to Non-Metrical Vector Algebra. 



127 



not re-cross one another; for they already crossed one 

 ■ another in T n . 



Thus we have the announced distributive property, 



A(B + C)=AB + AC. 

 And since the commutative law holds as well, we have also 



(A + B)(C + D)=AC + AD-hBC + BD, 



and so on. 



In fine, all ordinary rides hold for the generalized scalar 

 product of vectors, as defined above by means of the standard 

 conic. 



The far-reaching geometrical consequences of this simple 

 property are obvious. Every formula known from euclidean 

 geometry (or "trigonometry") will continue to hold, with 

 the only difference that tensor or "size" of a vector will 

 not stand for the number of centimetres or inches contained 

 in it, but for the number of equal projective steps with 

 reference to the conventional unit-conic fc and 7-line, and 

 that right angles (orthogonality), equal angles, etc., have in 

 our case a different, more general meaning. 



