Descartes's Angle Trisection

Descartes used the intersection of a circle and a parabola to trisect an angle. The equations of the circle and parabola are and , respectively. The coordinates of the intersection satisfy . Since , by taking , the smaller positive root of the last equation is .

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Reference
[1] W. W. Rouse Ball and H. S. M. Coxeter, Mathematical Recreations and Essays, 13th ed., New York: Dover Publications, 1987 p. 346.
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