Witch of Agnesi - History

History

The curve was studied by Pierre de Fermat in 1630. In 1703, Guido Grandi gave a construction for the curve. In 1718 Grandi suggested the name 'versoria' for the curve, the Latin term for sheet, the rope which turns (adjusts the trim of) the sail, and used the Italian word for it, 'versiera', a hint to sinus versus that appeared in his construction.

In 1748, Maria Agnesi published her famous summation treatise Instituzioni analitiche ad uso della gioventù italiana, in which the curve was named according to Grandi, 'versiera'. Coincidentally, the contemporary Italian word 'Aversiera'/'Versiera', derived from Latin 'Adversarius', a nickname for Devil, "Adversary of God", was synonymous with "witch". Probably for this reason Cambridge professor John Colson mistranslated the name of the curve thus. Different modern works about Agnesi and about the curve suggest slightly different guesses how exactly this mistranslation happened. Struik mentions that:

The word is derived from Latin vertere, to turn, but is also an abbreviation of Italian avversiera, female devil. Some wit in England once translated it 'witch', and the silly pun is still lovingly preserved in most of our textbooks in English language. ... The curve had already appeared in the writings of Fermat (Oeuvres, I, 279-280; III, 233-234) and of others; the name versiera is from Guido Grandi (Quadratura circuli et hyperbolae, Pisa, 1703). The curve is type 63 in Newton's classification. ... The first to use the term 'witch' in this sense may have been B. Williamson, Integral calculus, 7 (1875), 173; see Oxford English Dictionary.

On the other hand, Stephen Stigler suggests that Grandi himself "may have been indulging in a play on words".

The Witch of Agnesi is also a fiction novel by Robert Spiller, in which a teacher gives a version of the history of the term.