TODAY IN SCIENCE HISTORY ®  •  TODAYINSCI ®
Celebrating 24 Years on the Web
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “The Superfund legislation... may prove to be as far-reaching and important as any accomplishment of my administration. The reduction of the threat to America's health and safety from thousands of toxic-waste sites will continue to be an urgent�issue �”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index G > Category: Geometrician

Geometrician Quotes (6 quotes)

Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be said to be some equal to others. Multiplications, Divisions, and such sort of Computations, are newly received into Geometry, and that unwarily, and contrary to the first Design of this Science. For whosoever considers the Construction of a Problem by a right Line and a Circle, found out by the first Geometricians, will easily perceive that Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Ancients did so industriously distinguish them from one another, that they never introduced Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegance of Geometry consists. Wherefore that is Arithmetically more simple which is determined by the more simple Equation, but that is Geometrically more simple which is determined by the more simple drawing of Lines; and in Geometry, that ought to be reckoned best which is geometrically most simple.
In 'On the Linear Construction of Equations', Universal Arithmetic (1769), Vol. 2, 470.
Science quotes on:  |  Ancient (198)  |  Arithmetic (144)  |  Arithmetical (11)  |  Avoid (123)  |  Best (467)  |  Both (496)  |  Circle (117)  |  Computation (28)  |  Confound (21)  |  Confounding (8)  |  Consider (428)  |  Consist (223)  |  Construction (114)  |  Contrary (143)  |  Design (203)  |  Determine (152)  |  Distinguish (168)  |  Division (67)  |  Draw (140)  |  Drawing (56)  |  Easily (36)  |  Elegance (40)  |  Equal (88)  |  Equation (138)  |  Expression (181)  |  Far (158)  |  Find (1014)  |  First (1302)  |  Geometry (271)  |  Industrious (12)  |  Introduce (63)  |  Invent (57)  |  Line (100)  |  Lose (165)  |  Modern (402)  |  More (2558)  |  Most (1728)  |  Multiplication (46)  |  Never (1089)  |  Other (2233)  |  Perceive (46)  |  Place (192)  |  Problem (731)  |  Proportion (140)  |  Quantity (136)  |  Reckon (31)  |  Right (473)  |  Simple (426)  |  Simplicity (175)  |  Solid (119)  |  Sort (50)  |  Surface (223)  |  Teaching of Mathematics (39)  |  Tedious (15)  |  Term (357)  |  Terms (184)  |  Truly (118)  |  Two (936)  |  Wherefore (2)  |  Will (2350)

I have often thought that an interesting essay might be written on the influence of race on the selection of mathematical methods. methods. The Semitic races had a special genius for arithmetic and algebra, but as far as I know have never produced a single geometrician of any eminence. The Greeks on the other hand adopted a geometrical procedure wherever it was possible, and they even treated arithmetic as a branch of geometry by means of the device of representing numbers by lines.
In A History of the Study of Mathematics at Cambridge (1889), 123
Science quotes on:  |  Algebra (117)  |  Arithmetic (144)  |  Branch (155)  |  Device (71)  |  Eminence (25)  |  Essay (27)  |  Genius (301)  |  Geometry (271)  |  Greek (109)  |  Influence (231)  |  Interesting (153)  |  Know (1538)  |  Line (100)  |  Mathematics (1395)  |  Mean (810)  |  Means (587)  |  Method (531)  |  Never (1089)  |  Number (710)  |  On The Other Hand (40)  |  Other (2233)  |  Possible (560)  |  Procedure (48)  |  Produced (187)  |  Race (278)  |  Represent (157)  |  Selection (130)  |  Single (365)  |  Special (188)  |  Thought (995)  |  Wherever (51)  |  Write (250)

Logic teaches us that on such and such a road we are sure of not meeting an obstacle; it does not tell us which is the road that leads to the desired end. For this, it is necessary to see the end from afar, and the faculty which teaches us to see is intuition. Without it, the geometrician would be like a writer well up in grammar but destitute of ideas.
…...
Science quotes on:  |  Afar (7)  |  Desire (212)  |  Destitute (2)  |  End (603)  |  Faculty (76)  |  Grammar (15)  |  Idea (881)  |  Intuition (82)  |  Lead (391)  |  Logic (311)  |  Meet (36)  |  Necessary (370)  |  Obstacle (42)  |  Road (71)  |  See (1094)  |  Teach (299)  |  Tell (344)  |  Writer (90)

Men of science belong to two different types—the logical and the intuitive. Science owes its progress to both forms of minds. Mathematics, although a purely logical structure, nevertheless makes use of intuition. Among the mathematicians there are intuitives and logicians, analysts and geometricians. Hermite and Weierstrass were intuitives. Riemann and Bertrand, logicians. The discoveries of intuition have always to be developed by logic.
In Man the Unknown (1935), 123.
Science quotes on:  |  Analyst (8)  |  Belong (168)  |  Joseph Bertrand (6)  |  Both (496)  |  Develop (278)  |  Different (595)  |  Discovery (837)  |  Form (976)  |  Charles Hermite (10)  |  Intuition (82)  |  Intuitive (14)  |  Logic (311)  |  Logician (18)  |  Mathematician (407)  |  Mathematics (1395)  |  Men Of Science (147)  |  Mind (1377)  |  Nevertheless (90)  |  Owe (71)  |  Progress (492)  |  Pure (299)  |  Purely (111)  |  Bernhard Riemann (7)  |  Structure (365)  |  Two (936)  |  Type (171)  |  Use (771)  |   Karl Weierstrass, (10)

The principles of Geology like those of geometry must begin at a point, through two or more of which the Geometrician draws a line and by thus proceeding from point to point, and from line to line, he constructs a map, and so proceeding from local to gen maps, and finally to a map of the world. Geometricians founded the science of Geography, on which is based that of Geology.
Abstract View of Geology, page proofs of unpublished work, Department of Geology, University of Oxford, 1.
Science quotes on:  |  Begin (275)  |  Beginning (312)  |  Construct (129)  |  Construction (114)  |  Draw (140)  |  Drawing (56)  |  Founding (5)  |  Geography (39)  |  Geology (240)  |  Geometry (271)  |  Line (100)  |  Map (50)  |  More (2558)  |  Must (1525)  |  Point (584)  |  Principle (530)  |  Proceeding (38)  |  Through (846)  |  Two (936)  |  World (1850)

When the greatest of American logicians, speaking of the powers that constitute the born geometrician, had named Conception, Imagination, and Generalization, he paused. Thereupon from one of the audience there came the challenge, “What of reason?” The instant response, not less just than brilliant, was: “Ratiocination—that is but the smooth pavement on which the chariot rolls.”
In Lectures on Science, Philosophy and Art (1908), 31.
Science quotes on:  |  American (56)  |  Audience (28)  |  Bear (162)  |  Brilliant (57)  |  Challenge (91)  |  Chariot (9)  |  Conception (160)  |  Constitute (99)  |  Generalization (61)  |  Great (1610)  |  Greatest (330)  |  Imagination (349)  |  Instant (46)  |  Less (105)  |  Logician (18)  |  Name (359)  |  Nature Of Mathematics (80)  |  Pause (6)  |  Pavement (2)  |  Power (771)  |  Ratiocination (4)  |  Reason (766)  |  Response (56)  |  Roll (41)  |  Smooth (34)  |  Speak (240)  |  Speaking (118)


Carl Sagan Thumbnail 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
Quotations by:Albert EinsteinIsaac NewtonLord KelvinCharles DarwinSrinivasa RamanujanCarl SaganFlorence NightingaleThomas EdisonAristotleMarie CurieBenjamin FranklinWinston ChurchillGalileo GalileiSigmund FreudRobert BunsenLouis PasteurTheodore RooseveltAbraham LincolnRonald ReaganLeonardo DaVinciMichio KakuKarl PopperJohann GoetheRobert OppenheimerCharles Kettering  ... (more people)

Quotations about:Atomic  BombBiologyChemistryDeforestationEngineeringAnatomyAstronomyBacteriaBiochemistryBotanyConservationDinosaurEnvironmentFractalGeneticsGeologyHistory of ScienceInventionJupiterKnowledgeLoveMathematicsMeasurementMedicineNatural ResourceOrganic ChemistryPhysicsPhysicianQuantum TheoryResearchScience and ArtTeacherTechnologyUniverseVolcanoVirusWind PowerWomen ScientistsX-RaysYouthZoology  ... (more topics)
Sitewide search within all Today In Science History pages:
Visit our Science and Scientist Quotations index for more Science Quotes from archaeologists, biologists, chemists, geologists, inventors and inventions, mathematicians, physicists, pioneers in medicine, science events and technology.

Names index: | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

Categories index: | 1 | 2 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
Thank you for sharing.
- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton


by Ian Ellis
who invites your feedback
Thank you for sharing.
Today in Science History
Sign up for Newsletter
with quiz, quotes and more.