DES Sciences yaf 



[{(A'B — AÉ') (A'D — A'D -+- B'C— BC) — (A'C — AC')^\ y (B'E — EFJ -H CD — Ciy) 

 ^_ \(A'D — AD') (A'C—AC') — (A'B — AB'){A'E — A£'-^D'D—BD')] (A'E — AE'-^ R'D— BU) 

 -t- {(AC— AC) (A'E — AE' — B'D — BD'J — (A'D — AD')(A'D — AD'-^~B'C—BC')] fAD — AD')]}, 



^ (D'E — DE') -+- [[(A'C—AC)' — {A'B — AB') (A'D — AD' -4- B'C— BC) ] (CE — CE'} 

 ^_ [■ ^^'^ _ ^^y (B'E—BE'J — ^.-l'c: — /^C; (A'E — AE') ] (^^J'£ — AE'-t-B'D — /?£>'; 

 + [/>4'£ — AE') (A'D—AD'-^B'C—BC) — /^'C— -4CV (B'E—BE)] (A'D — AD')]] 



y ^C'E — C£9-i- /■ [ ('.^T — ^ £7 ^^"L — ^C; — ^//'^ —^57 (B'E — BE')] (B'E — BE'-\-C'D — CD'j 

 ■^_ {(A'B — A B') (A'E — AE'-k- B'D — BD') — (A'C — A C')A'D — A D') ] (CE — CE') 

 ^ {(A'D — AD') (B'E— BE') — (A'E — AE') (A'E — AE' ^ B'D — BD')] (A'D — AD') 



X (B!E—BE')^[{(AC—AC') (B'E— BE')— (A'E—AE') (AD-AD-^-B'C—BC)] (B'E—BE'+C'D—CD') 

 .4- [ (A'E — AE') (A'E ^AE'-t- B'D — BD') — (A'D — AD') (B'E— BE')] (A'E — AE' -\- B'D—BD') 

 -4- {(A'D — AD')(A'D — AD'-^^B'C—BC') — (A'C—AC')(A'E — AE'-^B'D — BD')](C'E-~CE')]l 



X (A'E — AE) =: o, 



équation qu'on réduira facilement à l'équation (M) fui\ante, 

 en failànt attention 



r ." qu^ (AC— AC) (B'D — BD') — (A'D — AD') (B'C— BC) = (A'B — AB') x (CD — CD'). 



2.° que (A'E — AE') (B'C— BC) — (A'C— AC) (B'E — BE') = — (A'B — AB') (CE — CE'). 



3 .° que (A'D — AD') (B'E—BE'J — (A'E — AC) (B'D — BD') — (A'B — AB') (D'E — DE'). 



4." que (CD — CD) (B'E — BE') — (B'D — BD') (CE — CE') — — (B'C — BC) (D'E— DE'), 



YA'E—AE')* — } (A'B—AB'I(D'E—DE'J ' 



-^(A'C-ACl(CE-CE'){ ■ -^i(A'B-AB')(B'E-BE') (CE-CE) 



.(M).... - (A'D-AI»(B'E-BE')V^'^-'^^'^'-i(-^'^-^'^')(B'I>-SD'J(D'E-DE')i 



- (AD-ADJ(CD-Ciy)) ■*-zlA'D-AD')'(CE-CE') \(A'E-AE'X 



-H (A'C—AC) (B'E—BE')'- / = "• 



H- 2 (A'C—AC')(A'D—AD')(D'E—DE') \ 

 — (A'C—AC')(B'C—BC)(D'E—DE') 



:-V î (A'B—AB') (A'D— AD') (B'E— BE') ^ _h (A'C— AC)' (CE— CE') 



^ (A'D—AD')'~(A'B—AB')(B'D—BD')' j —2(AB—AB')(A'D—AD')(C'E—CE') 



l 



2(A'B—AB') (A'D— AD') (CD— CD') I — (A'B—AB')(B'C—BC)(CE-CE'N'^^~^^'^' 



- (CD-CD) (A'C-AC)' \ ^2(AB-AB')(B'E-BE')(B'D-BD'j\ 



— (B'E-BE')(A'C-AC)' f^^^ ^^ ^ — (AC-AC)(A'D-AD')(B'E-BE') 

 (A'C—AC) (A'D—AE^l (WD-BEy) 



i 



r^(A'B—AB')(B'C—BC)'(B'E—BE/\ ^A'B—AB')(B'E—BE*l 



Cfc (A'B-AB-) (B'C-BC) (CD— CD'J J ^ A'B-^AB') (CD-CD'\ ^^'^~ ^^^'^ 



Mém. iy(i^\ ■ $ Ç 



