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Salmon's Theorem


There are at least two theorems known as Salmon's theorem. This first states that if P and S are two points, PX and SY are the perpendiculars from P and S to the polars of S and P, respectively, with respect to a circle with center O, then OP/OS=PX/SY (Durell 1928; Salmon 1954, §101, p. 93).

The second Salmon's theorem states that, given a track bounded by two confocal ellipses, if a ball is rolled so that its trajectory is tangent to the inner ellipse, the ball's trajectory will be tangent to the inner ellipse following all subsequent caroms as well (Salmon 1954, §189, pp. 181-182).


See also

Billiards, Polar

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References

Durell, C. V. Modern Geometry: The Straight Line and Circle. London: Macmillan, p. 95, 1928.Salmon, G. A Treatise on Conic Sections. New York: Chelsea, 1954.

Referenced on Wolfram|Alpha

Salmon's Theorem

Cite this as:

Weisstein, Eric W. "Salmon's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SalmonsTheorem.html

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