280 Demonstration of a Problem in Conic Sections. 
Our thanks are due to the following gentlemen, for spe- 
cimens and information. 
Gov. Cass of the Michigan Territory. __ 
Capt. D. B. Douglass, ideaaeaphicnl Engineer tothe N. 
W. Expedition. 
Mr. H. R. Schoolcraft, Mineralogist to the N. W. Expe- 
dition. 
Mr. Thomas Say, Philadelphia. 
Doctor S. L. Mitchill, 
Majer 28 : ; 
Mr. S. B. Collins, 
Mr. J. M. Bradhurst, of New-York. 
Rev. J. Sears, 
Mr. R. N. Have 
Havens, 
Mr. E. Norcross, of the American Museum. 
MATHEMATICS. 
—_ 
Ant. IX.— Demonstration of a Problem in Conic Sections. 
By Assistant Professor Davies. — 
Military Academy, West-Point, Jan. 20, 1823. 
To the Editor. . 
Sirr—In the first volume of Dr. Hutton’s Mathematics. 
(second American edition. p. 470,) we find the following 
article—“ If there be four cones, having all the same ver- 
tex, and all their axes in the same plane, and their sides 
touching, or coinciding in common intersecting lines ; then. 
if these four cones be all cut by one plane, parallel to the 
common plane of their axes, there will be formed four hy- 
perbolas, of which each two opposites are equal, and the 
other two are conjugates.” The intersections of a plane, 
and the surfaces of four cones, having a common vertex; 
touching each other in right-lined elements, and having 
their axes in one plane, are not conjugate hyperbolas, a¢ 
