ii8 ESSAYS AND OBSERVATIONS 



rectangle contained by CH and the excefs of 

 the arc FH above FN will be double of the 

 fpace contained by the arc FH and the 

 chord FH; therefore the redangle LHE 

 will be equal to the redtangle contained by 

 CH and the excefs of the arc FH above 

 FN ; therefore LH will be to HC as the 

 excefs of the arc FH 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 of the arc FH above FN to HE. 



From tbisy the followhig con/iriiBio?2 may be 

 deduced. 



CONSTRUCTION. 



Let the femicircle be to the feclor 

 BCF as ^ is to ^; join DF, draw 

 CH parallel to DF meeting the 

 circle in H ; join DH, draw CM 

 parallel to DH meeting HM a 

 tano-ent to the circle at H in M ; 

 and let FN perpendicular to CH 

 meet CH in N 5 in the tangent 



HM 



