(114) = 



__^«^ (i + a cot. d)) — ^P^(i + f5cot. (|5) ___y 

 ~~ ^"^ 'J* (a — cot. (p) — fl^ ^ (|3 — co.. (pj x' 



Tantum igitur fupereft, vt aequatio ~ rz: -—■ integretur. 



■Vtamur autem potius pofteriore aequatione: 



S X w 3 f) ( I -I- fi u) 



~x' (I -Hf f))^ ' 



quae ob i-+-ptt:=^-±^ transmutatur in hanc: 



ix , — tt 30 



X (I -l-fiJ) (I -i-fxj)' 



quae porro, ob prcot.Cj), tranfit in hanc: ~ — ^ " ^ ?oi d )' ^"^*^ 

 igitur loco ^ fcribatur valor inuentus, ac reperietur: 

 dx _ «a0(ae«'^ — (BfP^J^) 



X ' f"<J' (a — cot. Cp) — ^P^ (p — cot. (P) ' 



fiue 



X ^^"^ (a fin. <P — coi: Cpj ^P^ ( ^ fin. — cof. Cp) 



Haec autem formula nimis complicata videtur, quam vt cius 

 integrationem exfpedare liceat; verum fi denominatorem dif^ 

 ferentiemus, dejyehendemus fore: 



r"^ a Cj) (a a 4- i) fin. Cf) — fP^ 3 Cj) (p (3 -f- i) fin. (p. 



Quia vero eft aa-|-i— «a ct (3p4-i— «p, iftud diffe- 

 rentiale erit: 



nae''^d(pfin.(p-n(^e^^d!prin.(p — nd(pCm.(p(ae^^-'^e^'^), 



cui ipfe numerator praccife cft acqualis, ex quo ftatim adi- 

 pifcimur 



lx=zl [f"^ (a fin.Cl) - cof.Cl)) - fP^ (|3 fin.Cp - cof.Cl))] -+- / a^ 

 vnde concludimus 



x=za e'^^ (a fin. Cf) — cof. (p) — a e^^ (p fin. Cj) — cof Cj)). 

 Quodfi nunc fradioncm pro ^ inuentam fupra ct infra in 

 fin. $) ducamus, habebimus: 



