6.I. SYLVESTER'S PROBLEM OF COLLINEAR POINTS
If a set of non collinear points in the plane is such that the line through any two points of the set contains a third point of the set, then the set is infinite.
J. J. Sylvester. Question 11851. The Educational Times 46 (NS, No. 383) (1 Mar 1893) 156.
H. J. Woodall & editorial comment. Solution to Question 11851. Ibid. (No. 385) (1 May 1893) 231. A very spurious solution.
(The above two items appear together in Math. Quest. with their Sol. Educ. Times 59 (1893) 98 99.)
E. Melchior. Über Vielseite der projecktiven Ebene. Deutsche Math. 5 (1940) 461 475. Solution, but in a dual form.
P. Erdös, proposer; R. Steinberg, solver & editorial comment giving solution of T. Grünwald (later = T. Gallai). Problem 4065. AMM 50 (1943) 65 & 51 (1944) 169 171.
L. M. Kelly. (Solution.) In: H. S. M. Coxeter; A problem of collinear points; AMM 55 (1948) 26 28. Kelly's solution is on p. 28.
G. A. Dirac. Note 2271: On a property of circles. MG 36 (No. 315) (Feb 1952) 53 54. Replace 'line' by 'circle' in the problem. He shows this is true by inversion. He asks for an independent proof of the result, even for the case when two, three are replaced by three, four.
D. W. Lang. Note 2577: The dual of a well known theorem. MG 39 (No. 330) (Dec 1955) 314. Proves the dual easily.
H. S. M. Coxeter. Introduction to Geometry. Wiley, 1961. Section 4.7: Sylvester's problem of collinear points, pp. 65-66. Sketches history and gives Kelly's proof.
W. O. J. Moser. Sylvester's problem, generalizations and relatives. In his: Research Problems in Discrete Geometry 1981, McGill University, Montreal, 1981. Section 27, pp. 27 1 -- 27 14. Survey with 73 references. (This problem is not in Part 1 of the 1984 ed. nor in the 1986 ed.)
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