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† Professor R. E. Allardice.

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† The figure and demonstration refer only to this case. The other case and the consideration of what happens when BC is divided externally are left to the reader.

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* The theorem that A₁B₁C₁ hat the same centroid as ABC will be found in Pappus's, Mathematical Collection, VIII. 2.Google Scholar Chasles has some remarks on the theorem in his Aperçu historique, 2nd ed., p. 44.Google Scholar

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† The figure has been taken from Grunert's article “Dreieck” previously referred to.

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† This property, proved in the manner given, will be found in Maclaurin's Algebra (1748) in the Appendix, De Linearum Geometricarum Proprietatibus generalibus Tractatus, §98 or p. 57.Google Scholar A proof by DrHunyady, E. V. of Pesth, by meant of transversals, will be found in Schlöimilch's Zeitschrift, VII. 268–9 (1862).Google Scholar