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Early History of the Symmedian Point

Published online by Cambridge University Press:  20 January 2009

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In 1873, at the Lyons meeting of the French Association for the Advancement of the Sciences, Monsieur Emile Lemoine called attention to a particular point within a plane triangle which he called the centre of antiparallel medians. Since that time the properties of this remarkable point and of the lines and circles connected with it have been investigated by various writers, foremost among whom is Monsieur Lemoine himself. The results obtained by them are so numerous (indeed every month adds to their number) and so widely scattered through the mathematical periodicals of the world that it would be a task of considerable magnitude to make even an undigested collection of them. It is the purpose of the present paper to state those properties of the point which had been discovered previously to 1873. A short sketch of some of them will be found at the end of a memoir read by Monsieur Lemoine at the Grenoble meeting (1885) of the French Association, and in a memoir by Monsieur Emile Vigarié at the Paris meeting (1889) of the same Association. The references given by Dr Emmerich in his Die Brocardschen Gebilde (1891) are very valuable. It is a pity they are not more explicit.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1892

References

page 93 note * Nouvelles Annales de Mathtématiques, 2nd series, XII. 364 (1873).Google Scholar

page 93 note † Nouvelles Annales de Mathématiquet, 3rd series, II . 451 (1883).Google Scholar

page 93 note ‡ DrGrobe, B. W. in Grunert's Arckiv der Mathematik, IX. 251 (1847).Google Scholar

page 93 note § DrEmmerich's, A. Die Brocardschen Gebilde, p. 37 (1891).Google Scholar

page 93 note ‖ ProfNeuberg's, J. Mémoire sur le Tétraèdre, p. 3 (1884).Google Scholar

page 93 note ¶ Educational Times, XXXVII. 211 (1884).Google Scholar

page 94 note * I am not quite certain at what date, for my copy of Vol. III. is imperfect. But at p. 80 a letter is printed, dated March 1st, 1802, and at p. 83 another dated Sept; 8, 1802. It may therefore be presumed that the question was published in 1803.

page 95 note * See Pappus's Mathematical Collection, VI., 12. The same theorem differently stated is more than once proved in Book VII, among the lemmas which Pappus gives for Apollonius's treatise on Determinate Section.

page 96 note * This account of Schulz's articles is taken from Férussac's Bulletin des Sciences Mathématiques, VIII. 2 (1827).Google Scholar

page 97 note * Republished in Steiner's Gesamnulte Werke, I. 191–210 (1881)

page 97 note † See the following paper on Adams's Hexagons and Circles.

page 98 note * Monsieur Clément Thiry in Le Troisième Livre dt Geométrie, p. 42 (1887).