Abstract
MR. J. S. MACKAY of the Edinburgh Academy, though not able to trace “Simson's line” to Simson's works (see my notice of Dr. Casey's “Euclid,” NATURE, October 23, p. 607), has furnished me with the following account, which may be of general interest:—“The theorem that the orthogonal projections of a point on the circumference of a circle upon the sides of an inscribed circle are collinear is ascribed to Robert Simson by Catalan in his Théorèmes et Problèmes de Géométrie Elémentaire,' and he speaks several times of la droite de Simson. This book of Catalan's is, I fancy, better known in the United Kingdom than many other Continental works where the same statement is made; and I conjecture that we have adopted the name from Catalan. It may, however, be the case that we have taken the information from Poncelet's Propriétés Projectives,' § 468, where it is said that Servois attributes the theorem to R. Simson. The passage where Servois makes this ascription occurs in Gergonne's Annales de Mathématiques, vol. iv. p. 250, and it is unsatisfactory enough: La méthode qui vient d'être indiqué plus haut pour déterminer le point C repose sur le théorème suivant, qui est, je crois, de Simson. I cannot carry the ascription of the theorem to Simson farther back than to Servois, and though I am not positive that Servois has made a mistake, yet I think it highly probable. The extension of the theorem to the oblique projections is attributed by Catalan to Chasles. It is due to Poncelet, and is given in the section quoted above.”
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THE WRITER OF THE NOTICE Simson's Line. Nature 30, 635 (1884). https://doi.org/10.1038/030635a0
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DOI: https://doi.org/10.1038/030635a0
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