motusPlanetarum. 15 



§. VII. Jam iterum ambas vires V & T commode a 

 fe invicem feparare licet , ut pateat quid utraque feor- 

 fim praiftet. Nam I x cof. -p -+- II x fin. <p dat 



d dp cof. q> -*- dd qfin. <p = — | V d t- 

 Deinde II x co/^ <p — I x fin. <p prxbet banc a:quationem 



</ </ <7 cq/T (p — c/ d p fin. <p = — 4 T d t % 

 at ex tertia vi i? nafcitur xquatio ddr~ — | R dth 

 Nunc igitur recordandum ell nos fupra pofuifle 



p = cof. q> ; q — x fin. q> & r = .v fang". 4- 

 unde loco quantitatum fubfidiariarum^, 5;, /-, elementa 

 noftra principalia cp, 4 & ■* in calculum introduci pore- 

 runt. Tres autem emergent sequationes , qua; propterea 

 his tribus dementis deriniendis fufficient : atque ita tota 

 inveltigatio a principiis mechanicis ad Analyfm puram 

 traducetur. 



§. V 1 1 1. Cum fit p =s x cof. (p&q = xfin. <p erit dif- 

 ferentiando > 



dp—dxcof. cp — x d<pfin. <p & dq=dxfin. <Q-*-xdip cof.Q 

 denuoque differentiando 



ddp=ddx cof<p — 1 dxdq fin . <p — xdq 1 cof. <p —*-xdd <pfin.<p 

 ddq=ddxfin. q>-i-zdxdq cof.q> — xd<p -fin. Q-\-xdd($ cof. cp 

 unde per combinationem elicitur 



ddpcoj.<$-\-ddqfin.<p = d d ' x — xdty 1 

 & d dqcof.q>~ddpfin.qi=idxdq)-i-xddq). 

 .Valorem autem ipfius r = x tang. 4 nulla adhibita evo- 

 lutione tantifperretineamus, donee compererimus, quo~ 

 modo aptilfime eum traftari conveniat. Hoc itaque 

 pa&o totum negotium ad refolutionem triura fequen- 

 tium azquationum erit perdu&um : 



I. ddx — x dtp- = — £ Vd t z 

 II. 2dxdq>-*-xdd($== — i Tdt 1 



III. dd. x tang. 4, as — f R dt\ 



