' PHYSICAL ann LITERARY. 123 
BCF is (Prop. 2.) greater than the fector 
BDK, but lefs than the fector BDH; there- 
fore the fector BDE is greater than the 
feftor BDK, and lefs than the fecor 
BDH;; therefore the line DE falls between 
the lines DH, DK; and therefore the 
point E falls between the points H, K, 
Again, becaufe the fector BDE is equal to 
the fector BCF, and the fector BCK is 
common to both, the fpace KCDEK will 
be equal to the fetor KCF; and, becaufe 
the triangles KCD, KCF, are equal, (be- 
caufe KC, DF, are parallel), therefore the 
feGtor KDE is equal to the {pace KEFK; 
and, becaufe the triangles GDK, GFK are 
equal, taking the common {pace GHK 
from both, the fe@tor KDH will be equal . 
to the {pace KEFK together with the {pace 
GFHG; but the feor KDE is equal to 
_thefpace KEFK ; therefore the fe@tor EDH 
is equal to the fpace GFHG, | 
ie _ Because the femicircle is to the fe@or 
_ BCF as P to 7; therefore the angle BCF is 
% given ; and therefore the angle FCD is 
| hikeways given: And, in the triangle FCD, 
 becaufe the fides CF, CD, are given, and 
Be se like- 
