128 ESSAYS anD OBSERVATIONS ~ 
~ 
arc HF and the chord FH. Again, bes 
caufe the fector BDE is equal to the fec- 
tor BCF, and the fetor BCF is [Prop. 2.] 
greater than the fector BDH, and lefs 
than the fector BDK, the fector BDE will 
be greater than the feCtor BDH and lefs 
than the fetor BDK: Therefore the 
point E is in the arc HK between the 
points H, K. |Let the arc HK be called 
the limiting arc]. Becaufe. the point D 
is not very excentric, the limiting are will 
be little. In the orbit of Mercury, the 
moft excentric of all the planets, the li- 
miting arc will be lefs than fixteen mi- 
nutes in that part of the orbit where it 
is greateft; therefore EH may be confi- 
dered as coinciding with the tangent to 
the circle at the point H; and therefore 
_ the triangle ELH will be equal to the fec- 
tor EDH, that is, equal to the {pace con= 
tained by the arc FH and the chord FH 3 
therefore the rectangle LHE will be 
double of the {pace contained by the are 
FH and the chord FH. Becaufe the rect- 
angle contained by GH and the are FH 
is double of the fector CFH, and the reét- 
angle contained by CH, FN is double of 
the 
