AEQVATIOWM DIFFERENTIAUVM, 3 . 

 ex quarum prima deducimus : 



m Q, Qdx 



€t exfecunda: N = ~- 



qui valores pro M et N in tertia fubftituti , dant : 

 Cum autem fit , fumto differentiali dx conftante , 



,»« P _L ,-LdP PL_g d_d L .^ _ g_ L 



" iV1 Q, " Q.Q. T Q.dx ~T- Q^Q^d x > ent 



TSJ — R __ pdL _ . Ldp 1 PLd Q . 1 __i?L L - dgdx 

 ^— Q_ ~ 2 Q.Q_dx~ * Q_Q.dx-i~ 2 Q?dx~r 2 Qj^dx*~ 2 Qi _■** 



_. ji\j — ppdL 1 ?_____ ppL ^Q - _P <*<*__. 1 _______ ____• 



etfli\_ _ac_."T _ac_r »0? "jaQ^T^- a 

 quod ergo illius difFerentiali debet aequari , vnde fit : 

 o - QQd*L -3 Q_dQddL -P P QQ</ L ^x*-2 Q_Qd?dLdx 



+ 3 </QV L + 2 P QdQdL dx - QdLddQ++Q_*RdLdx m 



-?QQLd?dx*-±-??Q_LdQdx* -QQLdxdd? 



-\~?QLdxddQ 

 <+- 3 QLd?dQdx-3 ?LdQ*dx-{- *Q_'LdRdx u 



-zQ^RLdQdx* 



Haec autem aeqnatio fi per q+ multipltcetur , integrari 

 poterit , eritque eius integralis 



f ft Iddl L d L _ Q. _ L* P P L L d x» ILdP_ * 



vonit. — aa — - q3 _ aa ■ 2 aQ _ aa~ 



PLLdad* , 5 RLL(i„l 



quae in hanc formam abit : 



2 E Q 3 „V ± 2 QL „VL - 2 VdL dQ- QdL* - P P QL L* 7 ** 



-2QLL_/P^+2PLL_'Q^r + 4QQRLL_'.;\ 



Qnodfi ponatur L — z z, aequatio induet hanc formam: 



*-—,— --: 4Qddz-4dQdz~z{??Qdx*+zQd?dx 



--VdQdx-^.QQRdx' 2 ). 

 E 2 Coroll. 1. 



