^4 ESSAYS AND OBSERVATIONS 



Because BE is the fine of the angle 

 BCD, and DF the tangent of the angle 

 DCF, that is, of the angle SDC ; BE will 

 be to DF as the excefs of the arc BD aboye 

 BE to the arc DG j therefore [Prop. 5,] the 

 fedor ASG is equal to the fedor ACB ; 

 therefore the angle ACQ is the anomaly of 

 the excentric. 



The computation is as follows : In the 

 triangle BCS, as the fum of the fides BC, CS, 

 is to the difference of the fides BC, CS, fo is 

 the tangent of half the angle ACB to the 

 tangent of half the difference of the angles, 

 CSB, CBS ; therefore the angles, CSB, CBS • 

 will be given, that is, the angles, ACD, 

 DCB, will be given. Again, in the triangle 

 CSD, the fum of the fides, CD, CS, is to 

 the difference of the fides CD, CS, as the 

 tangent of half the angle ACD to the tangent 

 of half the difference of the angles, CSD, 

 CDS } therefore the angle CDS will be 

 given. Again, becaufe as the fine of the angle 

 BCD is to the tangent of the angle CDS, fo 

 is the excefs of the arc BD above its fine to 

 the arc CD ; fay as the radius is to the fine 

 of the angle BCD, fo is ST'~9S179S ^^' 

 |he number of degrees in an angle fubtended 



"^1 



