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BESACE
Curve studied and named by Cramer in 1750. 
Cartesian equation:
or , with . Or .
, of , where . Rational
quartic.

Given a diameter [AB] and a point O on a circle (C), the associated besace is the locus of the points M on a moving line (D) parallel to (OA) such that QM=OP where P is an intersection point between (D) and (C) and Q is the projection of O on (D) (here, A(a,0) and B(0,b)).
The third form of the Cartesian equation shows that besaces are the polyzomal curves median of the coaxial parabolas and .
Besaces are the projections of Viviani's curve on the planes passing by the axis of the cylinder on which the curve is traced.
When b = 0 (i.e. when the circle is tangent to
Oy), we have the lemniscate of Gerono
and when a = 0, a parabolic segment.
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© Robert FERRÉOL
2017