[size=150]Witch of AgnesiStudied by Maria Gaetana Agnesi (1718 to 1799) in 1748. Also studied by Fermat (1666), and Guido Grandi (1703). The name of this curve has a colorful history. [i]Versaria[/i] is the name given by Grandi, meaning “turning in every direction”. In the course of time, the word [i]versaria [/i]took on another meaning. The Latin words [i]adversaria[/i], and aphaeresis, [i]versaria[/i], signify a female that is contrary to God. Thus gradually the curve versaria is understood in English as the Witch.The witch of Agnesi (Versiera) is defined as follows.Step by step description:[list=1][*]Let there be a circle of radius a with center at {0,a}.[/*][*]Let there be a horizontal line L passing through {0,2 a}.[/*][*]Draw a line passing the Origin and any point M on the circle. Let the intersection of this secant and line L be N.[/*][*]Witch of Agnesi is the locus of intersections of a horizontal line passing through M and a vertical line passing through N[/*][/list][/size][list=1][*][/*][/list][img]https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcTOOrrh6bxSuvnH_9ICXabP1sKC6fBbZ0kLGw&usqp=CAU[/img]