Not
From 'Grammar' part of The ABC Of Plain Words by Sir E Gowers (1951)

(a)"Not all"
It is idiomatic English, to which no exception can be taken, to write "all officials are not good draftsmen" when you mean that only some of them are. Compare "All that glitters is not gold". But it is clearer, and therefore better, to write "Not all officials are good draftsmen".

(b) "Not . . . but"
It is also idiomatic English to write "I did not go to speak but to listen". It is pedantry to insist that, because logic demands it, this ought to be "I went not to speak but to listen". But if the latter way of arranging a "not . . . but" sentence runs as easily and makes your meaning clearer, as it often may, it should be preferred.

See Because.

For double negative, see Negative.