12 GEE AND A DAMSON, Trisecting an Angle. 



deduced the proofs of the methods of trisecting an angle 

 by means of a rectangular hyperbola. His methods, 

 somewhat modified, are as follows : — 



Let angled Off (Fig. S) = /3 and let OA=d. Take O 



Fig. 8. Illustrating triple solution. 



as origin and OB as axis of x. 



The conic : 



ax- + 2 hxy + by 1 + 2 gsc + 2fy-¥e~0. 



will be a rectangular hyberbola if a+d= 0, and will have 

 OA as a diameter if: 



and 



ad -, hd . n p. 



— cos ft + ■smp+ < § = 



2 2 



lid j rt^ • ,-» , r r\ 



cos (3 - ■ sin /;> +/=0. 



2 2 



The equation then becomes : 



^(' v " ~y 2 ) + 2 ^ A 7 " *£t*(/% sin/3 + a cos /3) - dy(h cos [3 - a sin ft) = 0, 



