Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T07:06:57.603Z Has data issue: false hasContentIssue false
  • English
  • Français

Isogonic Centres of a Triangle

Published online by Cambridge University Press:  20 January 2009

J. S. Mackay
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If on the sides of a triangle ABC equilateral triangles LBC MCA NAB be described externally, AL BM CN are equal and concurrent.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , February 1896 , pp. 100 - 118
Copyright
Copyright © Edinburgh Mathematical Society 1896

References

page 100 note * Davies, T. S. in the Gentleman's Diary for 1830, p. 36.Google Scholar

page 101 note * In the Appendix to his treatise De Maximis et Minimis, pp. 144, 150 1659).

page 102 note * See Nova Acta Academiae … Petropolitanae XI. 235–8 (1798)

page 103 note * W. S. B. Woolhouse in the Lady's and Gentleman's Diary for 1865, p. 81. His proof of (1) ia different from that in the text.

(1) and (2) are said to be given by Heinen, Ueber Systeme von Kräften (1834).

page 103 note † Turnbull, John in the Lady's and Gentleman's Diary for 1865, p. 78.Google Scholar

page 103 note ‡ Rev.Mason, William and Dobson, Thomas in the Lady's and Gentleman's Diary for 1865, pp. 76, 78.Google Scholar

page 104 note * D will be used for a different point in (9).

page 104 note † Rev. Mason, William in the Lady's and Gentleman's Diary for 1865, p. 75. His proof is different from that in the text.Google Scholar

page 104 note ‡ Rev. Mason, William in the Lady's and Gentleman's Diary for 1865, p. 74Google Scholar

page 104 note § The first of these expressions is given in T. 8. Davies's edition of Hutton's Course of Mathematics, I. 470 (1841). It is said to occur also in Heinen, Ueber Systeme von Kräften (1834)

page 105 note * Levy, W. H. in the Lady's and Gentleman's Diary for 1855, p. 71Google Scholar

page 105 note † Woolhouse, W. S. B. in the Lady's and Gentleman's Diary for 1865, p. 81.Google Scholar

page 105 note ‡ (11)–(14). Rev. Mason, William in the Lady's and Gentleman's Diary for 1865, pp. 74, 75.Google Scholar

page 107 note * (15)–(17). Woolhouse, W. S. B. in the Lady's and Gentleman's Diary for 1865, pp. 84, 82. See the reference to Fuss on p. 102.Google Scholar

page 107 note † Dr Rutherford in the Ladies' Diary for 1825, p. 47. Probably, however, the theorem dates farther back.

page 107 note ‡ Prof. Uhlich ascribes this method to Kunze.

page 108 note * This is substantially the mode of proof given in the Ladies' Diary for 1826, p. 38.

page 108 note † Dr John Casey. See his Euclid, p. 264 (2nd ed., 1884)

page 108 note ‡ Ascribed by Professor Uhlich to Féaux, Arnsberg Programm, p. 4 (1873).

page 109 note * Stated by Reuschhle in Schlömilch's Zeitschrift, xi. 482 (1866).

page 109 note † (23)–(29) Woolhouse, W. S. B. in the Lady's and Gentleman's Diary for 1865, pp. 86, 83, 84.Google Scholar

page 111 note * MrWatson, Stephen in the Lady's and Gentleman's Diary for 1865, p. 78Google Scholar

page 111 note † (31–(36). Woolhouse, W. S. B. in the Lady's and Gentleman's Diary for 1865, pp. 84, 85Google Scholar

page 113 note * Thomas Weddle in the Mathematician III. 1ll (1848). The solution is taken from p. 165.

page 115 note * The proof given here will be found in Steiner's Gesammelte Werke II. 729 (1882)