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)
“However backwards the world has been in former ages in the discovery of such points as GOD never meant us to know,—we have been more successful in our own days:Mthousands can trace out now the impressions of this divine intercourse in themselves, from the first moment they received it, and with such distinct intelligence of its progress and workings, as to require no evidence of its truth.”
—Laurence Sterne (1713–1768)
“The new supplants the old. Yet men’s minds are stuffed with outworn bunk. Educating the young in the latest findings of authorities and scholars in the social sciences is important. It is equally important to devise ways and means for aiding the middle-aged and old to reexamine hang-over unscientific doctrines and ideas in the light of recent discovery and research.”
—Mary Barnett Gilson (1877–?)