# 4. Constructing a Point on a Cassini Oval

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This Demonstration shows another construction of Cassini's oval. Start with the hyperbola with equation of eccentricity , . Select any point on . Let be the opposite point of and a point on different from and . The tangents on at and are parallel and meet the tangent at at points and , respectively. Then .

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Contributed by: Marko Razpet and Izidor Hafner (July 2018)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

In *Conics*, Book III, theorem 42, Apollonius has shown that for and for the ellipse.

References

[1] T. Heath, *A History of Greek Mathematics, V**olume II: From Aristarchus to Diophantus*, New York: Dover Publications, 1981, p. 155.

[2]. A. Ostermann and G. Wanner, *Geometry by Its History*, New York: Springer, 2012, pp. 76–78.

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