Jfi INVESTIGATION of fame 



Qjo the fame, = 5|f x r , = n x I^_7 x r4< When p coin- 



tides with B, Oc is = r, and A* -f B 4 -f C 4 -f- &c to ^"~ ' 



4 



terms, +^ + ^ + f 4 + &c. to ^=-1 terms, (when /z — i is a 



multiple of 2 by an even number) is a 3." ° x r 4 • and A 4 4- 



16 ' ~ 



B4 + C4 + &c to £Xi terms, + a* + ^ + & c . to ^- 3 terms. 



4 . 4 



(when » — i is a multiple of 2 by an odd number) is = 



3"- 8 X r*. 

 16 



In like manner is it demonftrated, that the fum of the fifth 

 powers of perpendiculars drawn from P to the fides of any regu- 

 lar circumfcribing figure of a greater number n of fides than 5, 

 is equal to the fum of the fifth powers of perpendiculars drawn 



from Q^to the fame ', and that As -f- B 5 -f Cs -f & c . to n l 



4 



terms, — a> — & — cs — &c. to terms, (when n — 1 is a 



4 



rs 



multiple of 2 by an even number) is — — , and A 5 -f- B 5 -f C 5 



4- &o to terms — a$ — b$ — &c. to -terms, (when 



4 4 



n — 1 is a multiple of 2 by an odd number) is ± — . 



