->¥.^ ) X74 ( IfS- 



(^xdy —J^x) {tdy — ydt) + [xdz — zdx) {t^z — zdt) 

 zz xtidy'-\-dz^)-{xdt-\-tdx) {ydy-{-zdz)-\-{y^-\-z^]dxdt 

 — xt^div^-i-iVdf^^-^-ivdzv^xdt-i-tdx^-^iv^^dxdt , 

 quae etiam hac forraa repraefentari potcfl;: 



{x d IV — IV d x) {( d IV — IV d t) -\~ t X w* d C|)*. 

 Nunc quum fit: 



d w zn d V fm. yi -^ V d 7} cof. -y) ; 



d X ::r d V cof. 7] — v dy^ fin. -v] ; erit 



x dw — w d X — 'd'' dy\\ fimilemque ob rationem: 



t d '-u; — IV d t ~ u" d ^ ; hinc 



{x d IV — w d x) [t d w — nv d t) — v"^ u^ d 1] d ^, 

 Vlterius eft 



m- a' cot. e cot. y^ - ^illi^-^oli^ — LiL^^.^' ; 



ob cot.?/:z^^; cot.^— ^^. Denique cof.-vi — ^; cof.O:^-^, 



quamobrem patct iflam aequationem: 



(xdiy — 00 Jar) (/dio - ludf) -1- /xiu-d(p« /i/A* i_Bf i n^ 



s^» » liT "j~ r 'T- ^; j 



perfede coincidere ciim illa: 



■u-v^i-f,i<i-^-m^j(i>^coKim .j^ ~a{k cof. -v] -f B cof. 0} + F ; 



pofito nimirum F — « D. Ideoque hinc conchiditur quo- 

 modo in fubfidium vocata hac aequatione (V.) fi illa com- 

 binetur cum aequatione (IV.) modo in §. 1 1 expHcato, 

 ad aequationem (111.) pcruenire licet, quac iterum cum 

 acquaiione (IV.) combinata Problematis fohitionem exhibet. 



%. 15. Caeterum diredc quidem per combinatio- 

 nem nequationum (IV.) et (V.) nc^ntium fcquenti ratione 

 perficitur. Ob cof v{^ — ^-1±-"'.^' fiec 



[v -\- uY — a' — 2 u V {i + cof \|y) ; 

 [v — u^ — a' zz — 2^' u {i — cof. v|v ) ; 



hinc 



