also need to make sure that all statements included in the paper itself make sense in the notation of that paper. So you do need to rephrase the statement if the original author did not use the same notation (and if you just cite the result as part of a proof, it can also sometimes be a good service to the reader to make a brief note explaining how the notation differs between your paper and the cited one).