Osgood, William F. (William Fogg), 1864-1943, Graustein, William Caspar, 1888-1941, joint author · New York, The Macmillan company · leaf 12
PQ on L iszero. Such a directed line-segment MN, whose end-points areidentical, we may call a nil-segment; to it corresponds thenumber zero. It is evident that in taking the sum of a num-ber of directed line-segments, any of them which are nil-segments may be disregarded, just as, in taking the sum… … M M2 Mx M, Fig. 6segments PP1} PiP2, Pn-iQ, or MMX + M,M2 + • + Mn_xN. This sum has the same value as MN, the projection on Lof the directed line-segment PQ; cf. § 1, (3) : MMX -f MYM2 + • • • + Mn_xN = MN. 6 ANALYTIC GEOMETRY Hence the theorem: Theorem 1. Hie sum of the projections on L of the…
Geometry, Analytic
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