“Sheer necessity,—the proper parent of an art so nearly allied to invention.”

The Twin Rivals (1702), Act i. Compare: "Necessity is the mother of invention", Wycherly, Love in a Wood (1672), act iii. sc. 3.; "Art imitates Nature, and necessity is the mother of invention", Richard Franck, Northern Memoirs (written in 1658, printed in 1694); "Magister artis ingenique largitor Venter" (translated: "Hunger is the teacher of the arts and the bestower of invention"), Persius, Prolog., line 10.

Commonly misattributed due to Benjamin Jowett's popular idiomatic translation (1871) of Plato's Republic, Book II, 369c as "The true creator is necessity, who is the mother of our invention." Jowett's translation is noted for injecting flowery, if not florid, language familiar to his Victorian era audience. (See "Note on the Translation", by Elizabeth Watson Scharffenberger, ed., in Republic (2005), Spark Educational Publishing, ISBN 1593080972, p. liii http://books.google.com/books?id=9FLdTCiaI_MC&pg=PR53.) Jowett himself, in Plato's Republic: The Greek Text, Vol. III "Notes", 1894, p. 82, gives a literal translation of Plato as "our need will be the real creator," without the proverbial flourish. The Greek text is: ποιήσει δὲ αὐτήν, ὡς ἔοικεν, ἡ ἡμετέρα χρεία. Perseus.tufts.edu http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0167%3Abook%3D2%3Asection%3D369c
Misattributed

Love in a Wood (1671), Act III, scene 3. (This was already a common proverb before Wycherley, cf. Invention, Necessity.)

"Detached Thoughts : On Writing and Books", p. 129
Essays on Men and Manners (1804)

1970s, The argument: causality in the electric world (1973)

As quoted in the "Greta Gaines" profile page at Artist Direct http://www.artistdirect.com/artist/bio/greta-gaines/702133
Context: My parents wrote their own rules, so it didn’t seem odd to me to invent my life as I went along. …  I picked up a guitar and started writing songs late, when I was 22, but quickly became devoted to the craft of song writing, relieved that I had found my inner calling.

Veblen (1914) "The Instinct of Workmanship and the State of the Industrial Arts". p. 314