xxe, neque alibij quotiescunque de multiplicatione et diui- 

 fione angulorum egerit, alias feries huic fcopo magis ac- 

 commodatas, legeque magis perfpicua procedentesj in me- 

 dium protuliffe, cuiusmodi varias excogitare licet facilli- 

 mae indaginis, quibusque adeo demonftrandis prima calculi 

 angulorum principia fufficiunt, quemadmodum, vt vnicum 

 fpecimen afferam, ex fequente Theoremate patebit. 



Theorema. 

 J. 12^ Demtante Cf) angulum et n numerum quem- 

 cunquej, femper erlt 



rm.n(p = cof (})^ ( -+-[?] tg.(|) - [|] tg.$3 H- [5] tg.Cl^-etc.), 

 cof./zCl)z=cof.(I)^(i-[^]tg.$2-i-[J]tg.$^-[^]tg.$^-^etc.), 



vhi charaUeres [-], [|], [|] , etc. denotant coefficientes 

 n™"^ poteftatis hinomii. 



Demonftratio. 



Ponatur fin. Cf)^ + cof (p~ ~pq, ita vt fit 

 pz=coi<p-\~y — I fin. $ , 

 (/ = cof Cf> — / — I fm. (J) , 

 eritque, vti ex elementis Calculi fmuum conftat, 

 p"" ~ co[. n p -}- }/ — I fm. n (J), 

 q"^ ~coLn(p — ■/ — i fm. n (p, 

 vnde fequitur fore ' 



-.n „n 



fm. n(p~ £_=JL , 

 2 y — I 



cof.n(t)=z£l±^. 



2 



Noua AUa Acad, Imp. ScienL Tom. DC E e Hinc 



/ 



