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, Topographical Engineer to the N. 

 W. Expedition. 



Mr. H. R. Schoolcraft, Mineralogist to the N. W. Expe- 

 dition. 



Mr. Thomas Say, Philadelphia. 



Doctor S. L. Mitchill, 



Majsr Delafield, 



Mr. S.B.Collins, 



Mr. J. M. Bradhurst, f 



Rev. J. Sears, I 



Mr. R. N. Havens, J 



Mr. E. Norcross, of the American Museum. 



MATHEMATICS. 



S of New- York. 



Art. IX. — Demonstration of a Problem in Conic Sections: 

 By Assistant Professor Davies. 



Military Academy, West-Point, Jan. 20, 1823. 

 To the Editor. 



Sir — In the first volume of Dr. Button'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, as 



