PHYSICAL AND LITERARY. ji7 



fore the leiftor EDH will be equal to the 

 fpace contained by the arc HF and the chord 

 FH. Again, becaufe the feclor BDE is 

 equal to the fedor BCF, and the feftor BCF 

 is [Prop. 2.] greater than the fe(5lor BDH, 

 and lefs than the fedor BDK, the fedor 

 BDE will be greater than the fedor BDH, 

 and lefs than the fedor BDK: therefore the 

 point E is in the arc HK between the points 

 H, K. [Let the arc HK be called the limi- 

 ting arc]. Becaufe the point D is not very 

 excentric, the limiting arc will be little. In 

 the orbit of Mercury y the mod excentric of 

 ^11 the planets, the limiting arc will be lefs 

 than fixteen minutes in that part of the orbit 

 where it is greateft ; therefore EH may be 

 confidered as coinciding with the tangent to 

 the circle at the point H j and therefore the 

 triangle ELH will be equal to the fedor 

 EDHj that is, equal to the fpace contained 

 by the arc FH and the chord FH; therefore 

 the redangle LHE will be double of the 

 fpace contained by the arc FH and the chord 

 yH. Becaufe the redangle contained by 

 CH and the arc FH is double of the fedor 

 CFH, and the redangle contained by CH^ 

 FN is double of the triangle CFH; the 



redangle 



