MATHEMATICAL SECTION. 
97 
notes and memoranda, with a view to the preparation of a fairly 
complete collection of solutions of the problem and the preparation 
of a bibliography. 
Progress in the work had been slow, and the results are still very 
incomplete, especially the bibliographic part, which was deemed the 
most important. 
The present collection of notes contained about a dozen different 
solutions of the problem and a suggested classification for a digest 
of the subject as follows: 
1. Historical Introduction. 
2. Trisection by the conic sections. 
3. Trisection by special or higher curves. 
4. Trisection by mechanical devices. 
5. Trisection by approximation. 
6 . False trisections. 
7. Bibliography. 
Of the trisections by the conic sections five were enumerated, 
viz: 
1. By parabola and circle. 
2. By parabola and parabola. 
3. By parabola and hyperbola. 
4. By the equilateral hyperbola. 
5. By the hyperbola, whose asymptotes form an angle of 120°. 
Trisections by the following curves were also enumerated: 
1. Conchoid of Nicomedes. 
2 . Conchoid on circular base= trisectrix = planetary curve of 
Ptolemy = special case of limacon of Pascal. 
3. Cycloid. 
4. Epicycloid or trochoid. 
5. Quadratrix of Dinostratus or Hippias of Elis. 
6 . Quadratrix of Tschirnhausen. 
7. Spiral of Archimedes. 
Respecting the cissoid of Diodes, it was remarked that no solu¬ 
tion of the trisection problem, by its a:id, had been found. Also 
respecting the cycloid, which Sir Isaac Newton is said to state may 
be used to trisect an angle, no solution by means of it had been 
found, but the author had himself made one recently. 
