RESULTANTS. 145 
It will be observed that these determinants differ only in 
the last column. 
179. Equations of Condition. Equating coefficients of a, 
y, and z, in the two forms of T., viz., equations (15’’) and 
(17), we get the following nine equations : 
B g A B G 0 
1s (Oh Ab Bie Ciee cA Bt ice! 0 
| BY GC! eet = BUEN CU CEAE TUBES GU Ca I 
Bo! Cy! Ito! Aa!’ 0 0 A, B, C, A, 
0 0 An Bike Gi! VerAGl 
0 0 A By! Cy! ky! Ay! 
4 Cones Bee aC 0 
ii eae kee Wore Al Cl kA kB kC 0 
A,! C. InAs! == | A” GUAM Ti BM kiG! 0 Il 
Ao!’ Coll Kol Ao! 10 0 A, B, C, AG le 
0 0 A, By Cy! kA 
0 0 A By Cy" iy Ay! 
A B a B C 0 
Ab B, Ab AUB cA kBY VicC! 0 
| Ao! Bi ican! ea AY Bi kKEAU KBE iu @ | Ill 
Aol! Boll Keo! Aa!’ 0 0 A) B, Cy A, | 
OPO AL SBE NCH ierAy! 
On Oe AG! BUG) ViePAnt! 
Be CoP ABU RG. Aso. 1) 
| 7 - + i CW It Al af BU A Ol 0 
BOC ar ere ae ne few ees: 7 
2 2 ie ON OAT Bia RCT Ski By 
10 OF FAG Bi Gi ky/By! | 
|A C A B (63 0 
|A’ C’ kA’ kB’ kC’ 0 
me as nee 2 AV (Off? kl A” k/B” kc” 0 V 
ee Ce le ORO neAG BN C.- SB. |* 
: = = Pia 0 0 A,’ By Gi! ky, By 
lo 0 Ai’ Bi" Ci! ky By" 
TAR BY 7A! B (G; 0 
AIBA SicB? kC’ 0 
A a 4s 
ve — at | A” BURA" BBY kev 0 VI 
‘Aa! Bo! Keo! Bol! | emer li ()) 0 A, B, Ci B, % 
2 3 See | @ © AW TEV Gi Valext 
0 OARS EBV CHO Tet B! 
