There are dozens, perhaps hundreds of published proofs. New ones (which are probably rediscoveries of old ones) are published every year. If yours is brief and attractive, you should send it to a Journal like MATH MAG or THE COLLEGE MATH JOURNAL. Even if it is not new, anything nice should be brought back from time to time for the next generation.
I know that I've seen it in calculus texts as well as books that
provide problems and nice solutions. Three examples were included in A
CENTURY OF CALCULUS Part II (1969-1991), ed,. by Tom M. Apostol et al., on
pages 445-449. (It is published by the Mathematical Association of
America, 1992.) Other references are provided there. These 3 items were
taken from The TWO-YEAR COLLEGE MATH JOURNAL VOL 3, no. 2, pp 13-15