Discovery
Although he is credited for its discovery, Karl Wilhelm Feuerbach did not entirely discover the nine-point circle, but rather the six point circle, recognizing the significance of the midpoints of the three sides of the triangle and the feet of the altitudes of that triangle. (See Fig. 1, points D, E, F, G, H, and I.) (At a slightly earlier date, Charles Brianchon and Jean-Victor Poncelet had stated and proven the same theorem.) But soon after Feuerbach, mathematician Olry Terquem himself proved the existence of the circle. He was the first to recognize the added significance of the three midpoints between the triangle's vertices and the orthocenter. (See Fig. 1, points J, K, and L.) Thus, Terquem was the first to use the name nine-point circle.
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Famous quotes containing the word discovery:
“It was one of those evenings when men feel that truth, goodness and beauty are one. In the morning, when they commit their discovery to paper, when others read it written there, it looks wholly ridiculous.”
—Aldous Huxley (1894–1963)
“The discovery of the North Pole is one of those realities which could not be avoided. It is the wages which human perseverance pays itself when it thinks that something is taking too long. The world needed a discoverer of the North Pole, and in all areas of social activity, merit was less important here than opportunity.”
—Karl Kraus (1874–1936)
“I have known no experience more distressing than the discovery that Negroes didn’t love me. Unutterable loneliness claimed me. I felt without roots, like a man without a country ...”
—Sarah Patton Boyle, U.S. civil rights activist and author. The Desegregated Heart, part 1, ch. 10 (1962)