# What is the origin of the phrase “as desired” in mathematics?

This is a sort of strange question that popped into my head when I was reading a paper. In writing mathematics, many authors use the phrase "as desired" to conclude a proof, usually written to indicate that one has reached the result originally stated. I know that this is perfectly good English, but the phrase is so widespread, despite the fact that there are many other similar alternatives. Does anybody know whether the phrase has any specific origins?

• It seems very natural thing to say something with that meaning, and as desired is nice and short. I’ve used it for so long that I can’t be sure whether I picked it from reading or came up with it independently, but think that it was the latter. I suspect that many have done so. While it’s similar in spirit to QED, it’s sufficiently different that I’m inclined to see it as an independent expression of the same basic idea. – Brian M. Scott Feb 8 '13 at 5:38
• Wikipedia on Q.E.D. "...There is no common formal English equivalent, though the end of a proof may be announced with a simple statement such as "this completes the proof", "as required", "hence proved", "ergo", or a similar locution. WWWWW or $W^5$ - an abbreviation of "Which Was What Was Wanted" - has also been used." – amWhy Feb 8 '13 at 5:43
• I guess it seems very unnatural to me. I don't really think of myself as "desiring" a result, perhaps because of the connotations of the verb. – Christopher A. Wong Feb 8 '13 at 5:44
• If you don't desire the result, why would you prove it? – Euler....IS_ALIVE Feb 8 '13 at 6:10
• Well, as I said, "desire" seems a strong word for something I aim to prove. – Christopher A. Wong Feb 8 '13 at 23:19

## 1 Answer

From Wikipedia http://en.wikipedia.org/wiki/Q.E.D.:

Q.E.D. is an initialism of the Latin phrase quod erat demonstrandum, originating from the Greek analogous hóper édei deîxai (ὅπερ ἔδει δεῖξαι), meaning "which had to be demonstrated". The phrase is traditionally placed in its abbreviated form at the end of a mathematical proof ...

...however, translating the Greek phrase ὅπερ ἔδει δεῖξαι produces a slightly different meaning. Since the verb "δείκνυμι" also means to show or to prove, a better translation from the Greek would read, "what was required to be proved." The phrase was used by many early Greek mathematicians, including Euclid and Archimedes.

But I don't know how close this translation of Q.E.D. "what was required" is to the phrase "as desired", as desired by the OP.