187 

 NOTE 11. 



This property is derived in a similar manner. 



AH X AI = AOx AG+AI -v whence by addition 



AH X — AF-AOX-AD-AH i(AH+AB) x (AI— AF) 



V = AO X (AG+ AE+ AC—AD)— 

 AB X AI=AOx AC— AB l(AH + AB+ AF— AI) 

 AB X — AFri AO X AE— AF J = (by Lemma II.) AO x AO, or AO*. 



NOTE III. 



In like manner this property is derived. 



AG X AD=AO X AG— ABv whence by addition 



AG X— AC = AO X AC— AF |(AG+AE) x (AD— AC) 



> = AOx (AG+AE+AC— AD)— 

 AE X AD = AO X AI— AD\(AH+AB+AF— AI) 

 AE X— AC= AO X AE— AH'^ =(by Lemma II.) AO X AO, or AO*. 



cc2 



