227 



c . Hoj = !(£ . u + e . 0))" + ice . w — e . 0))" , 



©. »u =: 1 (S . co + e . w)" — i ((S . w — e . w)" , 

 ex quibus porro seqnilui- fore 



((E . w — <S . 0))" =: (E . 72CJ — <S . /î(j 



S. 16. Quod si igitur ponatur (S . co zn a: et S • co m »/, 



dit 



C . nu =: i (2/ + ■^)" 4- 1(2/ — ^)" , 

 <Q . n^ù z=. liy -^ xY — i iy — xY . 



Hiiic autem Sinus et Cosinus hjperbollci multiplorum ipsius oj sequcn- 

 tes oriuntur : 



€. Où3=: 1 



£.10) nz y ubi nof andum esse 



S . 20) zr; 2/2/ + ^^ ^-^ =■!/!/— ^ 



£ . 3ùJ m y' -h 3xxy 

 iî . Àb} zzz y'^ -f- byyxx -\- x'^ 

 . d . 5ù) :=z 7/^ -I- 1 Oy^xx -f- Sî/o.* 

 etc. etc. 



© • Où) rz: 



© . 1 0) zr: .r 



. 2o) 1==: 2yx 



(Q . 3(3} ZZl Z-yyx -[- :j:;^ 



. 4ù) :ii: ^?/'^a; -f- 4î/a'^ 



(0.50) = ^tj'^x -\- i Oy^x^ -+- .-c\ etc. etc. 



^. 1 7. Eulerus olini invenit hanc fractionem continuam 

 1 1 



n-f- 



1 1 ^- 3n+l 



£" g n Sri -4- 1 



~"7"n^l 



