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
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AGNESI  , in
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geometry, a cubic
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curve invented by Maria Gaetana
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Agnesi . It is constructed by the following method: Let
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AQB be a semicircle of
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diameter AB, produce MQ the
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ordinate of Q to P so that MQ : MP :: AM : AB . Then the
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locus of P is the
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witch . The cartesian
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equation, if A be taken as origin and AB(=2a) for the
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axis of x, is xy2=4a2(2a-x) . The curve consists of one
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branch entirely to the
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left of the
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line x=2a and having the axis of y as an asymptote .

End of Article: WITCH OF AGNESI
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