226 J NEW mid UNIVERSAL SOLUTION 



The more accurate value of BC, according to the computa- 

 rion of M. EuLER, is 47" 39' i 2" 46" : fo that the ]aft approxi- 

 mation is ah-eady ahnofl exaifl. This example is well fitted to 

 illuflrate the convergency of the feries, p, p', p'\ &c. even in the 

 moft unfavourable circumftances. 



Example 2. Prob. From a given point A, in the circumfe- 

 rence of a circle, to draw two chords, AH and AK, that flaall 

 divide the circle into three equal parts. 



Draw the diameter 

 AB, and, from the cen- 

 tre D, draw the radius 

 DF, making the angle 

 BDF = 60°. Becaufe 

 the fegment AH is one- 

 third part of the whole 

 circle, it will be two- 

 third parts of the femi- 

 circle : therefore the 

 fedor HAB will be one 

 third part of the femi^ 

 circle, and will be e- 

 qual to the fedor BDF. Wherefore it is evident, that BF, being 

 the mean anomaly, BH will be the aaomaly of the ecc|^5itrie : 

 fo that in this cafe we have m — 60, and e = i. ■ _ 



I. To compute the fipft term p : we have ^ = s = i, and tfte 

 cubic equation becomes fimply, x'^ ■=. fm m ; whence x — fin <p 

 = ^y/ fin OT =: V fin 60° : therefore 



log. fin <p=: 9.979-1769, 

 and (p — J2° 24' . 



Now 



cof ^+^^ ; coitlZJH : -. cof ?l : cof ^.. 



eof 



