io6 



Pf^// 



At == 5;du4-Taa+ . . 



dp = 5>clii ^ irda 4" - • 



d q =s= Cl d II + q d a -jr 



dr = 9ldu4- tda+ . . 



Tum aequalio proposita in haue alAi; 



o = PX 

 + QY 

 + RZ 



+ st 



+ W9I 

 — 1 



du -j-Tx 



+ H 



+ St 



+ T-K 



+ Uq 

 + Wt 



da-f P;*:' 



-f TW 

 + Uq 

 + Wc' 



db 



+ P%'' 



+ sV' 



+ T'7r" 

 + Uq" 



dh. 



Ouae aequalio ut a du et u libe'relur, ponendiim est 



1 = px+ qy-hrzh-s?; +Tg)-+- uü + wa 



.d"(P:^ + 9n + R^ + ST + T7r + UqH- Wc) 



Deinde quotiens - — i — :^ — — — — 



P::c + Q» + RC + St + T^ + Uq -f Wc 



\alorem eundem servare debet, ponendo 



X, v',... v; . . . . ■)C\ n", . . . r" pro %, r, • • • r. 

 Kst aiitem nunierator 



._ ( Pd";^ + Qd"n + Rd«^ -I- Sd»T +Td''7r4- Ud"q -f ^Vd"c 



( + >i d"P + >,d"Q + ^d»R 4- Td"S 4- Trd'-T + qd"U -j- rd"W 



_ U'd'X+Qd'Y + Rd^Z + Sd'^ + Td^g) 4-Ud»a + Wd»9I 

 ( + ;^jd"P + >id"Q + ^dTi 4- Td"S + ird^'T + qd"U 4- rd"W 



/d\(PX 4- QY 4- RZ 4- S5 4- Tg3 4- U£l 4- W9I) 

 = I — Xd'P — Yd"Q — Zd"R — td-S— ^d*T — üd'U — «KdnV 



' 4-:ed"P4- »id"Q 4-^d"R + Td"S 4-'3rd"T 4- qd"U 4- cd"W, 

 nbi prima pars ex aequaiione f i) evanescit. Et porro i 



d'P = Pd"x 4- Pd"/ 4- P"'d"7. 4- F'M't 4- P'-d'p 4- P'-'d'q 4- P'"d-'r 



= Px 4- f-'n 4- ^'"i + P'^'T 4- P'"^ 4- P"'-.! 4- P'"r; 

 d"r = pd"x4- p"d'v4- p"'d" 7.4-1" -^d-t 4- p^d"p 4-p'-'d"q4- p-"d"r4-p^"' 



= P X 4- P V 4- P"'Z 4- P" 5 4- P\5> 4- P^' 0. 4- P'" 91 4- P>"'; 



