17(> Division of the Circle into seventeen equal Parts, 



of z in the foregoing quadratic equation, will be 2p and 2p' :• 



and hence 



jw — — = 2p 



m - — = 2/y ; 

 from which we derive four values of m, vizi. 

 m = p + 'v/p'+ I 

 m'=p - ^/p^~i = -- 



m"=p'+ vp'"- + r 



And, by substituting these values in the formula for /z', we gel 

 four corresponding values of m, viz, 



7t' = /\/8 + 2m — m'^ 



7t"= ^8 + 2OT"-m"^ 



72'"= ^ S + 277i"— m"'* : 

 And finally, from the values of m and n now found, we deduce 

 all the values of x and ?/, or the eight cosines that determine the 

 points of a polygon of seventeen sides inscribed in a circle, viz. 



4 ' 4 



The numerical values of all the cosines sought are thus found j 

 but the investigation does not determine to which arc any nu- 

 merical value belongs. This must be made out by means of the 

 relative magnitude of the (juantities ; the largest number an- 

 swering to the greatest cosine. One thing only we learn from 

 the analysis, which is, that every two corresponding numbers, or 

 two found by adding and subtracting the same values of w and«, 

 belong to two arcs, one of which is quadruple of the other, 



A, B. 



XXVI. Some 



