i5o 



aequatio piior in hanc abit : 



XVI. uda 



2 (V:lx -h Ç_dy ■+- Rdz) 



M 



12) Sint pono dy ^^ pdx , d%:=:qdx; erit 



dy z:=. pd-x -\- dpdx y d^-L^iqd^x -\- dqdx, 



d'P=- d/ > et dq~ ^^— , 



in qnibus si loco d^x, d^y et dH eorundem valores, ex 

 aequationibus I, Il et III substituantur; erit 



dp = '£ (Q- Prt et dq = lS^AR-Rq), 

 sive ob -: = li^2!, dp^ °^"'r:^''' (a-P/.) et 

 d7 =: '■"'■ t.r^^'' (R-P-y): "nde ob p = g et <,=:g, 

 sequentes prodeunt aequationes : 



XVII. adx — Vdy — '-^^^^^^^^gp^'^ 



XVIII. Rdx — Pdz = ""^^'"^ir"' — . 



Si pono aequatio XVII. ducatur in dz et XVIII. in 

 dy et una ab altéra subtrahatur, erit 



X'TV J? J r\J mi^(dyd'z — dzd^y) 



XIX. Kdy • — Q_dz rz: ■ — ^^^^^ — . 



lisdem autem aequationibus, priore per altéra m divisis, 

 qanciscemur aequatioiiem 



^^' Rdx — Pdz dxd"z — dzd^x ' 



ex qua colligitur sequens : 



XX. P (didy — dyd^z) -h Çl{dxd'z — dzd'x) 

 + R (dyd^x — dxdy) :^ O. 



