Euclid Quotes

• I told myself, "Lincoln, you can never make a lawyer if you do not understand what demonstrate means." So I left my situation in Springfield, went home to my father's house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what "demonstrate" means, and went back to my law studies.

  Abraham Lincoln

  Education, Father, Book

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• We think of Euclid as of fine ice; we admire Newton as we admire the peak of Teneriffe. Even the intensest labors, the most remote triumphs of the abstract intellect, seem to carry us into a region different from our own-to be in a terra incognita of pure reasoning, to cast a chill on human glory.

  Walter Bagehot

  Science, Thinking, Ice

  Walter Bagehot, Richard Holt Hutton (1891). “Literary studies ; Religious and metaphysical essays ; Letters on the French coup d'état”

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• The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry.

  Eric Bell

  Moving, Math, Cowboy

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• Euclid Alone Has Looked on Beauty Bare.

  Edna St. Vincent Millay

  Math, Mathematical Beauty, Sandals

  "Euclid Alone Has Looked on Beauty Bare" l. 11 (1923)

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• The early study of Euclid made me a hater of geometry.

  James Joseph Sylvester

  Study, Made, Geometry

  James Joseph Sylvester (1870). “The Laws of Verse: Or Principles of Versification Exemplified in Metrical Translations, Together with an Annotated Reprint of the Inaugural Presidential Address to the Mathematical and Physical Section of the British Association at Exeter”, p.126

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• Euclid alone Has looked on Beauty bare. Fortunate they Who, though once only and then but far away, Have heard her massive sandal set on stone.

  Edna St. Vincent Millay

  Stones, Far Away, Sandals

  "Euclid Alone Has Looked on Beauty Bare" l. 11 (1923)

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• Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.

  Eric Temple Bell

  Math, Intelligence, Taught

  Mathematics Magazine, Vol. 23-24, (p. 161), 1949.

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• About Thomas Hobbes: He was 40 years old before he looked on geometry; which happened accidentally. Being in a gentleman's library, Euclid's Elements lay open, and "twas the 47 El. libri I" [Pythagoras' Theorem]. He read the proposition "By God", sayd he, "this is impossible:" So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that truth. This made him in love with geometry.

  John Aubrey

  Love, Truth, Years

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• I have in later years taken to Euclid, Whitehead, Bertrand Russell, in an elemental way.

  Carl Sandburg

  Taken, Years, Literature

  Carl Sandburg, Margaret Sandburg, George Hendrick (1999). “Ever the Winds of Chance”, p.10, University of Illinois Press

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• The new painters do not propose, any more than did their predecessors, to be geometers. But it may be said that geometry is to the plastic arts what grammar is to the art of the writer. Today, scholars no longer limit themselves to the three dimensions of Euclid. The painters have been lead quite naturally, one might say by intuition, to preoccupy themselves with the new possibilities of spatial measurement which, in the language of the modern studios, are designated by the term fourth dimension.

  Guillaume Apollinaire

  Art, Intuition, Today

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• As to writing another book on geometry [to replace Euclid] the middle ages would have as soon thought of composing another New Testament.

  Augustus De Morgan

  Book, Writing, Science

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• Euclid avoids it [the treatment of the infinite]; in modern mathematics it is systematically introduced, for only then is generality obtained.

  Arthur Cayley

  Infinite, Modern, Mathematics

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• The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.

  Benoit Mandelbrot

  Nature, Science, Challenges

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• Detection is, or ought to be, an exact science, and should be treated in the same cold and unemotional manner. You have attempted to tinge it with romanticism, which produces much the same effect as if you worked a love-story or an elopement into the fifth proposition of Euclid.

  Arthur Conan Doyle

  Humorous, Sarcasm, Science

  The Sign of the Four ch. 1 (1890)

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• Detest it as lewd intercourse, it can deprive you of all your leisure, your health, your rest, and the whole happiness of your life.
  Having himself spent a lifetime unsuccessfully trying to prove Euclid's postulate that parallel lines do not meet, Farkas discouraged his son János from any further attempt.

  Farkas Bolyai

  Life, Son, Science

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• Let me tell you how at one time the famous mathematician Euclid became a physician. It was during a vacation, which I spent in Prague as I most always did, when I was attacked by an illness never before experienced, which manifested itself in chilliness and painful weariness of the whole body. In order to ease my condition I took up Euclid's Elements and read for the first time his doctrine of ratio, which I found treated there in a manner entirely new to me. The ingenuity displayed in Euclid's presentation filled me with such vivid pleasure, that forthwith I felt as well as ever.

  Bernard Bolzano

  Pain, Recovery, Science

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• Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

  G. H. Hardy

  Love, Sacrifice, Math

  G. H. Hardy, C. P. Snow (2012). “A Mathematician's Apology”, p.94, Cambridge University Press

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• I have given up newspapers in exchange for Tacitus and Thucydides, for Newton and Euclid; and I find myself much the happier.

  Thomas Jefferson

  Newton, Newspapers, Given

  Thomas Jefferson, Joyce Appleby, Terence Ball (1999). “Jefferson: Political Writings”, p.37, Cambridge University Press

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• I would say, if you like, that the party is like an out-moded mathematics...that is to say, the mathematics of Euclid. We need to invent a non-Euclidian mathematics with respect to political discipline.

  Alain Badiou

  Party, Discipline, Political

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• Euclid for children is barbarous.

  Oliver Heaviside

  Children

  Oliver Heaviside (1893). “Electromagnetic Theory”

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• It is shocking that young people should be addling their brains over mere logical subtleties in Euclid's Elements, trying to understand the proof of one obvious fact in terms of something equally .. obvious.

  Oliver Heaviside

  Science, People, Brain

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• Euclid 's manner of exposition, progressing relentlessly from the data to the unknown and from the hypothesis to the conclusion, is perfect for checking the argument in detail but far from being perfect for making understandable the main line of the argument.

  George Polya

  Data, Perfect, Progress

  George Pólya (1945). “How to Solve it: A New Aspect of Mathematical Method”

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• If Euclid's point, though incapable of being drawn by any human agency, has an imperishable value, my picture has its own for mankind to live.

  Mahatma Gandhi

  Men, Agency, Mankind

  Mahatma Gandhi, Anthony J. Parel (1997). “Gandhi: 'Hind Swaraj' and Other Writings”, p.189, Cambridge University Press

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• In geometry I find certain imperfections which I hold to be the reason why this science, apart from transition into analytics, can as yet make no advance from that state in which it came to us from Euclid.
  As belonging to these imperfections, I consider the obscurity in the fundamental concepts of the geometrical magnitudes and in the manner and method of representing the measuring of these magnitudes, and finally the momentous gap in the theory of parallels, to fill which all efforts of mathematicians have so far been in vain.

  Nikolai Lobachevsky

  Imperfection, Effort, Transition

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• It is curious to observe the triumph of slight incidents over the mind; and what incredible weight they have in forming and governing our opinions, both of men and things, that trifles light as air shall waft a belief into the soul, and plant it so immovable within it, that Euclid's demonstrations, could they be brought to batter it in breach, should not all have power to overthrow it!

  Laurence Sterne

  Men, Light, Air

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