4. METHODJ^S AEOrjTIOyjES DIFFERENT. 



teg"\tiones in^litiiend-.ic , aiitc.^uam ad ac.iu.itioncm qu;in- 

 tit icibiis finit.s txprcir.im pcnicniretiir. H.inc igitur ope- 

 rationum plcrum.]ue dilficillmnirum multiplicitatem per 

 mchodam mciun prordis euito , dum vnica opcratione 

 ft.itim verim acquationem intcgrnlcm clicio. 



§. 2. Qiunropcrc autem modum intcgmndi vulga- 

 rcm totics rcpctcndum , quoties diflcrcnti.ilitas in acqu.uio- 

 nc incd , fccuti in molcrtiirimos calculos incidannb , vni- 

 co c.xcmplo oltcudillc iuu.ibit. Sit crgo prop(»!ita hacc 

 acquatio diflTcrcntiali". tertii gradus d^y—ydx*^ in qui 

 elciiicntum dx conlhins ponitur. llacc aequatio , ctfi mca 

 mcthodo facillime ter intcgratur , tamcn ne quidem mo- 

 dus eam fcmcl tantum intcgr.indi pcrfpicitur. St;itim qui- 

 dcm , qui variabiiis x ip(a dc^lt , apparct cam ad gra- 

 dum (ccundum deprimi pofle. Si cnim ponatur dxzz 

 pdy, ob ^.v conlhns crit o — pddy-\-dpdy ct dcnuo 

 diffcrcnciando o—pd^y-^- "^^dpd dy-^-dyddp. vnde fit 



ddy — - ^p ^ ctd y^- jr-- - p — — Tp 



*^^^y^ , qiii valores in aequ.itione propolita d^y—ydx^ 

 (iibllituti dabunt : 



'-^^^-'-^-ypyy'Ccujp'dy' = 2dp'-pddp. 

 Qiiac cum ncciuc dp nccjuc dy fit confims , (cd con- 

 ftantiae ratio cx acquationc ddy^— -^^7— ^ dcfiniatur , pcr 

 niethodob l(»litas vix vltciius iradari poicll. Transmutaii 

 quidcm accju.iiio poteft in aham formam , in qua aullum 

 difTcrcntiale conft.ins iiifit. Ponatur dp~qdy \ crit 



ddp — qddy-\-dqdy ai ddy zi. ^ dibit ddyzz.^ 



*-p^ , vndc ddp zz — '^'^;— .-\- dq dy 



(icqut 



