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Encyclopedia Britannica



WITCH OF AGNESI

This article appears in Volume V28, Page 758 of the Encyclopedia Britannica.

Encyclopedia Britannica - Main :: WIL-YAK
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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