PHYSICAL anp LITERARY. 129 
the triangle CFH; the rectangle contain- 
ed by CH and the excefs of the are FH 
above FN will be double of the fpace con: 
tained by the arc FH and the chord FH ; 
therefore the rectangle LHE will be equal 
to the rectanzle contained by CH and the 
excefs of the arc FH above FN; therefore 
LH will be to HC as the excefs of the arc 
i above FN to HE: But, becaufe the | 
triangles DLH, CHM are fimilar, LH will 
be to HC as DL or FN to HM;; therefore 
FN will be to HM as the excefs cr the arc 
FH above FN to HE. | 
From this, the following conftruétion shay be 
deduced. 
CONSTRUCTION, 
Tet the femicircle be to the fe@or BCE Ht: 
ee is to g; join DF, draw CH parallel 
_ to DF meeting the cirle in H; join DH, 
draw CM parallel to DH meeting HM, 
a tangent to the circle at H, in M; and 
_. det FN perpendicular to CH meet CH in 
" Vor. Il, Peet ae N; 
