Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 24
PQ on L iszero. Such a directed line-segment 3fX, 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… … ill M^ ilf J il/3 n-2 M^.iN Fig. 3segments PPi, P1P2, • • •, Pn-iQ, or 3f3f, + 3f,3f2 -f- • • • + 3f„_rN. This sum has the same value as 3fN, the projection on Lof the directed line-segment PQ; cf. § 1, (3): JOfi 4- 3Ii3L -\- ■•■ + M„_,y= 3fN. 6 ANALYTIC GEOMETRY Hence the theorem: Theorem 1. The…
