traced upon the Surface of the Sphere. 

 FIG. 15. 



309 



This is identical with BERNOULLI'S solution, and differs from that given 

 above only in having a different origin of Q, 



It may be remarked in passing, that the other known properties of this 

 section, given by BOSSUT*, MONTUCLA-J-, and IVORY|, may be easily 

 obtained by methods analogous to those above employed. To take as an 

 instance, that of MONTUCLA, viz. that the surface of the intercepted por- 

 tion of the cylinder itself js quadrable. Take any corresponding points D 

 and E in the base of the cylinder and the curve of penetration. Then 



* Mem. de 1'Institut. torn. ii. p. 228. 



f Hist, des Math. torn. ii. p. 94. 



\ LEYBOURN'S Mathematical Repos. vol. i. pt. ii. p. 1. New Series. See also WOOD- 

 HOUSE in Phil. Trans. 1801, p. 153. Other works are referred to by historical writers : 

 but as additional detail would be inconsistent with my plan, I shall not consider further 

 examination to be at present necessary. 



VOL. XII. PART I. R F 



