112 ESSAYS AND OBSERVATIONS 



fedor BCF, the fedlor BDE will be equal to 

 the fedor BCF: but the fedor BCF is 

 [Prop. 2.] greater than the fedor BDK, but 

 lefs than the fedor BDH j therefore the fedor 

 BDE is greater than the fedor BDK, and lefs 

 than the fedor BDH j therefore the line DE 

 falls between the lines, DH, DK j and there- 

 fore the point E falls between the points, H, 

 K. Again, becaufe the fedor BDE is equal 

 to the fedor BCF, and the fedor BCK is 

 common to both, the fpace KCDEK will be 

 equal to the fedor KCF ; and, becaufe the 

 triangles, KCD, KCF, are equal, (becaufe 

 KC, DF, are parallel), therefore the fedor 

 KDE is equal to the fpace KEFK j and, be- 

 caufe the triangles, GDK, GFK, are equal, 

 taking the common fpace GHK from both, 

 the fedor KDH will be equal to the fpace 

 KEFK together with the fpace GFHG; but 

 the fedor KDE is equal to the fpace KEFK, 

 therefore the fedor EDH is equal to the 

 fpace GFHG. 



Because the femicircle is to the fedor 

 BCF as^ to q, therefore the angle BCF is 

 given, and therefore the angle FCD is lii^e- 

 ways given : and, in the triangle FCD, be- 

 caufe the fides, CF, CD, are given, and like- 

 ways 



