54 



facta evolntione eiit u = |^f^t-'^'°"6 J^r- Unde patct 

 serici, vjloicm ipsiiis u cxpiiincniis, piimum Icrmimiin fore 

 tj sequentes \cio per potcstatcs inip:nes ipsius t piogredi. 



Ç. 18. Cmn iizitui- sit z/ r=:-^^ — -, eiit e*'n:— ", id- 

 eoqiie 2t^r/'"^"", unde dilTcrentiando fit^tm--"-, ita ut 



du ... 



^--|-uu — 1 :zz o, qiuie est ipsa aequatio pro casii pnorc 

 inventa. Neque ta mon piopterea pro u eadcni séries prove- 

 nit. Quoniaiii cniin hic jjriimis seriei terminus débet esse 

 inf, fingenda est hiijusmodi séries: 



u r= t — 5it' -f- 'Zt^ — dt' -f- 019 __ (Pt" H- etc. 

 ficrique debebit facta substitLitione: 

 ^^ —i-S^tt^ 5':e>t*- 7(r/<s_^9f?)/8_ 1 1 (Tf «o _^ etc. 

 uuziz -t- 1 — 2 SI -i-2liô— 2(J -+- 2*1) — etc. 



4- ^' -2S(S3-i- 2 5(S -etc. 

 -+- ^^ —etc. 



atque hinc sequentes oriuntur determinationes : 

 3St =: 1 ideoque S(=:|, 



5 33=:2St ideoque S3 = f^:^=f5, 



7(5: = 2S5-f-?i^ hinc (5:=i:?^:5 4-p:t^ = /fp 



9© — 2 (5; _f- s;)|s:5 ergo zn 5 (T + ^îi^:^ = .ffj, 

 etc. etc. 



