„How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!“

—  Archimedes, kniha On Spirals

On Spirals (225 B.C.)

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Archimedes foto
Archimedes4
řecký matematik, fyzik, inženýr, vynálezce a astronom -287 - -212 př. n. l.

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„There are infinitely many variations of the initial situation and therefore no doubt indefinitely many theorems of moral geometry.“

—  John Rawls, kniha A Theory of Justice

Zdroj: A Theory of Justice (1971; 1975; 1999), Chapter III, Section 21, pg. 126

„How many things there are in this world which do not seem to be, and how many which seem to be and are not.“

—  Alessandro Pepoli Italian writer 1757 - 1796

In questo mondo, quante cose sonc e non sembrano! e quante poi sembrano e non sono!
La Scomessa, Act I., Sc. III. — (Il Marchese.). Translation reported in Harbottle's Dictionary of quotations French and Italian (1904), p. 325.

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„Geometry has two great treasures: one is the Theorem of Phythagoras, the other the division of a line in extreme and mean ratio. The first we can compare to a mass of gold; the other we may call a precious jewel.“

—  Johannes Kepler, kniha Mysterium Cosmographicum

As quoted by Karl Fink, Geschichte der Elementar-Mathematik (1890) translated as A Brief History of Mathematics https://books.google.com/books?id=3hkPAAAAIAAJ (1900, 1903) by Wooster Woodruff Beman, David Eugene Smith. Also see Carl Benjamin Boyer, A History of Mathematics (1968).
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„We find in the history of ideas mutations which do not seem to correspond to any obvious need, and at first sight appear as mere playful whimsies — such as Apollonius' work on conic sections, or the non-Euclidean geometries, whose practical value became apparent only later.“

—  Arthur Koestler Hungarian-British author and journalist 1905 - 1983

as quoted by Michael Grossman in the The First Nonlinear System of Differential and Integral Calculus (1979).
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„Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved.“

—  Isaac Newton, kniha Philosophiae Naturalis Principia Mathematica

Preface (8 May 1686)
Philosophiae Naturalis Principia Mathematica (1687)
Kontext: The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical; what is less so is called mechanical. But the errors are not in the art, but in the artificers. He that works with less accuracy is an imperfect mechanic: and if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved.

Antoni Lange foto

„How many times have I created to destroy?“

—  Antoni Lange Polish writer and philosopher 1862 - 1929

Vita Nova

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„You have to work out how not to die tomorrow.“

—  Martin Firrell British artist and activist 1963

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„Music is geometry in time.“

—  Arthur Honegger Swiss composer 1892 - 1955

I am a Composer (1951)

„How many more times will you watch the full moon rise? Perhaps twenty. And yet it all seems limitless.“

—  Paul Bowles, kniha The Sheltering Sky

The Sheltering Sky (1949)
Kontext: Because we don't know when we will die, we get to think of life as an inexhaustible well. Yet everything happens only a certain number of times, and a very small number really. How many more times will you remember a certain afternoon of your childhood, some afternoon that is so deeply a part of your being that you can't even conceive of your life without it? Perhaps four or five times more, perhaps not even that. How many more times will you watch the full moon rise? Perhaps twenty. And yet it all seems limitless.

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