# Why is it Called the "Witch of Agnesi"?

In the History of Analytic Geometry by Carl Boyer In footnote 41 on page 179 one learns that:
The name "witch," customarily used in English, apparently is due to a mistranslation. The word "versiera" which Grandi coined in 1718 to indicate the manner in which the curve is generated, has also the meaning "witch" in Italian, but this has no connection with what Grandi and Agnesi had in mind.

Further to this, Alfred Ross says that:
...Luigi Guido Grandi (1671-1742) studied this curve in 1703. He named it the versaria, meaning "turning in every direction." In 1748, Maria Gaetana Agnesi (1718-1799), in Istituzioni Analitiche, the first calculus book written by a woman, called the curve the versiera. The British mathematician John Colson (1680-1760), translating Agnesi's work into English, translated the Italian word versiera (intended to mean "turning curve") as "the witch curve." (The Italian word avversiera can be translated "wife of the devil.") Some sources indicate Colson mistranslated the word; other sources indicate Agnesi had confused an old Italian word meaning "free to move" with another meaning "witch."and contributes the following web site as a reference.

David Fowler provides a slightly different view on the matter:
The treatise Instituzioni analitiche ad uso della gioventu italiana contains no original mathematics by Agnesi. Rather the book contains many examples which were carefully selected to illustrate the ideas; one review calls it an: ... exposition by examples rather than by theory.

The book includes a discussion of the cubic curve now know as the 'witch of Agnesi'. There has been much argument over the reason why the curve is called a 'witch'. The curve was discussed by Fermat and, in 1703, a construction for the curve was given by Grandi. In 1718 Grandi gave it the Latin name 'versoria' which means 'rope that turns a sail' and he so named it because of its shape. Grandi gave the Italian 'versiera' for the Latin 'versoria' and indeed Agnesi quite correctly states in her book that the curve was called 'la versiera'.

John Colson, who had translated Newton's De Methodis Serierum et Fluxionum from Latin to English for publication in 1736, translated Agnesi's Instituzioni analitiche ad uso della gioventu italiana into English before 1760 (the year of Colson's death) although his English translation was not published until 1801. Colson mistook 'la versiera' for 'l'aversiera' which means 'the witch' or 'the she-devil'. See [17] for a detailed description of how the curve has become known as the 'Witch of Agnesi'.

17. C Truesdell, Correction and Additions for Maria Gaetana Agnesi, Archive for History of Exact Science 43 (1991), 385--386. and provides the following reference

On the other hand, Antdeas Hatzipolakis contributes the following:
A 18th c, Greek mathematician, namely Balanos Basilopoulos, had "solved" the Delian problem. He sent mss of his "solution" to varius European Academies, and mathematicians. Among them was Euler (who replied with a proof that the solution was wrong) and an unnamed "philosopher". Here the "an" is of feminine gender. This "philosopher" was Maria Agnesi. Basilopoulos had sent to a Greek in Italy, namely Zarzoulis, his "solution". Zarzoulis met Maria, and showed to her the "solution". Then he wrote a letter to Basilopoulos in 1754. Here is the relevant passage:

.... thn edeica [the construction] en Benetia kai th filosofw, mhpws auth genhtai meq' hmwn, htis epainhse thn meqodon, omws mou apekriqh, oti exei na thn skefqh akribws. Ths eixa dwsh, en xeirografon sas Ellhnikonm ap' ekeina opou mas epemyate, kai to anegnwse qaumasiws diati eixe spoudach kai thn Ellhnikhn dialekton kai anaginwskei, kai ginwskei kai auton toon Dhmosqenhn. Toiauths agxinoias h gunh mou eipen, oti qelei mou apokriqh, thn gnwmh ths meta eis thn ekeise epanodon mou....<\i>

In brief: I showed to the philosopher [:of feminine gender] in Venice a ms. with your construction in Greek. She had studied Greek and is able to read and understand Demosthenes himself! She told me that will examine your construction, and will let me know later. Unfortunately, we have no other information, but most likely Agnesi didn't reply.

Mike Zabrocki