Maria Gaetana Agnesi's Other Curves (More Than Just the Witch)

摘要

Maria Gaetana Agnesi's name is commonly associated with the curve known as "the Witch of Agnesi." However, the versiera (or versoria), as Agnesi called it, is only one of many curves she introduced in her mathematical compendium, the Instituzioni Analitiche (1748). Some of the other curves are much more interesting and complex than the versiera, and they are grouped in the lengthy section (pp. 351-415) titled "On the construction of Loci of degree higher than second degree." This article showcases Agnesi's presentation of some of them, made without using calculus. Instead, her tools of choice were geometry, algebra, and the method of using easier and already-known curves to build more challenging ones.