120 ESSAYS AND OBSERVATIONS 



and therefore the triangle LHE will be equal 

 to the fpace contained by the arc FH and 

 the chord FH : but, becaufe DL, HE 

 are parallel, the triangles DHE, LHE are 

 equal ; therefore the triangle DHE is equal 

 to the fpace contained by the arc FH and 

 the chord FH : and, becaufe DF, CH are 

 parallel, the triangles CDH, CFH are equal ; 

 therefore the fpace HCDE will be equal to 

 the fecflor CFH. Let the fedor BCH be 

 added to both, and the fedor BDE will be 

 equal to the fedor BCF : but, becaufe the 

 fedlor BCF is greater than the fedor BDH 

 and lefs than the fedor BDK, therefore the 

 fedor BDE is greater than the fedor BDH 

 and lefs than the fedor BDK, and therefore 

 DE falls between DH, DK : and, becaufe 

 the point D is not very excentric, the limi- 

 ting arc HK will be little ; therefore the 

 tangent HE may be confidered as coinciding 

 with the arc HK : becaufe the fedor BDE 

 is equal to the fedor BCF, the femicircle 

 will be to the fedor BDE as the femicircle 

 to the fedor BCF : but the femicircle is tof 

 the fedor BCF as / is to 5- ; therefore the 

 femicircle is to the fedor BDE as p is to q, 

 Q^E. D. 



Kepler^ 



