[ 3 ° ] 
not vain enough to think it may not be performed 
in a more elegant manner. I have the honour 
to be, 
Gentlemen, 
Your moil obedient- 
humble fervant. 
Fleet-Street, 
Jan. 7,1767. 
George Witchell. 
LEMM A. 
If any fpheroid is cut by a plane, in any direction 
whatever (excepting that which is perpendicular to 
its axis), the figure of the fedtion will be an ellipfis. 
This is demonftrated in Simpfon’s Fluxions, Vol. II. 
P . 456. 
PROPOSITION I. 
Tab. III. fig. 1. Let the fphere BEGK be cut 
through its center by the planes BGK, BPD, BoD, 
BOD, EAK, and LPH j it is required to determine 
the inclination of the planes LPH, BOD, and alio 
the inclination of the right lines AC, BC, which is 
meafured by the arc AB ; there being given the angles 
of inclination EBF, FB#, together with the arc BF : 
the angles AFB, EAL, being right angles, and the 
inclination of the required plane BOD, but little ex- 
ceeding that of the given plane BoD. 
Let 
