74 OBSERV. CIRCA RAD. AEQV^AT: 



redigantur partes cum ab y liberae, tum vero ipfam f 

 eiusquc quadratum j/j/ continentes ,. vbi commode 

 eueniet , vt rimul ac binis conditionibus fuerit fatis- 

 fadum , tertia fponte adimpleatur. Hoc autem modo^ 

 calculum inftituendo reperietur. 



l a ppqd p'^ 2 ( s p^ — 27 qq)dlpdq — SA-pqdq '^ i ^pddq- zqddp - 



— {z]dp — 2 pd.^ ) (+ p' -i- 27 (]<]; ^~ z qdp — zpdq, 



•o 6p (d .(? ^ -f-.p d p- dq — qdp^' ) _ ■ dqddp — dpddq 



^ [zqdp~-2.pdq){Ap''-jf-i7qq)~^ zqdp zpdq 



Haec autem aequat^o per ±^-^^2AAA :>pdy-ydp\ 

 multiplicata integr^bil'S redditur , indeque porro pro 

 j aequatio cub;ca latius patens quam propofua elicietur.. 



XXV. 



Aequatio differentialis fecundi gradiis magis- fit 



concinna fi ponatur q q "::=■ ^-~- , fiet enim 



ddv-dv{—'\'^ ^^- ^^ \^^.,{ Apddx _ddpy_tdp*- 

 uuj ^y\dx^p 2X 2ii^x)i~-^ 2 pdx 2p^^^i>p. 



dpd X d p dx __ —dx'^^ \ 



^pX 4p{i-+-JC) z€>X{\~\^x)i 



quae per ^^.'. "^^f ( 2.p dy —y dp) multiplicata et ia* 

 tegrata praebet ,^\\o ^ 



x(' -h x)y J _ydp\^ — c i_-jyy 

 pdx^ ^"-^ Tp I — '^^TTp, 



et ponendo / — ^yp hinc reperitur 



g d z V ; d x 



V ( C -+. « 2 ) -^ X{ I _f-3C) 



quae denuo integrata dat : 



unde tandem eruitur : 



zzz^^-Ail-^-x+Vx^i-^-x^f^Bil-^-x-^Vxd^+xjf 

 ac cubo fumendo 



^'^lABz-\-{A'+B'){l-^'X)+{A'-B')Vx(i+r) 



