28 Gee AND A DAMSON, Trisecting an Angle. 



by moving a handle till the strip DC lies along the 

 other bounding line. 



It is interesting to note that as the instrument is 

 moved in this manner the point D describes a curve 

 which is a portion of a special form of limacon. 



The linkage apparatus represented in Fig. 22 was 

 devised by Professor J. J. Sylvester. 15 The lines in the 

 diagram represent links which are hinge-jointed at each 

 point of intersection. The points F, G, H, K, Z, Aland N 



o £ 



Fig. 22. Sylvester's u Angle-divider." 



are all equidistant from B. The lengths OG, OH, PK, 

 PL, QM and QN are all equal, as also are RF, RG, SH, 

 SK, TL and TAT. Consequently the angles at F, G } H, 

 K, L, Al and N are all equal or supplementary. Hence 

 the angles FBG, HBK and LBAl are equal, as also are 

 the angles GBH, KBL and MBN. Therefore the angles 

 ABD, DBE and EB C are equal, and the angle ABC is 

 trisected by the links BD and BE. 



Obviously by adding more links the angle between 

 the extreme links could be divided into any required 

 number of equal parts. 



1 •" Proc. London Math. Sotr., Vol. VI., pp. 78 and 196. It is con- 

 structed by Adam Hilger, Ltd., 75,7, Camden Road, London, N.W. 



