PERTVRBATI PLANETARVM. X47 

 T = ^ + jT^ + -jdr , vel 



dZ d_v ^^ dgcoS.ir , dv j^jo/.i^ , , d^^/m.w 



Z — V ^ jin.j -T- icn^.a- OD rfW — 7^^|:F' 



Cum igitiir fit rt'C|)irrt'o--{-</v{ycorw , adipiscimur 



dZ dv, dt • ^ ^^ 



rfXcor.^+^Yfm.O^^^^-cor.fx+^^^-^-i»^^ 



<fi'cof|ji.+ 7J^(r(fin.crcof.a-cor.wlin.(^— vp]+cor.o-W(^-\{^) 



-cof(0-vl.)) 



idcoqiic 



r/Xcof.0 + ^Yfm.^=rt'i'cof./j.-cv/4)(nn.o-cof(^-v|^) 



— cof 0- coC u fm. (0 — v{^)). 

 Qiiocirca acquatio noftra inucnta crit: d.{dv'^i-rj(/(p^j 



— —io.dt^dv{r~ + .iJ— B?/cof \x[~i — —^ 



— 2 v.^dt' d(^. f/ v( fin. (7 cof ( ^ — vj^)- cof ccof co fin; 



XVII. . 



Ilanc cuoUitioncm formulac fl^Xcof O + ^/Yfin.d 

 nimis prolixam nuilto concinnius cx ipfis valoribus 

 pro X ct Y inucntis conficcrc licct. Cum cnim 

 eorum differentialia rite prodcant , fi anguli v^/ ct cj 

 vt conflantcs tr.nftentur ct pro drj fcribatur d(^ hacc 

 difTerentiatio pracbct : 



^X— fl^iJ^cofo-cofvly-fin.o-cofwfin.vly^-rrt^Cl^^nii.o-cof vp 



-^ cof 0- cof 0) fin. vj^) 

 </Y— </t-(cof o-fm. vl-^+fin .ccof ucof ^^^^-Crt^Cp^fin .crfi n . v|y 



— cof crcofw cof v}y) 

 T a vude 



