Geodesic
Extensions of Sylvester's Theorem
Canadian mathematical bulletin, Tome 9 (1966) no. 1, pp. 1-14

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DOI

Sylvester [7] proposed the following question in 1893. If a finite set of points in a plane is such that on the line determined by any two points of the set there is always a third point of the set, is the set collinear? Equivalently, given a finite planar set of non-collinear points, does there exist a line containing exactly two of the points? 
Balomenos, Richard H.; Bonnice, William E.; Silverman, Robert J. Extensions of Sylvester's Theorem. Canadian mathematical bulletin, Tome 9 (1966) no. 1, pp. 1-14. doi: 10.4153/CMB-1966-001-6
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     title = {Extensions of {Sylvester's} {Theorem}},
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