The locus of points from which, four given points are seen along four harmonic rays is a point-row of the second order through them.
68. A further theorem of prime importance also follows:
Any two points on the locus may be taken as the centers of two projective pencils which will generate the locus.
69. Pascal's theorem. The points A, B, C, D, S, and S' may thus be considered as chosen arbitrarily on the locus, and the following remarkable theorem follows at once.
Given six points, 1, 2, 3, 4, 5, 6, on the point-row of the second order, if we call
L the intersection of 12 with 45,
M the intersection of 23 with 56,
N the intersection of 34 with 61,