1911 Encyclopædia Britannica/Witch of Agnesi

From Wikisource
Jump to: navigation, search
EB1911Witch of Agnesi-Pict1.svg

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 (=2a) for the axis of x, is xy2=4а2(2ах). The curve consists of one branch entirely to the left of the line x=2a and having the axis of y as an asymptote.