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VISIERA
Curve studied by Agnesi (17181799).
Visiera: visor in Italian. The name visiera was given by Peano in 1887, probably by analogy with versiera. 
Polar equation: .
Cartesian equation: . Right rational circular cubic with an isolated point (> Sluze cubic) 
The visiera is the antihyperbolism of the versiera with respect to its base and the symmetric image of its vertex with respect to its base; in the above equation, the visiera is the antihyperbolism with respect to O and x = a of the versiera: .
Like all rational
circular cubics, the visiera can be defined as:
 The cissoid
of a circle and a tangent at A to this circle, with pole O,
the point diametrically opposed to A (here, A(0,2a)).
 The inverse of an ellipse with eccentricity with respect to one of its secondary summits (here, the ellipse ).
 by the Newton setsquare method:   by the Kiernan construction: 

Do not mistake the visiera for the conchoid
of Nicomedes.
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© Robert FERRÉOL 2017