30 GEE AND ADAMSON, Trisecting an Angle. 



exceeding that given as the error when the angle to be 



trisected is 45 . 



Method A™ — The construction depends upon the fact 



that the equation : 



sin (/3 - a) = - sin /3 + - sin a 

 2 2 



is true if 



= - + -(-) when we neglect (- 



fr* 



3 3^3' v 3' 



Method B 17 was suggested by Method A. In this case 

 the construction solves the equation : 



sin (/3 - o) = - sin /3 + * sin a, 

 4 4 



which is true when 



a = £-l(^Y, if (£Y is neglected. 



Method C) 8 — The construction solves the equation : 

 6 sin a + 3 sin (/3 - a) = 8 sin /3/2, 

 which is true when 



a-P + lf?) 9 if (^Y be neglected. 



3 6V3/ \3/ 



B O £ 



Fig. 23. Snell's Approximate Method. 



Method D was used by Snell (1546-1613) and is ex- 

 tremely simple. Let A OB {Fig. 23) be the angle to be 



10 C. S. Bingley in Knowledge, Nov., 191 1. 



i- R. F. Davies, Mathematical Notes, Edinburgh Math. Soc, May, 1912. 



isNevil Maskelyn, Philosophical Magazine, April, 1912. 



