Opuscula. 193 
Eadem methodua , quse in potentiis attrahentibus , va-» 
let etiam in repellentibus , Centrum repulfionis initio fit in 
A ( Fig. 3.) ejus velocitas — C; corpus fit in B, ejus ve- 
locitas rrr r j diltantia A B ~ . Duni centrum percurric 
A S ~ j- , corpus conficiat B X =: ^ : diitantia S X ~ z. — <? 
'^s-^x. Vocata velocitate centri in S — Vy corporis in X 
— «, eodem , ac antea , modo pervenies ad xquationem 
. — — - — . -D - — ; led vocato tempore — ^ , eit — — — : 
crgo ^-^- ~ ~^ . -D , & fumpto tamquam mancnte ele* 
mento a t , fiet z dt — . —r- . Pone — r r , ql ma^ 
p dt tfp ^ 
veniet z d t'' = r^ dd x ; kd d x ^ d z< — d s ^ ^ddx^dd-L 
— d d s: igitur zdt^ — r^dd% — r^dds, Quoniam Q^i ds ^ 
, erit difFerentiando i- = -^-^r^ : Wimxzdt^ = r^dd% 
r ^^^^5 ^ tranfpofitis terminis dVdt z d t^ 
— r^ d d s z= o , 
Ut methodum applicem , multiplico aequationem per q?, 
ut fit — p d Vd t ~\- zcp d t^ — r^ cp d d z :zz o i quam in hunc 
modum diftribuo 
~<pdVdt-\-zcpdt'--+r'-d(pdz'^r'-(pddx> _ Omnes 
— r^z d do;) -^r ^ d d (p — r^ d(p d z> 
termini integrabiles funt , fecundo excepto ; igitur fi hic — o , 
integrabiiis erit aquatio. In hac fuppofitione fi fiat inte* 
gratio proveniet f(pd F-f- r^ z d(p — r^(p d z —o^ feu fa- 
da divifione per r^ crit ^fcpdV-i-zdip — (p d z ~ o . In 
accipienda fummatoria conftans addenda eft. Fiat jam fe- 
cundus terminus = o , & determinabitur (p . Erit (p d t^ 
~ r^ d d (p . A^Tumpto finu toto r, integratio compieta 
Cft 0) zr: ^ . C h . ^ -4- jB . S h . ^ . 
Duos valores maxime fmiplices (p eligamus, nempe 
= Ch.2f,qDr=Sh.^, quibus fubilitutis in acquatione inven^ 
ta duas scquationes formemus dt 
Tom, VL B b T 
