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:
“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–?)
“There is a great discovery still to be made in literature, that of paying literary men by the quantity they do not write.”
—Thomas Carlyle (1795–1881)
“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)