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Reuschle's Theorem
In elementary geometry, Reuschle's theorem describes a property of the cevians of a triangle intersecting in a common point and is named after the German mathematician Karl Gustav Reuschle (1812–1875). It is also known as Terquem's theorem after the French mathematician Olry Terquem (1782–1862), who published it in 1842. In a triangle ABC with its three cevians intersecting in a common point other than the vertices A, B or C let P_a, P_b and P_c denote the intersections of the (extended) triangle sides and the cevians. The circle defined by the three points P_a, P_b and P_c intersects the (extended) triangle sides in the (additional) points P'_a, P'_b and P'_c. Reuschle's theorem now states that the three new cevians AP'_a, BP'_b and CP'_c intersect in a common point as well. References *Friedrich Riecke (ed.): ''Mathematische Unterhaltungen''. Volume I, Stuttgart 1867, (reprint Wiesbaden 1973), , p. 125 (German) *M. D. Fox, J. R. Goggins: "Cevian Axes and Related Curves." ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Satz Von Reuschle3
' (German for ''sentence'', ''movement'', ''set'', ''setting'') is any single member of a musical piece, which in and of itself displays a complete sense, (Hugo Riemann, Riemann 1976: 841) such as a sentence (music), sentence, phrase (music), phrase, or movement (music), movement. Notes Sources *Riemann (1976). Cited in Jean-Jacques Nattiez, Nattiez, Jean-Jacques (1990). ''Music and Discourse: Toward a Semiology of Music'' (''Musicologie générale et sémiologue'', 1987). Translated by Carolyn Abbate (1990). . Formal sections in music analysis German words and phrases {{music-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
