Manchester Memoirs, Vol. lix. (19 1 5), No. \%. 3 



The indirect methods referred to above may be 

 classed as follows : — 



Methods involving the use of loci other than the 



circle and straight line. 

 Trial methods, with or without the use of special 



measuring instruments. 

 Mechanical methods involving the use of a linkwork 



arrangement. 

 Approximate methods. 

 The application of these methods to the various solutions 

 of the trisection problem will now be given in order. 



Use of Loci. 



I. The Trisectrix of Maclaurin* 



This curve is defined as the locus of a point P 

 {Fig. 2), such that the angle PAC is three times the angle 

 PBC, where A and B are fixed points and C lies on BA 









f ^^ 





P 









F < 



t _,*•**' 













1^ 













"*&* 







~^^^ 







• / B 







D 



A 





C 



Fig. 2. Trisectrix of Maclaurin. 



produced. The curve can easily be constructed as follows: 

 Bisect AB at D. Draw DE perpendicular to BA. 

 Through B draw any straight line intersecting DE at F. 

 1 !■'. Gomes Teixcira, Proc. Edinburgh Math. Soc, Vol. 30, p. 96, 191 1-12. 



