# 1911 Encyclopædia Britannica/Witch of Agnesi

Jump to navigation
Jump to search

**WITCH OF AGNESI**, in geometry, a cubic curve invented
by Maria Gaetana Agnesi. It is constructed by the following
method: Let AQB be a semicircle of diameter
AB, produce MQ the ordinate of Q to P so that
MQ : MP :: AM : AB. Then the locus of P is the
witch. The cartesian equation, if A be taken as
origin and AB ( = 2*a*) for the axis of *x*, is *xy*^{2} = 4*а*^{2}(2*а* − *х*). The curve consists of one
branch entirely to the left of the line *x* = 2*a* and
having the axis of *y* as an asymptote.