&nf?= &nv fin(t/?— II), tangf^ tangv fin(t/— -11), h. e. 



fin (3 7 = 5 (i — | 5 2 ) fin (v" — H), 



proinde 



fin(z/- n) = (i- 1 5 2 ) fin (^— n) [i — S 2 fin 2 (i/'- U)f^ 

 = {i-l S 2 ) fin (i/'- II) [i + 1 5 2 - 1 S 2 cof 2 (i/'_ n;] 



— (* ~ ~P) fin (2/' — II) — |5 2 fin 3 "(f/'— ; n), 

 vnde fequitur 



i/ = i/' — 1 S 2 fin 2 (*" — n) . 

 Hinc enim fit 



fin(i/ — II) = fin(i/'— 17)— |5 2 cof(i/'— II) fin *(v" — II) 

 = (i — ^ 2 )fin(i/' — n) — |5 2 fm 3 (i/' — n), 

 uti requiritur. 



§. 37. Hoc valore loco 1/ fubftituto, nancifcimur 

 cof(i/— v) = cof(i/'— 1;) -h£fin(i/'— 0) fiiw^- II) = 

 cof^— ^-hfcof^H-i; — 2 n)— | 2 cof(3 z/' — u — 2 n), 

 \tque 



j' = /[i— 5 2 fin 2 (v v -n)] ($. 3<f0^*r^^.?car*^ r n> 



linc pofito 



r r -f- r' r' — 2 r r' cof (2/' — r) = p, & 



| r r' [cof (1/' — v) — cof (*/' + ^-2n)] = ( | ) fit 



Q = p-r-<?5 2 , qT* = p~* — lp~*q&> et 



R=P — p""^-f-lp"" 2 c/5 2 (5. 32.)- 

 In toto nempe hocce calculo ad fecundam tantummodo di- 

 menfionem quantitatum y, y' 9 ($• 29.), ideoque et B, pro- 



gredi 



