Mr. Garrard on a new Property of the Tangents, &c. 121 
Proposition II. In every obtuse angled plane triangle, the 
sum of the three tangents of the three angles multiplied by 
the square of radius, is equal to their continued product. 
Demonstration .— Let AH be an obtuse 
arc, and HE, ED the other two. 
Then BF, ED, and AG are the three 
tangents. 
Put BF = t and DE = u radius = r, 
then per trigonometry, as before, 
r*x = BT; 
r 1 — tu ’ 
But — BT = AG = — 
t — j— U 
r z — tu 
x r 
Wherefore t 4- u — - * + u . ■ x r 2 =s the 
sum of the three tangents, which being 
reduced 
is = — tu x anc * tnultiplied into 
r* is equal to 
tu x — “ xi" = the product. 
Q. E. D. 
MDCCCVIII. 
R 
