260 
THE APPLICATION OF A LG LB It A 
|a\/T = i a V 3. 
PROBLEM IX. 
The segments of the base AD and BD, and the ratio 
of the sides AC and BC, of any plane triangle ABC 
being given; to find the sides. 
Put AD ~ a, BD = b, 
AC = x\ and let the given 
ratio of AC to BC, be as m 
C 
to n, so shall BC — 
‘/£i 
\\ 
But AC 1 — AD 1 (= DC 1 ) 
zr BC 1 — BD 1 , that is, in 
— b\ Hence we have wrx* 
A D 
— n z x z — m z x aa — bb, 
aa — bb 
mm — 7i n 
and x — m 
PROBLEM X. 
The base AB faJ, the perpendicular CD r: b, and the 
difference (dj of the sides AC — BC, of any plane tri 
angle ABC, being given; to determine the triangle (see 
the preceding figure). 
Let the sum of the sides AC 4~ BC be denoted by x: 
then [by Prop. 11. Sett. 18.) we shall have a : x :: d : ~ 
= the difference of the segments of the base; therefore 
the greater segment AD will be rr 4- — 
aa 4- dx 
2 a 
But AD 1 f DC 1 = AC 1 ; that is, 
c 4 + 2 a*dx 4--d\r* . t _ x* 4- Qdx 4- dd 
A r. r. 1 ' . 
4 aa 
4