1911 Encyclopædia Britannica/Trisectrix

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1911 Encyclopædia Britannica, Volume 27 Trisectrix

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See also Limaçon trisectrix on Wikipedia, and our 1911 Encyclopædia Britannica disclaimer.

TRISECTRIX, a curve which is a variety of the limaçon (q.v.) of Pascal, and named from its property of trisecting an angle. The polar equation is $r = 1 + 2 \cos \theta$ and the form of the curve is shown in the figure. To trisect an angle by means of this curve, describe a circle with centre O and radius OE, and let the given angle which is to be trisected be laid off from OE and cut the circle at S; let the chord ES cut the trisectrix in J. Then OJ trisects the given angle.