DIERENTIO-BIFFFFNERE TIAL. 1 3 1 



eadem manet. Poffent adhiic addi f.v 'j~"'~'^.v' 

 4j^—i et huiusmodi quotquot libuerit •, prout exem- 

 plaparticularia , adquacreducenda generalis accom- 

 modaridebet,pluribuspaucioribusue conftant termi- 

 nis.Tres veroterminos,vt dixijasfumfiire lufiicit: cum 

 plurcs aiium reducendimodum non requirant. 



12. Aequationem propofitam reduco fubfti- 

 tuendis loco z, f^ et iocoj, c^^t. Cum igitur fit x— 

 c'^ et j— f^/; erit dx—c^^chv et dy — c^dt-^-tdv): por- 

 roque ddxzzLc^^^ddv -{- dv^ ) et ddyn:c\ddt-\-2.dtdv-{- 

 td-v'^-^- tddv). Quia vero dx ponitur conftans , erit 

 ddx—Q', liincigitur ddv—-dv-j hanc ob remhabebi- 

 tur ddy—c^^i^ddt-^-zdtdv). Ponanturhi valores in ae- 

 quatione loco x^y^dx.dy et ddy^ transformabitur ea ia 

 fcquentem:rt'f^/-'^' ' dv'^(dt-{-tdv)--^-i-bc'"t-''- ' dv^dt-h 

 tdv)'^-i—c'' {ddt-\- zdtdv). Qiiae diuifi per c"^ abibit in 

 hanc at—"^- ' dv^{dt-^tdv)'-P-\-bt -«- ' dv^^idt-^-tdv) 

 ^'-~'i—ddt -\- zdtdv .InhiQcnm d.Q^\tv ^ono dv—zdt e- 

 Xit ddv:=::zddt-{-dzdt, fed ddv — — dv-—-z^dt'^ ergo 

 ddt——zdt^-^^. Hinc ifla obtinebitur aequatio, 

 fil-m-i z^dt^idt-^-ztdt^^-P -f- ^/-"-' z^^dt^ 

 {dt-^rZtdtf-iziLzdt^^-^-^^-^-^zdf- feu haec ordinatior 

 (^-'^-''z^dti I -+- zt)^-P-\-bt-''- • z^dt{ I -\-zt) 2-5— zdt-'^*. 



^13. Aequatio haec differentialis primi gradus 

 vnico adu ex propofita elici potuiflet, fiftatimpo- 

 fitum effet x^c^^^^ tty^^^H-, vnde foret d.v~c^'"^^ 

 zdt et dy—c^^^^Xdt-^-tzdt) ; atque dd.x—c^^^^ (zddt-h- 

 dzdt-\-zzdt")—o. quare.ddt——zdt^-dzdt:z. Hocin 

 vfum vocato habebitur ddy—c^''^\zdt--dzdt:z). Pro- 

 pofitum fit hoc exemplum j®'"^' ddy—.x^d.x'^ , mute- 

 tur id in ddyzzLx^^y-^-^dx-. Oollato hoc cum gene- 



R 2 ra» 



