->S=4| ) 60 ( 



ponit, inter?m tamen quiim ad ea, qiiae infra tradentiir, 

 rreliiis intelligcnda, multum conducat, fi «numeratio ho- 

 rum cafuum ob oculos ponatur, eam heic ftatim expone- 

 re, animus eft. Primum itaque cafus heic contemplandi, 

 eo inter fe difFerunt, quod in expreflionis denominatore 

 occurrat, vel V {i -\- n z^), vclV(i— «s'), vel V («x:'— i). 

 Ex prima hypothefi pro ratione figni, quo httera ?n affici- 

 tur, fequentes refultant formulae: 



i-l-naa' i-Hnzz' i -h n z z 



Secunda hypothefis, pro diuerfo figno quantitatis m fe- 

 quentes fuppeditat formulas: 



dzV lJ±-^-^-^- dz V 1^:1:1.^ : dzV ^^^—-L. 



I — naz' I — n z z ' i — n z z 



Denique ex tertia Hypothefi hi fequentes emergunt cafus: 



</2:yij±L^^-^- dzy'-=^^- dzV^^^'. 



nez— i' nzz— I' nza— 1 



Tum vero pro finguHs his formuhs, binae habentur po- 

 fitiones « >> w vel jji^ n, exceptis tamen formulis : 



dzV!^^ Qt dzV^^^=^% 



' — n zz nss— I 



nam pro priori carnm, necefTario eft ni > « et pro fecun- 

 da ny>m, quippe quum ahoquin imaginaria in noftras 

 formulas inducerentur. Nam fi pro priori efle poflfet 

 n^ m, pofita i—nzz quantitate pofitiua, eflTe deberet 

 »22—1, negariuum , ideoque tanto magis m z z — i va* 

 lorem confequeretur negatiuum, vnde necefl"um eft, vt fi- 

 ■eret V "^— imaginarium. Simili quoque ratione de- 



monftratur, non fieri pofle, vt fit in cxprefllone . 



" " ', — I ' ^ 



nzz- 



§. 4. Nunc igitur hinc fcquentes cafus formula- 



rum difFcrentialium emergunt : 



I. dz 



