TIIE APPLICATION OF ALGEBRA 
2 m 
(from above) 
a f- ¿¡* — c* _ a + b f c ^ a \ h — c 
26 ~ b / 2 
= ~ X s — c: but DF (^~ i) is to DC 
2 / 
v s. s — c • s—b .s — a), so is the radius to the tan 
gent of F; and consequently s x s — c : s — b a s — a 
:: sq. rad. : sq. tang, of F; that is, in words, as the 
rectangle under half the sum of the three sides, and the 
excess of that half sum above the side opposite the re 
quired angle, is to the rectangle under the differences 
between the other two sides and the said half sum, so 
is the square of the radius, to the square of the tangent 
of half the angle sought. 
PROBLEM XVI. 
Hating given the base AB, the vertical angle ACB, 
and the right line CD, which, bisects the vertical angle, 
and is terminated by the base; to find the sides and angles 
of the triangle. 
Conceive a circle to be described about the triangle, 
and let EG be a diameter 
of that circle, cutting the 
base AB perpendicularly 
in F; also from the cen 
ter O, suppose OA and 
OB to be drawn, and let 
CD be produced to E 
(for it will meet the pe 
riphery in that point, be 
cause the angles ACD 
and BCD, being equal, 
must stand upon equal 
arches EA and EB), 
Now, because the angle AOB at the centre, standing 
upon the arch AEB, is double to the angle ACB at 
the periphery, standing upon the same arch (L>c,20.3.) 
G