226 A NEW and UNIVERSAL SOLUTION 



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

 tion of M. Euler, is 47 39' 12" 46" : fo that the laft approxi- 

 mation is already almoft exact. This example is well fitted to 

 illuftrate 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 mall 

 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 

 feclor HAB will be one 

 third part of the femi- 

 circle, and will be e- 

 qual to the fe&or BDF. Wherefore it is evident, that BF, being 

 the mean anomaly, BH will be the anomaly of the eccentric : 

 fo that in this cafe we have m — 60, and g = 1. 



1. To compute the firft term p : we have e -n z =z 1, and the 

 cubic equation becomes fimply, a?s r= fin m \ whence x — fin <p 

 — 3 V ' {m m — V fin 60 ° : therefore 



log. fin <p =: 9.9791769, 

 and <p — 72 ° 24'. 



Now 



J C0f ^ Pl - COf 2> ; ; C of <p : Cof ^, 



€0f 



