Page:The principle of relativity (1920).djvu/260

 D_{x} is therefore the projection on the y-z-l space of the perallelopiped formed out of these three four-vectors (P, U^*, V^*), and could as well be denoted by Dyzl. We see directly that the four-vector of the kind represented by (D_{x}, D_{y}, D_{z}, D_{l}) is perpendicular to the parallelopiped formed by (P U^* V^*).

Generally we have

(Pf) = PD + P^*D^*.

[therefore] The vector of the third type represented by (Pf) is given by the geometrical sum of the two four-vectors of the first type PD and P^*D^*.

[M. N. S.]