PHYSICAL AND LITERARY, n^ 



HM take HE towards F, fo that 

 FN may be to HM as the excefs 

 of the arc FH above FN to HE; 

 joInDE: the femicircle will be. 

 to the fedlor BDE as p is to q. 



Let DL, perpendicular to CH, meet CH 

 in L ; join FH, LE. Let CH meet FG, a 

 tangent to the circle at F, in Gj 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 J that is, as the excefs of the arc FHi" 

 above FN to HE : therefore the retftaingle 

 LHE will be equal to the reitangle con- 

 tained by HC and the excefs of the arc HF 

 above FN ; but, becaufe the red:angle con- 

 tained by CH and the arc HF is double of 

 thefedtor HCF, and the redangle contained 

 by CH, FN is double of the triangle CFH j 

 therefore the rectangle contained by CH and 

 the excefs of thp arc FH above FN will be 

 double of the fpace contained by the arc 

 FH and the chord FH j therefore the rect- 

 angle LHE will.be double of the fpace 

 contained by the arc FFI and the chord FHj 



and 



