Difference between revisions of "Simson straight line"
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| + | The straight line joining the feet of the perpendiculars from an arbitrary point $ P $ | ||
| + | of the circumscribed circle of a triangle onto its sides. It bisects the segment joining $ P $ | ||
| + | to the point of intersection of the altitudes of the triangle. The Simson line is named after R. Simson, although its discovery predates him. | ||
====Comments==== | ====Comments==== | ||
Latest revision as of 08:14, 6 June 2020
The straight line joining the feet of the perpendiculars from an arbitrary point $ P $
of the circumscribed circle of a triangle onto its sides. It bisects the segment joining $ P $
to the point of intersection of the altitudes of the triangle. The Simson line is named after R. Simson, although its discovery predates him.
Comments
In the work of Simson (1687–1768) there is no mention of this line. It was really discovered by W. Wallace in 1799 (see, e.g., [a1], Chapt. V and p. 300; [a2], p. 16; [a3]).
References
| [a1] | N. Altshiller-Court, "College geometry" , New York (1952) |
| [a2] | H.S.M. Coxeter, "Introduction to geometry" , Wiley (1989) |
| [a3] | C.G. Gillispie, Dictionary of scientific biography , 14 (1976) pp. 140 |
| [a4] | M. Berger, "Geometry" , 1–2 , Springer (1987) (Translated from French) |
| [a5] | J.L. Coolidge, "A treatise on the circle and the sphere" , Chelsea, reprint (1971) |
How to Cite This Entry:
Simson straight line. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Simson_straight_line&oldid=48713
Simson straight line. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Simson_straight_line&oldid=48713
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article