GEOMETRICAL CONSTRUCTIONS FOR CUT- 
TING FROM A CONE OF REVOLUTION 
PLANE SECTIONS (a) OF GIVEN ECCEN- 
TRICITY, (0) OF GIVEN LATUS REC- 
TUM.* 
Epmunp A. ENGLER. 
(a) The formula generally used to express the eccentricity 
of a section of a cone of revolution ist 
_ cos (8+a) 
COs @ 
(1) 
in which 
é = the eccentricity of the section. 
a. = half the angle at the vertex of the cone. 
=the angle which the plane of the section makes 
with that element of the cone which it inter- 
sects nearest the vertex of the cone. 
and therefore 
6+a =the angle which the plane of the section makes 
with the axis of the cone. 
*Presented by title to The Academy of Science of St. Louis, May 16, 
1892; read before the New York Mathematical Society, May 6, 1893. 
+See Todhunter’s ‘Conic Sections,” 7th Ed., p. 310, Soda Mac- 
millan & Co, 1881. 
