Online Encyclopedia

WITCH OF AGNESI

Online Encyclopedia
Originally appearing in Volume V28, Page 758 of the 1911 Encyclopedia Britannica.
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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=4a2(2a-x). The curve consists of one branch entirely to the left of the line x=2a and having the axis of y as an asymptote.
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