[ 296 ■] 
XXVIII. of triangles defcribed in Circles and about tbem^ 
By John Steelman, M. D. 
Rcdde, March 23, 1775. 
PROPOSITION I. 
An equilateral triangle inferibed within a circle ii lat'ger 
than any other triangle that can be inferibed within the 
fame circle, 
L et ABC (tab. VIII. fig. I.) be an equilateral trian- 
gle, inferibed in the circle adcb; and let ad e be a 
triangle fuppofed larger than abc. Let ade be di*awn 
with one of its angles at the fame point with one of the 
angles of the equilateral triangle, fuppofe at a, and then 
its other two angles will fall either on the fegments adb 
and a EC, or one of the angles will on the fegment ^Ci 
Firfi, let one of its angles fall at D, between A and b ; and 
the other at e, between a and c, and draw the line be. 
- Tn the triangles abc, abe, the triangle abf is common, 
and the two remaining triangles bfc, afe, are fimilar; 
for the angle afe is equal to its oppofite angle bfc; and 
the two angles eac, ebc, are eqilal, being fubtended by 
the fame fegment ec, and fo the two remaining angles 
aef, 
