130 ESSAYS anp OBSERVATIONS 
N; in the tangent HM take HE to- 
wards F, fo that FN may be to HM as 
the excefs of the arc FH above FN to 
HE; join DE: The femicircle “will be 
to the fector BDE as pis to g. 
Tet DL, perpendicular to CH, meet 
CH in L; join FH, LE. Let CH meet 
_ FG, a tangent to the circle at F, in G3; 
join DG meeting the circle in K. 
Because the triangles DLH, CHM. 
are fimilar, LH will be to HC as DL or 
FN to HM; that is, as the excefs of the 
arc FH above FN to HE: Therefore the 
rectangle LHE will be equal to the rect- 
_angle contained by HC and the excels of — 
the arc HF above FN: But, becaufe the 
reCtangle contained by CH and the arc 
HF is double of the fector HCF, and the 
rectangle contained by CH, EN is double 
of the triangle CFH ; therefore the rect- 
angle contained by CH and the excefs of 
the arc FH above FN will be double of 
the {pace contained by the arc FH and the 
chord FH; therefore the rectangle LHE 
will be double of the {pace contained by 
the 
f 
: 
f 
