# 1911 Encyclopædia Britannica/Witch of Agnesi

**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.