But the symbols of ordinary algebra do not necessarily denote numbers; they may, for instance, be interpreted as coplanar points or vectors.
For his speculations on sets had already familiarized him with the idea that multiplication might in certain cases not be commutative; so that, as the last term in the above product is made up of the two separate terms ijyz' and jizy', the term would vanish of itself when the factorlines are coplanar provided ij = - ji, for it would then assume the form ij(yz' - zy').
Coplanar substitution in four hydrogen atoms would involve the pushing apart of the iodine atoms in four horizontal directions.
Since CE equals BE these directions are equally inclined to, and coplanar with, the normal to the mirror.
Addition of their several projections agreed with the assumption of Buee and Argand for the case of coplanar lines.