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Euclid Quotes

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Euclid Quotes

“Is it possible that the Pentateuch could not have been written by uninspired men? that the assistance of God was necessary to produce these books? Is it possible that Galilei ascertained the mechanical principles of 'Virtual Velocity,' the laws of falling bodies and of all motion; that Copernicus ascertained the true position of the earth and accounted for all celestial phenomena; that Kepler discovered his three laws—discoveries of such importance that the 8th of May, 1618, may be called the birth-day of modern science; that Newton gave to the world the Method of Fluxions, the Theory of Universal Gravitation, and the Decomposition of Light; that Euclid, Cavalieri, Descartes, and Leibniz, almost completed the science of mathematics; that all the discoveries in optics, hydrostatics, pneumatics and chemistry, the experiments, discoveries, and inventions of Galvani, Volta, Franklin and Morse, of Trevithick, Watt and Fulton and of all the pioneers of progress—that all this was accomplished by uninspired men, while the writer of the Pentateuch was directed and inspired by an infinite God? Is it possible that the codes of China, India, Egypt, Greece and Rome were made by man, and that the laws recorded in the Pentateuch were alone given by God? Is it possible that Æschylus and Shakespeare, Burns, and Beranger, Goethe and Schiller, and all the poets of the world, and all their wondrous tragedies and songs are but the work of men, while no intelligence except the infinite God could be the author of the Pentateuch? Is it possible that of all the books that crowd the libraries of the world, the books of science, fiction, history and song, that all save only one, have been produced by man? Is it possible that of all these, the bible only is the work of God?”

LightInspirationScienceFictionProgressBooksBibleIndiaTragedyMathematicsIntelligenceChinaMathExperimentsWriterChemistryRomePoetsEgyptGreeceNewtonPioneersShakespeareFranklinSongsLibrariesWilliam ShakespeareDiscoveriesThe BibleEuclidGoetheInventionsOpticsCopernicusDescartesKeplerIsaac NewtonLaws Of MotionGalileoLeibnizBurnsJames WattSchillerTheory Of GravityAeschylusJohannes KeplerNicolaus CopernicusPentateuchBenjamin FranklinGalileo GalileiRobert BurnsWattMorseGottfried LeibnizGottfried Wilhelm LeibnizJohann Wolfgang Von GoetheRené DescartesCavalieriPneumaticsAlessandro VoltaBerangerBonaventura CavalieriBonaventura Francesco CavalieriFultonGalvaniGottfried Von LeibnizGottfried Wilhelm Von LeibnizHydrostaticsJohann Von GoetheLuigi Aloisio GalvaniLuigi GalvaniPierre Jean De BérangerRichard TrevithickRobert FultonSamuel Finley Breese MorseSamuel MorseTheory Of Universal GravitationTrevethickVoltaÆSchylus
Book:Some Mistakes of Moses
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“Euclid's Elements has been for nearly twenty-two centuries the encouragement and guide of that scientific thought which is one thing with the progress of man from a worse to a better state. The encouragement; for it contained a body of knowledge that was really known and could be relied on, and that moreover was growing in extent and application. For even at the time this book was written—shortly after the foundation of the Alexandrian Museum—Mathematics was no longer the merely ideal science of the Platonic school, but had started on her career of conquest over the whole world of Phenomena. The guide; for the aim of every scientific student of every subject was to bring his knowledge of that subject into a form as perfect as that which geometry had attained. Far up on the great mountain of Truth, which all the sciences hope to scale, the foremost of that sacred sisterhood was seen, beckoning for the rest to follow her.”

TruthSciencePerfectKnowledgeProgressElementsEncouragementMathematicsSacredMathApplicationPlatoConquestGeometryStudentGuidePlatonicScientificEuclidAlexandriaSubjectScientific ThoughtRelience
Book:Lectures and Essays by the Late William Kingdon Clifford, F.R.S.
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“These estimates may well be enhanced by one from F. Klein (1849-1925), the leading German mathematician of the last quarter of the nineteenth century. 'Mathematics in general is fundamentally the science of self-evident things.' ... If mathematics is indeed the science of self-evident things, mathematicians are a phenomenally stupid lot to waste the tons of good paper they do in proving the fact. Mathematics is abstract and it is hard, and any assertion that it is simple is true only in a severely technical sense—that of the modern postulational method which, as a matter of fact, was exploited by Euclid. The assumptions from which mathematics starts are simple; the rest is not.”

HardScienceMathematicsMathAbstractMathematicianEuclidTechnicalEstimatesFelix Klein
Book:Mathematics: Queen and Servant of Science
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“It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it.”

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Author:Bernhard Riemann
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“When one day Lagrange took out of his pocket a paper which he read at the Académe, and which contained a demonstration of the famous Postulatum of Euclid, relative to the theory of parallels. This demonstration rested on an obvious paralogism, which appeared as such to everybody; and probably Lagrange also recognised it such during his lecture. For, when he had finished, he put the paper back in his pocket, and spoke no more of it. A moment of universal silence followed, and one passed immediately to other concerns.”

ScienceMathematicsMathEuclidLagrangeJoseph Louis LagrangeGiuseppe Luigi LagranciaTheory Of Parallels
Author:Jean-Baptiste Biot
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“... I left Caen, where I was living, to go on a geological excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.”

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Author:Henri Poincaré
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“Please give it up. Fear it no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in 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.]”

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Author:Farkas Bolyai
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“In Euclid's Elements we meet the concept which later plays a significant role in the development of science. The concept is called the "division of a line in extreme and mean ratio" (DEMR). ...the concept occurs in two forms. The first is formulated in Proposition 11 of Book II. ...why did Euclid introduce different forms... which we can find in Books II, VI and XIII? ...Only three types of regular polygons can be faces of the Platonic solids: the equilateral triangle... the square... and the regular pentagon. In order to construct the Platonic solids... we must build the two-dimensional faces... It is for this purpose that Euclid introduced the golden ratio... (Proposition II.11)... By using the "golden" isosceles triangle...we can construct the regular pentagon... Then only one step remains to construct the dodecahedron... which for Plato is one of the most important regular polyhedra symbolizing the universal harmony in his cosmology.”

HarmonyPlatoGeometryEuclidGolden RatioPlatonic Solids
Book:"GOLDEN" NON-EUCLIDEAN GEOMETRY, THE: HILBERT'S FOURTH PROBLEM, "GOLDEN" DYNAMICAL SYSTEMS, AND THE FINE-STRUCTURE CONSTANT
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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.”

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Author:Guillaume Apollinaire
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“I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid - a term used in this work to denote all of standard geometry - Nature exhibits not simply a higher degree but an altogether different level of complexity ... The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous."”

DifferentFormScienceUsedTermChallengesLevelsExistenceStudyHigherDegreesStandardsClaimsPatternsComplexityGeometryExhibitsDifferent LevelsFragmentedEuclidMorphology
Author:Benoit Mandelbrot
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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!”

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Author:Laurence Sterne
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“The science of the church is neglected for the study of geometry, and they lose sight of Heaven while they are employed in measuring the earth. Euclid is perpetually in their hands. Aristotle and Theophrastus are the objects of their admiration; and they express an uncommon reverence for the works of Galen. Their errors are derived from the abuse of the arts and sciences of the infidels, and they corrupt the simplicity of the gospel by the refinements of human reason.”

HumansArtReasonHandsEarthHeavenLosesChurchStudyObjectsAbuseSightMathematicsErrorsSimplicityAdmirationReverenceEmployedNeglectedGeometryUncommonRefinementMeasuringArt And ScienceInfidelHuman ReasonEuclidGalen
Book:Delphi Complete Works of Edward Gibbon (Illustrated)
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“Did chemistry theorems exist? No: therefore you had to go further, not be satisfied with the quia, go back to the origins, to mathematics and physics. The origins of chemistry were ignoble, or at least equivocal: the dens of the alchemists, their abominable hodgepodge of ideas and language, their confessed interest in gold, their Levantine swindles typical of charlatans and magicians; instead, at the origin of physics lay the strenuous clarity of the West-Archimedes and Euclid.”

IdeasLanguageInterestGoldMathematicsLaysWestPhysicsSatisfiedClarityChemistryTypicalMagicianAlchemistTheoremsDensCharlatansIgnobleEuclid
Author:Primo Levi
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“Every night as I gazed up at the window I said softly to myself the word paralysis. It had always sounded strangely in my ears, like the word gnomon in the Euclid and the word simony in the Catechism. But now it sounded to me like the name of some maleficent and sinful being. It filled me with fear, and yet I longed to be nearer to it and to look upon its deadly work.”

LooksSaidNightNamesLanguageWindowEarsFilledLook UpEvery NightParalysisEuclidCatechismMaleficent
Book:The Dead and Other Stories: A Broadview Anthology of British Literature Edition
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“It would be foolish to give credit to Euclid for pangeometrical conceptions; the idea of geometry deifferent from the common-sense one never occurred to his mind. Yet, when he stated the fifth postulate, he stood at the parting of the ways. His subconscious prescience is astounding. There is nothing comperable to it in the whole history of science.”

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Author:George Sarton
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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.”

StatesReasonCertainEffortTheoryConceptsMethodFundamentalsVainReason WhyBelongingGapsTransitionImperfectionMathematicianParallelsGeometryObscurityRepresentingMagnitudeMeasuringAnalyticsEuclid
Author:Nikolai Lobachevsky
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“[T]he 47th proposition in Euclid might now be voted down with as much ease as any proposition in politics; and therefore if Lord Hawkesbury hates the abstract truths of science as much as he hates concrete truth in human affairs, now is his time for getting rid of the multiplication table, and passing a vote of censure upon the pretensions of the hypotenuse.”

IfsHumansMightScienceHateLordVoteTablesAffairPassingPassingsEaseAbstractConcretePropositionsPretensionCensureMultiplicationEuclid
Book:The works
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“My venture investing career has three phases, all roughly 6-8 years long. The first, at Euclid, was software to Internet. The second, at Flatiron, was Internet to bubble. And the third, at USV, has been web 2 to mobile. I have always used a new firm to denote a new investment phase for me. Throw away the old. Start with the new.”

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Author:Fred Wilson
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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.”

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Author:Benoit Mandelbrot
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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.”

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Book:A Mathematician's Apology
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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.”

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Author:Bernard Bolzano
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“Euclid alone has looked on Beauty bare. Let all who prate of Beauty hold their peace, And lay them prone upon the earth and cease To ponder on themselves, the while they stare At nothing, intricately drawn nowhere In shapes of shifting lineage; let geese Gabble and hiss, but heroes seek release From dusty bondage into luminous air. O blinding hour, O holy, terrible day, When first the shaft into his vision shone Of light anatomized! 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.”

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Author:Edna St. Vincent Millay
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“Like a young heir, come a little prematurely to a large inheritance, we shall wanton and run riot until we have brought our reputation to the brink of ruin, and then, like him, shall have to labor with the current of opinion, when COMPELLED perhaps, to do what prudence and common policy pointed out, as plain as any problem in Euclid, in the first instance.”

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Book:Words of Washington
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“At the age of eleven, I began Euclid, with my brother as my tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world. From that moment until I was thirty-eight, mathematics was my chief interest and my chief source of happiness.”

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Book:Autobiography
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“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.”

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Author:Abraham Lincoln
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“Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.”

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Book:How to solve it: a new aspect of mathematical method
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“Four circles to the kissing come, The smaller are the benter. The bend is just the inverse of The distance from the centre. Though their intrigue left Euclid dumb There's now no need for rule of thumb. Since zero bend's a dead straight line And concave bends have minus sign, The sum of squares of all four bends Is half the square of their sum.”

NeedsLeftLinesJusticeHalfFourKissingMathematicsDistanceMathCirclesMathematicalDumbZeroSquaresCentreIntrigueThumbsStraight LinesMinusInverseEuclid
Author:Frederick Soddy
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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.”

LoveYearsMadeTruthLastsImpossibleHappenedElementsLaysLibraryConvincedGentlemanPropositionsDemonstrationGeometryTheoremsHobbesEuclidMathematical Proof
Author:John Aubrey
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“Blaise Pascal used to mark with charcoal the walls of his playroom, seeking a means of making a circle perfectly round and a triangle whose sides and angle were all equal. He discovered these things for himself and then began to seek the relationship which existed between them. He did not know any mathematical terms and so he made up his own. Using these names he made axioms and finally developed perfect demonstrations, until he had come to the thirty-second proposition of Euclid.”

KnowsMeanMadeUsedNamesFunSidesTermPerfectWallEqualMarkRoundsSeekingCirclesMathematicalThirtyAnglePropositionsDemonstrationAxiomsTrianglesCharcoalPascalEuclid
Author:Catharine Cox Miles
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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.”

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Book:Literary studies ; Religious and metaphysical essays ; Letters on the French coup d'état
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