Mr. glente’s Proportions . 89 
they lie adjacent on different fides of the diagonal, are 
proportional to the unequal Tides of the trapezium, and 
to the two triangles into which the diagonal divides it. 
For op l : opc = lo : oc^oql: oqc. Therefore, opl : oql 
= opc : oqc=lpc : lqc = lp : lq^ 
PROPOSITION IX. THEOREM IV. 
If from the angles at the bafe of any right lined triangle , 
right lines be drawn to the alternate angles of rhomboids 
defcribed on the other two fides , and reciprocally applied 
to them produced , a right line drawn from the vertex 
through the interfeBion of thefe lines will cut the bafe into 
two parts , having to each other the proportion com- 
pounded of the proportion of the fides , and of the propor- 
tion of the other two lines comprehending the rhom- 
boids. 
I SHALL fubjoin a demonftration of this theorem, 
lince the firft proportion in thefe papers is only a parti- 
cular cafe of it. 
Vol. LXVI. 
N 
Let' 
