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The Trisection of a Given Angle

Published online by Cambridge University Press:  20 January 2009

Lawrence Crawford
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In a given circle let the arc AP subtend an angle 3a at the centre O, it is required to trisect the angle AOP, or the arc AP.

The three trisectors will be OQ1, OQ2, OQ3, where AOQ1 = a,

∴ Q1 Q2 Q3 form an equilateral triangle. (See Figs. 10 and 11.)

We proceed to solve the problem by drawing a conic through Q1, Q2, Q3, a nd we wish to find in what cases such a conic can be drawn, a conic cutting the circle in four points, three of which form an equilateral triangle.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , February 1897 , pp. 42 - 45
Copyright
Copyright © Edinburgh Mathematical Society 1897