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Who said: “I have no satisfaction in formulas unless I feel their arithmetical magnitude.”
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Home > Category Index for Science Quotations > Category Index C > Category: Circle

Circle Quotes (16 quotes)

Toutes les fois que dans une équation finale on trouve deux quantités inconnues, on a un lieu, l'extrémité de l'une d’elles décrivant une ligne droite ou courbe. La ligne droite est simple et unique dans son genre; les espèces des courbes sont en nombre indéfini, cercle, parabole, hyperbole, ellipse, etc.
Whenever two unknown magnitudes appear in a final equation, we have a locus, the extremity of one of the unknown magnitudes describing a straight line or a curve. The straight line is simple and unique; the classes of curves are indefinitely many,—circle, parabola, hyperbola, ellipse, etc.
Introduction aux Lieux Plans et Solides (1679) collected in OEuvres de Fermat (1896), Vol. 3, 85. Introduction to Plane and Solid Loci, as translated by Joseph Seidlin in David E. Smith(ed.)A Source Book in Mathematics (1959), 389. Alternate translation using Google Translate: “Whenever in a final equation there are two unknown quantities, there is a locus, the end of one of them describing a straight line or curve. The line is simple and unique in its kind, species curves are indefinite in number,—circle, parabola, hyperbola, ellipse, etc.”
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A grove of giant redwoods or sequoias should be kept just as we keep a great or beautiful cathedral. The extermination of the passenger pigeon meant that mankind was just so much poorer; exactly as in the case of the destruction of the cathedral at Rheims. And to lose the chance to see frigate-birds soaring in circles above the storm, or a file of pelicans winging their way homeward across the crimson afterglow of the sunset, or a myriad terns flashing in the bright light of midday as they hover in a shifting maze above the beach—why, the loss is like the loss of a gallery of the masterpieces of the artists of old time.
In A Book-Lover's Holidays in the Open (1916), 316-317.
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As to Bell's talking telegraph, it only creates interest in scientific circles, and, as a toy it is beautiful; but ... its commercial value will be limited.
Letter to William D. Baldwin, his attorney (1 Nov 1876). Telephone Investigating Committee, House of Representatives, United States 49th Congress, 1st Session, Miscellaneous Documents (1886), No. 355, 1186.
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Circles to square and cubes to double
Would give a man excessive trouble.
The longitude uncertain roams,
In spite of Whiston and his bombs.
In 'Alma', Canto III, in Samuel Johnson, The Works of the English Poets, from Chaucer to Cowper (1810), 203. The reference to longitude reflects the difficulty of its determination at sea, and the public interest in the attempts to win the prize instituted by the British government in 1714 for a successful way to find longitude at sea (eventually won by John Harrison's chronometer). In this poem, William Whiston (who succeeded Isaac Newton as Lucasian Professor at Cambridge) is being satirized for what many thought was a crack-brained scheme to find the longitude. This proposed, with Humphrey Ditton, the use of widely separated ships firing off shells programmed to explode at a set time, and calculation of distance between them made from the time-lag between the observed sounds of the explosions using the known speed of sound.
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De Morgan was explaining to an actuary what was the chance that a certain proportion of some group of people would at the end of a given time be alive; and quoted the actuarial formula, involving p [pi], which, in answer to a question, he explained stood for the ratio of the circumference of a circle to its diameter. His acquaintance, who had so far listened to the explanation with interest, interrupted him and exclaimed, 'My dear friend, that must be a delusion, what can a circle have to do with the number of people alive at a given time?'
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Dr. M.L. von Franz has explained the circle (or sphere) as a symbol of Self. It expresses the totality of the psyche in all its aspects, including the relationship between man and the whole of nature. It always points to the single most vital aspect of life, its ultimate wholeness.
In Aniela Jaffé, 'Symbolism in the Visual Arts', collected in Carl Jung (ed.), Man and His Symbols (1964, 1968), 266.
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If there is an underlying oneness of all things, it does not matter where we begin, whether with stars, or laws of supply and demand, or frogs, or Napoleon Bonaparte. One measures a circle, beginning anywhere.
Lo! (1931, 1941), 8.
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Indeed, we need not look back half a century to times which many now living remember well, and see the wonderful advances in the sciences and arts which have been made within that period. Some of these have rendered the elements themselves subservient to the purposes of man, have harnessed them to the yoke of his labors and effected the great blessings of moderating his own, of accomplishing what was beyond his feeble force, and extending the comforts of life to a much enlarged circle, to those who had before known its necessaries only.
From paper 'Report of the Commissioners Appointed to Fix the Site of the University of Virginia' (Dec 1818), reprinted in Annual Report of the Board of Visitors of the University of Virginia for the Fiscal Year Ending May 31, 1879 (1879), 10. Collected in Commonwealth of Virginia, Annual Reports of Officers, Boards, and Institutions of the Commonwealth of Virginia, for the Year Ending September 30, 1879 (1879).
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Many errors, of a truth, consist merely in the application of the wrong names of things. For if a man says that the lines which are drawn from the centre of the circle to the circumference are not equal, he understands by the circle, at all events for the time, something else than mathematicians understand by it.
In 'Prop. 47: The human mind possesses an adequate knowledge of the eternal and infinite essence of God', Ethic, translated by William Hale White (1883), 93-94. Collected in The English and Foreign Philosophical Library, Vol. 21.
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Mathematics … certainly would never have come into existence if mankind had known from the beginning that in all nature there is no perfectly straight line, no true circle, no standard of measurement.
From 'Of the First and Last Things', All Too Human: A Book For Free Spirits (1878, 1908), Part 1, section 11, 31. As quoted in The Puzzle Instinct : The Meaning of Puzzles in Human Life‎ (2004) by Marcel Danesi, p. 71 from Human All-Too-Human
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The chemist works along his own brilliant line of discovery and exposition; the astronomer has his special field to explore; the geologist has a well-defined sphere to occupy. It is manifest, however, that not one of these men can tell the whole tale, and make a complete story of creation. Another man is wanted. A man who, though not necessarily going into formal science, sees the whole idea, and speaks of it in its unity. This man is the theologian. He is not a chemist, an astronomer, a geologist, a botanist——he is more: he speaks of circles, not of segments; of principles, not of facts; of causes and purposes rather than of effects and appearances. Not that the latter are excluded from his study, but that they are so wisely included in it as to be put in their proper places.
In The People's Bible: Discourses Upon Holy Scripture: Vol. 1. Genesis (1885), 120.
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The greater is the circle of light, the greater is the boundary of the darkness by which it is confined. But, notwithstanding this, the more light get, the more thankful we ought to be, for by this means we have the greater range for satisfactory contemplation. time the bounds of light will be still farther extended; and from the infinity of the divine nature, and the divine works, we may promise ourselves an endless progress in our investigation them: a prospect truly sublime and glorious.
Experiments and Observations with a Continuation of the Observations on Air (1781), Vol. 2, ix.
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When the child outgrows the narrow circle of family life … then comes the period of the school, whose object is to initiate him into the technicalities of intercommunication with his fellow-men, and to familiarize him with the ideas that underlie his civilization, and which he must use as tools of thought if he would observe and understand the phases of human life around him; for these … are invisible to the human being who has not the aid of elementary ideas with which to see them.
In Psychologic Foundations of Education: An Attempt to Show the Genesis of the Higher Faculties of the Mind (1907), 265.
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Why is geometry often described as “cold” and “dry?” One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line… Nature exhibits not simply a higher degree but an altogether different level of complexity.
From The Fractal Geometry of Nature (1977, 1983), Introduction, xiii.
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Yet the widespread [planetary theories], advanced by Ptolemy and most other [astronomers], although consistent with the numerical [data], seemed likewise to present no small difficulty. For these theories were not adequate unless they also conceived certain equalizing circles, which made the planet appear to move at all times with uniform velocity neither on its deferent sphere nor about its own [epicycle's] center … Therefore, having become aware of these [defects], I often considered whether there could perhaps be found a more reasonable arrangement of circles, from which every apparent irregularity would be derived while everything in itself would move uniformly, as is required by the rule of perfect motion.
From Nicholaus Copernicus, Edward Rosen (trans.), Pawel Czartoryski (ed.) 'Commentariolus', in Nicholas Copernicus: Minor Works (1985), 81-83. Excerpted in Lisa M. Dolling, Arthur F. Gianelli and Glenn N. Statile (eds.) The Tests of Time: Readings in the Development of Physical Theory (2003), 40.
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[As a youth, fiddling in my home laboratory] I discovered a formula for the frequency of a resonant circuit which was 2π x sqrt(LC) where L is the inductance and C the capacitance of the circuit. And there was π, and where was the circle? … I still don’t quite know where that circle is, where that π comes from.
From address to the National Science Teachers’ Association convention (Apr 1966), 'What Is Science?', collected in Richard Phillips Feynman and Jeffrey Robbins (ed.), The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman (1999, 2005), 177.
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In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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