ELIMINANT OF A SET OF GENERAL TERNARY QUADRICS. 



25 



and expanding in exactly the same way, we have 



0000 +±1268 



+ ±00111 -±126'8 - 



-±0048 - ±0048 +±1268' 



+ ±004'8 -±126'8' 



+ ±0123 +±1556 



-±0158 - ±0158 -±1556' 



+ 0456 -±155'6 



-±0456' +±155'6' 



+ ±045'6' -±16711 



- 04'5'6' +±16711 

 + ±04911 +±1788 + 

 -±04'9lT +±17'88 



+ ±0789 + 0789 +±4488 



+ ±0789' -±44'88 



- 0'789 -±4589 

 + 0123 +±4'589 



±126'£ 



•±77812 



(28) The terms common to the two expressions are 



0000 





. +±1268 



+ ±00111 





-±126'8 



-±0048 - 



±0048 



+ ±1268' 



+ ±0123 





-±126'8' 



-±0158 - 



±0158 



+ ±1556 



+ 0456 





-±1556' 



-±0456' 





- ±16711 



+ ±04911 





+ ±1788 



+ 0789 





+ ±17'88 



+ ±0789' 





+ ±4488 



+ 0123 





-±4589. 



±1788 



The remaining terms in each case are fourteen in number, and of course the aggregate 

 of the one group must be equal to the aggregate of the other : that is to say, it must be 

 possible to show that 



-±0048' 



±004'8 



+ ±0456 



+ ±045'6' 



+ ±04911 



- 04'5'6' 



+ ±078'9' 



-±04'911 



+ 07'8'9' 



+±0789 



- 0'456 



- 0789 



+ ±1268' 



-±126'8 



+ ±1556 



-±155'6 



