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Properties connected with the Angular Bisectors of a Triangle

Published online by Cambridge University Press:  20 January 2009

J. S. Mackay
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When points and lines are not specifically designated in the course of the following pages it will be understood that the notation for them is that recommended in the Proceedings of the Edinburgh Mathematical Society, Vol. I. pp. 6–11 (1894). It may be convenient to repeat all that is necessary for the present purpose.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , February 1894 , pp. 37 - 102
Copyright
Copyright © Edinburgh Mathematical Society 1894

References

* Arthur Lascases in the Nouvellcs Annnles, XVIII. 171 (1859).Google Scholar

* Wilkinson, T.T. in the Lady's and Gentleman's Dairy for 1862, p. 74Google Scholar. The demonstration given is also clue to him, as well ax part of (4). See the Diary for 1863, pp. 54–5.Google Scholar

† Leybourn, 's Mathematical Repository, new series, Vol. I., p. 22 of the Questions (1804).Google Scholar

‡ Gergonne's Annales XVIII. 302 (1828) or Steiner's Gesammelte Werkc, I. 223

* Part of (11) is given in Hindi's Trigonometry, 4th ed., p.304(1841).Google Scholar

* (13) Half of this is given in Hind's Trigoonometry, 4th ed., p. 304 (1841).Google Scholar

* Levy, W.H. in the Lady's and Gentleman's Diary for 1856,p.49Google Scholar

* Levy, W.H. in the Lady's and Gentleman's Diary for 1856, p. 49. The first part of the theorem, however, is given in Leyboum's Mathematical Repository, old Series, II. 25 (1801).Google Scholar

* The first parts of (24) and (25) are found in Leybourn's Mathtmatical Repository, old series, II. 24, 235 (1801).Google Scholar

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

† Parts of (28), (29), (30), (31), are found in Leybourn's Mathematical Repository, old series, II. 236, 25 (1801).

* Levy, W.H. in the Lady's and Gentleman't Diary for 1867, p. 5Google Scholar

* Fuhrmann, 's Synthctische Bewcise planimetrischer Sätze, pp. 58–9 (1890).Google Scholar

† Townsend, Rev.R. in Mathematical Questions from the Educational Times, XIV. 76 (1870)Google Scholar.

* Whitley, John in the Gentleman's Mathematical Companion for 1803, p. 38.Google Scholar

* Part of this is found in Leybourn, 's Mathematical Repository, old series, I. 284 (1799).Google Scholar

* Parts of (7) and (8) are found in Leybourn, 's Mathematical Repository, old series, I. 283–4 (1799)Google Scholar

* Leybourn, 's Mathematical Repository, old series, I. 285 (1799).Google Scholar

* Leybourn, 's Mathematical Repository, old serieis I. 368 (1799)Google Scholar

* For (1),(2),(3),(5),(8) see Leybourn''s Mathematical Repository, old series. I. 285, 368, 367, 369, 368 (1799).

† (9) and (10) are given by Wilkinson, T.T. in Mathematical Questions from, the Educational Times, XXIV. 28 (1875).Google Scholar

MrRobinson, G. jun.,Hexham, , in the Lady's and Gentleman's Diary for 1862, p. 74. Two solutions will be found in the Diary for 1863, pp. 49–50.Google Scholar

* Levy, W.H. in the Lady's and Gentleman';s Diary for 1863, p. 77, and for 1864, pp. 54-3.Google Scholar

* The first of these proiierties is given by Rangeley, W.Dixon in the Gentleman's Diary for 1822, p. 47Google Scholar; the first and second (without any hint as to the third and fourth) by Levy, W.H. in the Lady's and Gentleman's Diary for 1849, p. 75.Google Scholar

* The value of HI2 is given by William, Mawson in the Lady's and Gentleman's Diary for 1843, p. 75Google Scholar ; the other values are given by Rutherford, William and Samuel, Bills in the Diary for 1844, p. 52.Google Scholar

* The first of these properties occurs incidentally in Walker, William's proof of a theorem in the Gentleman's Mathematical Companion for 1803, p. 50.Google Scholar

* The first three values are given by Levy, W.H. in the Lady's and Gentleman' Dairy for 1859, p. 51Google Scholar

* The first result in (3) is given by Levy, W.H. in the Lady's and Gentleman's Diary for 1858, p. 71.Google Scholar

† Of the four proportions in (6) the first is given by Ryley, John, Leeds, in the Gentleman's Mathematical Companion, for 1802, p. 59. The solution in the text is that of J. H. Swale, Liverpool.Google Scholar

* The property that UK=US is referred to as well known in the Gentleman's Mathematical Companion for 1803, p. 50.

* Proceedings of the Edinburgh Mathematical Society, Vol. XII., p. 98 (1894).Google Scholar

* Proceedings of the Edinburgh Mathematical Society, Vol. XII., p. 91 (1894).Google Scholar

* Proceedings of the Edinburgh Mathematical Society, Vol. XII., p. 98 (1894).Google Scholar

* Proceedings of the Edinburgh Mathematical Society, Vol. XII., p. 94 (1894).Google Scholar

* The first is Euclid VI. 3 and its extension, which also was known to the Greeks, as is evident from Pappus's Mathematical Collection, VII. 39, second proof. The first part of the Recond fundamental theorem is given in Schooten, 's Exercitationes Mathematicae, p. 65 (1657).Google Scholar