By FREDERIC R. HONEY, Ph.B., Yale University.
The following analysis shows that with the aid of an hyperbola any
arc, and therefore any angle, may be trisected.
If the reader should not care to follow the analytical work, the
construction is described in the last paragraph--referring to Fig. II.
Let a b c d (Fig. I.) be the arc subtending a given angle. Draw the
chord a d and bisect it at o. Through o draw e f perpendicular
to a d.
We wish to find the locus of a point c whose distance from a given
straight line e f is one-half the distance from a given point d.
In order to write the equation of this curve, refer it to the
co-ordinate axes a d (axis of X) and e f (axis of Y), intersecting
at the origin o.