Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T01:01:09.557Z Has data issue: false hasContentIssue false

On the Non-Euclidean Analogues of Tarry's Point

Published online by Cambridge University Press:  20 January 2009

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.

The point known in elementary geometry by the name of Tarry was first discussed by that writer as the point of concurrence of the perpendiculars respectively from the vertices of the base-triangle to the corresponding sides of Brocards first triangle. Tarry's point is the point of the circumcircle diametrically opposite to Steiner's point, which is the fourth common point of the circumcircle and Steiner's circumellipse

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1922

References

* Neuberg, , Mathesis (1) 6 (1886), pp. 57.Google Scholar

Neuberg, ibid. (1) 1 (1881), p. 184; (1) 2 (1882), pp. 42–6.

Berkhan, , Arch. d. Math. u. Phys. (3) 11 (1907), p. 18.Google Scholar

Gabbatt, V., Proc. Camb. Phil. Soc. 21 (19221923), pp. 297362 Google Scholar. References distinguished by an asterisk [thus: (*4.1)] are to that paper.

* Cayley, , Liouville, 9 (1844), p. 285=Papers, 1, p. 183.Google Scholar

A case of a theorem due to Grassmann and Clebsch; v. (* 17.1).

The symbol q. signifies with raped to.

* A case of a theorem due to Grasamann and Clebseh; v. (* 17.1).

* The euclidean analogue is due to Neuberg, , Mathesis (1) 5 (1885), p. 208.Google Scholar

Cayley, , loc. cit. (2.2).Google Scholar

* Neuberg, , Mathesis (1) 3 (1883), p. 144 Google Scholar; ibid. (1) 5 (1885), p. 208; ibid. (1) 6 (1886), p. 5. Cf. the remark Encyk d. math. Wiss. III. AB 10, p. 1266, II. 2–7.Google Scholar

The conic s 1 specified in (3.41) becomes the Steiner circumellipse of the base-triangle.