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The Eudemian Summary says that Eudoxus "first increased the number of general theorems, added to the three proportions three more, and raised to a considerable quantity the learning, begun by Plato, on the subject of the section, to which he applied the analytical method." By this 'section' is meant, no doubt, the "golden section" ( sectio aurea ), which cuts a line in extreme and mean ratio. The first five propositions in Euclid XIII. relate to lines cut by this section, and are generally attributed to Eudoxus.
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In 2001, Afghanistan was a totalitarian nightmare a land where girls could not go to school, where religious police roamed the streets, where women were publicly whipped, where there were summary executions in Kabul's soccer stadium.


— "President Bush Discusses Progress in Afghanistan, Global War on Terror". News & Policies. Whitehouse.gov (February 15, 2007). Retrieved on 2007-07-07.

Tags: Afghanistan, totalitarian, nightmare, land, girls, school, religious, police, roamed

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The Eudemian summary ascribes to Thales the invention of the theorems on the equality of vertical angles, the equality of the angles at the base of an isosceles triangle, the bisection of a circle by any diameter, and the congruence of two triangles having a side and the two adjacent angles equal respectively. The last theorem he applied to the measurement of the distances of ships from the shore. Thus Thales was the first to apply theoretical geometry to practical uses.


— p. 17 (The Greeks)

Tags: Eudemian, ascribes, Thales, invention, theorems, equality, vertical, angles, base

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In summary, our world is doomed.

charlie brooker

— Screenwipe S3E4
— Discussing My Super Sweet Sixteen YouTube video

Tags: our, world, doomed

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A law of nature is not a formula drawn up by a legislator, but a mere summary of the observed facts — a "bundle of facts." Things do not act in a particular way because there is a law, but we state the "law" because they act in that way.

joseph mccabe

— The Existence of God (1913)

Tags: law, nature, formula, drawn, legislator, observed, facts, bundle, Things

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Writing long books is a laborious and impoverishing act of foolishness: expanding in five hundred pages an idea that could be perfectly explained in a few minutes. A better procedure is to pretend that those books already exist and to offer a summary, a commentary.

jorge luis borges

— Preface; Variant translations:It is a laborious madness and an impoverishing one, the madness of composing vast books — setting out in five hundred pages an idea that can be perfectly related orally in five minutes. The better way to go about it is to pretend that those books already exist, and offer a summary, a commentary on them... A more reasonable, more inept, and more lazy man, I have chosen to write notes on imaginary books.
The composition of vast books is a laborious and impoverishing extravagance. To go on for five hundred pages developing an idea whose perfect oral exposition is possible in a few minutes! A better course of procedure is to pretend that these books already exist, and then to offer a resume, a commentary . . . More reasonable, more inept, more indolent, I have preferred to write notes upon imaginary books.

Tags: Writing, long, books, laborious, impoverishing, act, foolishness, expanding, five

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I have always directed my attempts at the figurative representation of objects by way of summary and not very descriptive brushstrokes, diverging greatly from the real objective measurements of things, and this has led many people to talk about childish drawing.. ..this position of seeing them (the objects, fh) without looking at them too much, without focussing more attention on them than any ordinary man would in normal everyday life..

jean dubuffet

— Prospectus et tous écrits suivants, Vol. II, Jean Dubuffet, Gallimard, Paris 1967, p. 105

Tags: directed, attempts, figurative, representation, objects, descriptive, brushstrokes, diverging, greatly

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If a wise man should ask, What are the modern virtues? and should answer his own question by a summary of the things we admire; if he should discard as irrelevant the ideals which by tradition we profess, but which are not found outside of the tradition or the profession ideals like meekness, humility, the renunciation of this world; if he should include only those excellences to which our hearts are daily given, and by which our conduct is motived, in such an inventory what virtues would he name?

john erskine

— The Moral Obligation to be Intelligent (1915, pg. 3)

Tags: wise, man, ask, What, modern, virtues, answer, own, question

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It is a fair summary of history to say that the safeguards of liberty have frequently been forged in controversies involving not very nice people.

felix frankfurter

— United States v. Rabinowitz, 339 U.S. 56, 69 (1950).

Tags: fair, history, safeguards, liberty, frequently, been, forged, controversies, involving

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Perhaps the most concise summary of enlightenment would be: transcending dualism . … Dualism is the conceptual division of the world into categories … human perception is by nature a dualistic phenomenon which makes the quest for enlightenment an uphill struggle, to say the least.

douglas hofstadter

— Chapter 9: "Mumon and Gödel"

Tags: most, concise, enlightenment, transcending, dualism, conceptual, division, world, categories

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We ought, as far as we can by law, to support the government of all societies and corporations, especially this of the city of London; and if the mayor and aldermen should not have power to punish offenders in a summary way, then farewell the government of the city.


— Holt, C.J., Clark's Case (1696), 5 Mod. Rep. 320.

Tags: We, far, can, law, support, government, societies, corporations, city

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An enterprise architecture is an abstract summary of some organizational component's design. The organizational strategy is the basis for deciding where the organization wants to be in three to five years. When matched to the organizational strategy, the architectures provide the foundation for deciding priorities for implementing the strategy.


— Sue A. Conger (1994) The new software engineering. p. 115

Tags: enterprise, architecture, abstract, organizational, design, strategy, basis, deciding, organization

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I heard the quotation read in a summary of the speech. I thought the words sounded familiar and suddenly it dawned on me that they were out of my little book.


— Her reaction on hearing her poem. Daily Telegraph, 16 Aug 2008

Tags: heard, quotation, read, speech, thought, words, sounded, familiar, suddenly

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A law of nature is not a formula drawn up by a legislator, but a mere summary of the observed facts a "bundle of facts." Things do not act in a particular way because there is a law, but we state the "law" because they act in that way.


— Joseph McCabe, in The Existence of God (1913)

Tags: law, nature, formula, drawn, legislator, observed, facts, bundle, Things

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The law has armed the High Court of Justice with the power, and imposed on it the duty of preventing brevi manu and by summary proceedings any attempt to interfere with the administration of justice. It is on that ground, and not on any exaggerated notion of the dignity of individuals that insults to Judges are not allowed.


— Bowen, L.J., In re Johnson (1887), L. R. 20 Q. B. D. 74.

Tags: law, armed, High, Court, Justice, power, imposed, duty, preventing

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It is necessary for Courts of Justice to hold a strict hand over summary proceedings before magistrates, and I never will agree to relax any of the rules by which they have been bound. Their jurisdiction is of a limited nature, and they must shew that the party was brought within it.


— Lord Kenyon, C.J., King v. Stone (1800), 1 East, 650.

Tags: necessary, Courts, Justice, hold, strict, hand, over, proceedings, before

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Perhaps the most concise summary of enlightenment would be: transcending dualism. … Dualism is the conceptual division of the world into categories … human perception is by nature a dualistic phenomenon which makes the quest for enlightenment an uphill struggle, to say the least.


— Douglas Hofstadter (1979) Gödel, Escher, Bach: an Eternal Golden Braid Chapter 9: "Mumon and Gödel"

Tags: most, concise, enlightenment, transcending, dualism, conceptual, division, world, categories

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A similar statement appears in the US Strategic Bombing Survey summary Report (European War) (30 September 1945): The great lesson to be learned in the battered towns of England and the ruined cities of Germany is that the best way to win a war is to prevent it from occurring.

george marshall

— Unsourced variant: The only way to win a war is to prevent it.

Tags: similar, statement, appears, US, Strategic, Bombing, Survey, Report, European

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The Eudemian summary says that "Pythagoras changed the study of geometry into the form of a liberal education, for he examined its principles to the bottom, and investigated its theorems in an immaterial and intellectual manner." His geometry was connected closely with his arithmetic. He was especially fond of those geometrical relations which admitted of arithmetical expression.


— p. 21 (A History of Mathematics (1893))

Tags: Eudemian, Pythagoras, changed, study, geometry, form, liberal, education, examined

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The Eudemian summary says that "Pythagoras changed the study of geometry into the form of a liberal education, for he examined its principles to the bottom, and investigated its theorems in an immaterial and intellectual manner." His geometry was connected closely with his arithmetic. He was especially fond of those geometrical relations which admitted of arithmetical expression.


— p. 21 (The Greeks)

Tags: Eudemian, Pythagoras, changed, study, geometry, form, liberal, education, examined

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Plato observed that geometry trained the mind for correct and vigorous thinking. Hence it was that the Eudemian summary says, "He filled his writings with mathematical discoveries, and exhibited on every occasion the remarkable connection between mathematics and philosophy."


— p. 30 (The Greeks)

Tags: Plato, observed, geometry, trained, mind, correct, vigorous, thinking, Hence

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Euclid's greatest activity was during the time of the first Ptolemy, who reigned from 306 to 283 B.C. Of the life of Euclid, little is known, except what is added by Proclus to the Eudemian summary .


— p. 35 (The Greeks)

Tags: Euclid's, greatest, activity, time, first, Ptolemy, who, reigned, BC

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