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P. Böhmer in an elegant paper, published in the Math. Annalen60 (1905), pp. 256–263, was the first to prove that for ananalytic oval, in which the osculating conic at each point is an ellipse, the conic through any five points is also an ellipse. The methods employed by him are by themselves quite interesting, specially the use he makes of thecurvature form.
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Mukhopadhyaya, S. Generalized form of Böhmer's theorem for an elliptically curled non-analytic oval. Math Z 30, 560–571 (1929). https://doi.org/10.1007/BF01187789
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DOI: https://doi.org/10.1007/BF01187789