PHYSICAL anpb LITERARY, 127 
granting the quadrature of the circle, it 
is required to draw a line DE,’ meeting 
the circle in E, fo.that the femicircle 
may be to the fector BDE in a given 
ratio, fuppofe that of 7p to 4. 
SupPosF the problem folved ; and let the 
femicircle be to the fector BCF as pis tog; 
join DF, and draw CG parallel to DF meet- 
ing FG a tangent to the circle at F in G; 
join DG, and let CG, DG meet the circle 
in H,K: Join DH, FH; draw CM parallel 
to DH meeting HM a tangent to the circle 
at H in M; draw DL perpendicular to CH 
meeting CH in L; join LE, and let FN, 
perpendicular to CH, meet CH inN, 
BeEcAUsE the femicirle is to the fector 
BDE as p is to g, that is, as the femi- 
circle to the fector BCF, the fefior BDE 
will be equal to the feCtor BCF : And, be- 
 caufe the fe¢ctor BCH is common to both, 
the {pace HCDE will be equal to the fec- 
tor HCF; but becaufe CH, DF are pa- 
 fallel, the triangle DCH is equal to the 
_ triangle FCH; therefore the feCtor EDH 
will be equal to the {pace contained by the 
ct iy arc 
