126 ESSAYS.anp OBSERVATIONS 
both, the fector KDH will be equal to the 
fum of the fpaces KEFK, GFHG ; there- 
fore the fector KDE is equal to the fpace 
KEFK. And, becaufe the triangle KDC 
is equal to the triangle KFC, the fpace 
KCDE will be equal to the fector KCF; 
therefore, (adding the fector BCK to both) 
the fector BDE will be equal to the fector 
BCF. Again, becaufe the arc AFB is to 
the arc BF as 7 is to 4, the femicircle will 
be to the fector BCF as 7 is to 7; therefore 
the femicircle will be to the feGtor BDE 
aspistog. Q.E.D. 
BuT, as this would require a good deal 
of trigonometrical calculation, the follow- 
ing method may be ufed; which will 
give the point fought very nearly, when 
this problem is of ufe in the planetary fy- 
ftem. 
PROP, V. Prosi. 3. Fig... 
Ler there be a femicircle whofe diameter 
is AB and centreC, and let D be a point 
in the diameter mot very excentric; 
grant- 
