n 
eh*msx 
PP 
¡whence wri- 
PP ° P 
l?m 2 ebb ms . . 
-, we have fix 1 \-egxzzh: 
which, solved, gives x — \/ t- ~r: from 
whence SQ will also he known : and then, again, by 
reason of the similar figures, it Avill be as QS : Qi* 
(unity) :: BD : AB ; which therefore is known, like 
wise : from whence the rest of the sides BC, CD, and 
DA will all be found by plane trigonometry. 
The last problem is indeterminate in that particular 
case, where the trapezium may be-inscribed in a circle, 
or where the sum of the two opposite angles is equal 
to two right ones; for, then, there can but one diago 
nal be given, in the question, because the value of the 
other depends entirely upon that, 
PROBLEM XXVI. 
Supposing BOD to be a quadrant of a given circle; 
to find the semi-diameter CE, or CL, of the circle 
CEGL, inscribed therein; and likewise the semi-diameter 
of the little circle nleniP, touching both the other circles 
DLB, LmE, and also the right-line OB. 
Let BQ, P?/, and CE, be perpendicular to BO; join 
C, n and O, n; and draw OC meeting BQ in Q,