Ideoque ratione ibi expofita tandem elicientur aequationes 

 vliimae, quae rationem difFerentialium d r\ ds^ exhibent, 



§. 22. Quum fit 



ddy coJ.(^-i- i d z fi^. (|> d d tu •— 'us d 0* 



dT^ ' d T' 



hinc obtinebimus : 



ddvj — rud(t)- — Aw Bw _ Apfin.J^ B pfin. $" , 



tl T» v^ u' v^ ' itS 1 



lam fi haec acquatio multiplicetur per 



2.b' dw—2.b'{dpC\\\.t,-Jrpd^QoL^), 

 tumque aequatio difFerentialis : 



pdd^^idpd?-pd^'tm.^cof.i t/?^ y ( J^ B\. 



dr- • T V ■uJ u^ ) 1 



multiplicetur pcr z p' d ^ ; et pofterius produdiiim a prlori 

 fubtrai^atur, confequemur hanc aequationem difFerentio- dif- 

 ferentialem : 



tb^^i-uiddiu — tb^^iudiud^t^ _ 'tp''d^(p^' dd^ + 2jpdp_djj_^^j_b*d<!)' d ^ f,n. ^cof i 

 Ur- dT- '— 



= -2b^p{\n.^i^-^^){dpf\n.^-i-pd^cor.4) 

 -2bp^d^f\n.^{^~±)- 

 cuius integrale erit: 



t2±iu^_P^.^^J^p^y^^' „ ^ , A(5-4-p cq/.^) _^ BSb-pcofJj , p. 



Quae aequatio integralis etiam ex ifta : 



lxdiu—iudx)(tdiu~vj inj^1x-ur-d<r)^ /Ax , Bf , 1-» \ 



facile deriuari pnteft , modo nimirum loco termini 



(^'-P')'-^ adhibeatur (^^ -Z)^ cof. ^^) li^J^f, 

 quippe qmim 



A a 2 Ybi 



