Veblen, Oswald, 1880-1960, Young, John Wesley, 1879-1932 · Boston, New York [etc.] Ginn and Company · leaf 102
2 is the point in which I meets the line of R2. Hence A2 is apoint of R2 (Theorem 7). Now let I be any line of the net R2, and let P, Q be two pointsof the net and on I (def.). If one of these points is a point of R1 orR2, the theorem is proved by the case just considered. If not, twolines, each… … Then if I meets the lines of R1 and R2 in ij* and P2 respectively, thequadrangle PQA1B1 gives rise to the quadrangular set Q(P2A2B2,OB2A2) of which five points are points of R2; hence P2 is a point of R2(Theorem 9). Px is then a point of Rx by the first case of this proof. Theorem 11. The…
Geometry, Projective
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