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CISSOID OF TWO CURVES
From the Greek Kissos: ivy. 
Polar equation of the cissoid of pole O of the
curves
and :

The cissoid of two curves (G_{1}) and (G_{2}) with respect to a point O is the locus (G) of points M such that where M_{1} is a point on (G_{1}) and M_{2} is a point on (G_{2}), with M_{1}, M_{2} and O aligned.
Therefore, the cissoid is the medial curve of pole O of the curves (G'_{1}) and (G'_{2}), the images of (G_{1}) and (G_{2}) by the homothety of centre O and ration 1/2.
Sometimes, the cissoid is defined as the locus of points M such that ; this amounts, of course, to changing (G_{1}) into its symmetrical image about O in the definition we adopted.
 The parabolic folium is the cissoid of a line and a semicubical parabola.
 the beetle curves are the cissoids of a circle and a fourleaved rose.
Remark: when the two curves (G_{1})
and (G_{2})
coincide, the cissoid is composed of the image of it by the homothety of
centre O and ratio 2, but also, possibly, of another part (because
the points M_{1} and M_{2}
can be different).
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© Robert FERRÉOL 2017