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:
“One of the laudable by-products of the Freudian quackery is the discovery that lying, in most cases, is involuntary and inevitable—that the liar can no more avoid it than he can avoid blinking his eyes when a light flashes or jumping when a bomb goes off behind him.”
—H.L. (Henry Lewis)
“We are all humiliated by the sudden discovery of a fact which has existed very comfortably and perhaps been staring at us in private while we have been making up our world entirely without it.”
—George Eliot [Mary Ann (or Marian)
“The virtues of society are vices of the saint. The terror of reform is the discovery that we must cast away our virtues, or what we have always esteemed such, into the same pit that has consumed our grosser vices.”
—Ralph Waldo Emerson (1803–1882)