Sect. 4, Lemma 26, Insigniores orbitae cometarum proprietates (1761) [Notable properties of comets' orbits] translated by Florian Cajori, A History of Mathematics https://books.google.com/books?id=kqQPAAAAYAAJ (1906) p. 259, from the German of Michel Chasles, Geschichte der Geometrie, haupsächlich mit Bezug auf die neuern Methoden https://books.google.com/books?id=NgYHAAAAcAAJ (1839) p. 183.
“Angles are measured by arcs, such that 360° and 2π correspond to each other.”
Source: Mathematics as an Educational Task (1973), p. 477
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Hans Freudenthal 27
Dutch mathematician 1905–1990Related quotes
“Anxiety and nothing always correspond to each other.”
Source: 1840s, The Concept of Anxiety (1844), p. 96-97
Context: Anxiety and nothing always correspond to each other. As soon as the actuality of freedom and of spirit is posited, anxiety is canceled. But what then does the nothing of anxiety signify more particularly in paganism. This is fate. Fate is a relation to spirit as external. It is the relation between spirit and something else that is not spirit and to which fate nevertheless stands in a spiritual relation. Fate may also signify exactly the opposite, because it is the unity of necessity and accidental. … A necessity that is not conscious of itself is eo ipso the accidental in relation to the next moment. Fate, then, is the nothing of anxiety.
Source: Factotum (1975), Ch. 56
Context: The bus ran along a very narrow strip of cement that stood up out of the water with no guard-rail, no nothing; that's all there was to it. The bus driver leaned back and we roared along over this narrow cement strip surrounded by water and all the people in the bus, the twenty-five or forty or fifty-two people trusted him, but I never did. Sometimes it was a new driver, and I thought, how do they select these sons of bitches? There's deep water on both sides of us and with one error of judgement he'll kill us all. It was ridiculous. Suppose he had an argument with his wife that morning? Or cancer? Or visions of God? Bad teeth? Anything. He could do it. Dump us all. I knew that if I was driving that I would consider the possibility or desirability of drowning everybody. And sometimes, after just such considerations, possibility turns into reality. For each Joan of Arc there is a Hitler perched at the other end of the teeter-totter. The old story of good and evil. But none of the bus drivers ever dumped us. They were thinking instead of car payments, baseball scores, haircuts, vacations, enemas, family visits. There wasn't a real man in the whole shitload.
"Gauss's Abstract of the Disquisitiones Generales circa Superficies Curvas presented to the Royal Society of Gottingen" (1827) Tr. James Caddall Morehead & Adam Miller Hiltebeitel in General Investigations of Curved Surfaces of 1827 and 1825 http://books.google.com/books?id=SYJsAAAAMAAJ& (1902)
Source: Mathematics as an Educational Task (1973), p. 476-477
Source: The Sociology of Secrecy and of Secret Societies (1906), p. 441: First lines of the article.
Truman Library address (2006)
Context: We are not only all responsible for each other’s security. We are also, in some measure, responsible for each other’s welfare. Global solidarity is both necessary and possible. — It is necessary because without a measure of solidarity no society can be truly stable, and no one’s prosperity truly secure. That applies to national societies — as all the great industrial democracies learned in the twentieth century — but, it also applies to the increasingly integrated global market economy that we live in today. It is not realistic to think that some people can go on deriving great benefits from globalization while billions of their fellow human beings are left in abject poverty, or even thrown into it. We have to give our fellow citizens, not only within each nation but in the global community, at least a chance to share in our prosperity.
Proposition XV. Thereom VIII.
The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 2 (1789)
Geometry as a Branch of Physics (1949)
Letter To Carl Alfred Meier (1950)