ant. Omnes autem operationes inftituendae innituntur fe- 

 quenti Lemmati: 



Lemma. 

 Si propofita fuerit ifta feries cofinuum : 

 i -+- cof. $) -+- cof. 2 <p -+- cof. 3 <P -+- cofr^. <p. . . . cof. n <p, 

 cuius ullimi termini angulus fit multiplum femiperipheriae 

 7r, invenire futnmam huius feriei. 



Solutio. 



J. i?. Ponamus fummam quaefitarn zz S, ut fit 

 S zz i -+- cof. <p -+- cof. 2 <p -+■ cof. 3 <p . . . . cof. n<p, 

 et multiplicando per fin. ^tp, ob 



2 fin. | $ cof. m <J> z= fin. (m -+- §) $ — fin. (m — |) (f), 

 nancifcemur : 

 ^Sfin.fCpzz 2fin.|Cp-f-finJ$H-fin.'|$-+-fin4(p...fin.(»-+-g(I>, 



-fin.i(f)~firi.|(J)-fin.|4)~fin.(^-|jcf, 

 ita ut fit 



/2 S fin. | (D zr fin. \ <p -f- fin. (h -f- §) $. 

 Quodfi iam fuerit n <P zzz tt , ultimus terminus erit 

 fin. (■*-+-§)$ = — fin.|(J), 



ideoque 2 S fin. £ j) — c , quod idem valet fi fuerit ?2 (f) vel 

 3 ix, vel 5 7r, vel in genere ( : i — }) J' } fin autem fuerit 

 n <p =z 2 7T, ultimus terminus e¥it zrfln. |(£ 3 ideoque ftim- 

 ma feriei erit zz i. 



$• 13. Duo igitur cafus hic occurrunt diftinguendi , 

 prouti ferrit vel n <p zz (2 i — 1) tt, vel n <p — 2 i tt. Priori 



fcili- 



