Celebrating 18 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “The path towards sustainable energy sources will be long and sometimes difficult. But America cannot resist this transition, we must lead it... That is how we will preserve our planet, commanded to our care by God. That’s what will lend meaning to the creed our fathers once declared.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index S > Category: Straight Line

Straight Line Quotes (17 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.”
Science quotes on:  |  Circle (55)  |  Curve (32)  |  Describe (56)  |  Ellipse (6)  |  Equation (93)  |  Locus (3)  |  Magnitude (41)  |  Parabola (2)  |  Unknown (105)  |  Whenever (9)

A tree nowhere offers a straight line or a regular curve, but who doubts that root, trunk, boughs, and leaves embody geometry?
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 172.
Science quotes on:  |  Bough (7)  |  Curve (32)  |  Doubt (159)  |  Embody (16)  |  Geometry (215)  |  Leaf (49)  |  Nowhere (28)  |  Root (60)  |  Tree (170)  |  Trunk (11)

Archimedes … had stated that given the force, any given weight might be moved, and even boasted, we are told, relying on the strength of demonstration, that if there were another earth, by going into it he could remove this. Hiero being struck with amazement at this, and entreating him to make good this problem by actual experiment, and show some great weight moved by a small engine, he fixed accordingly upon a ship of burden out of the king’s arsenal, which could not be drawn out of the dock without great labor and many men; and, loading her with many passengers and a full freight, sitting himself the while far off with no great endeavor, but only holding the head of the pulley in his hand and drawing the cords by degrees, he drew the ship in a straight line, as smoothly and evenly, as if she had been in the sea. The king, astonished at this, and convinced of the power of the art, prevailed upon Archimedes to make him engines accommodated to all the purposes, offensive and defensive, of a siege. … the apparatus was, in most opportune time, ready at hand for the Syracusans, and with it also the engineer himself.
Plutarch
In John Dryden (trans.), Life of Marcellus.
Science quotes on:  |  Accommodate (10)  |  According (9)  |  Actual (47)  |  Amazement (12)  |  Apparatus (37)  |  Archimedes (53)  |  Arsenal (6)  |  Art (284)  |  Astonished (8)  |  At Hand (4)  |  Boast (21)  |  Burden (27)  |  Convinced (22)  |  Cord (3)  |  Defensive (2)  |  Degree (81)  |  Demonstration (81)  |  Draw (55)  |  Earth (635)  |  Endeavor (41)  |  Engine (29)  |  Engineer (97)  |  Experiment (600)  |  Far (154)  |  Fix (25)  |  Force (249)  |  Freight (3)  |  Full (63)  |  Give (200)  |  Good (345)  |  Great (524)  |  Hand (141)  |  Head (80)  |  Hiero (2)  |  Hold (92)  |  King (32)  |  Labor (71)  |  Load (11)  |  Mathematicians and Anecdotes (123)  |  Move (94)  |  Offensive (4)  |  Passenger (10)  |  Power (358)  |  Prevail (16)  |  Problem (490)  |  Pulley (2)  |  Purpose (193)  |  Ready (37)  |  Rely (11)  |  Remove (26)  |  Sea (187)  |  Ship (44)  |  Show (90)  |  Siege (2)  |  Sit (47)  |  Small (161)  |  Smoothly (2)  |  State (136)  |  Strength (79)  |  Strike (39)  |  Syracuse (5)  |  Tell (110)  |  Time (594)  |  Weight (75)

Euclid always contemplates a straight line as drawn between two definite points, and is very careful to mention when it is to be produced beyond this segment. He never thinks of the line as an entity given once for all as a whole. This careful definition and limitation, so as to exclude an infinity not immediately apparent to the senses, was very characteristic of the Greeks in all their many activities. It is enshrined in the difference between Greek architecture and Gothic architecture, and between Greek religion and modern religion. The spire of a Gothic cathedral and the importance of the unbounded straight line in modern Geometry are both emblematic of the transformation of the modern world.
In Introduction to Mathematics (1911), 119.
Science quotes on:  |  Activity (128)  |  Apparent (39)  |  Architecture (43)  |  Beyond (104)  |  Both (81)  |  Careful (24)  |  Cathedral (15)  |  Characteristic (94)  |  Contemplate (17)  |  Definite (42)  |  Definition (191)  |  Difference (246)  |  Draw (55)  |  Enshrine (2)  |  Entity (31)  |  Euclid (52)  |  Exclude (7)  |  Geometry (215)  |  Give (200)  |  Gothic (3)  |  Greek (71)  |  Immediately (21)  |  Importance (216)  |  Infinity (72)  |  Limitation (30)  |  Line (89)  |  Mention (23)  |  Modern (159)  |  Modern Mathematics (36)  |  Modern World (3)  |  Point (122)  |  Produce (100)  |  Religion (239)  |  Segment (6)  |  Sense (315)  |  Spire (5)  |  Think (341)  |  Transformation (54)  |  Unbounded (5)  |  Whole (189)

Every body continues in its state of rest or uniform motion in a straight line, except in so far as it doesn’t. … The suggestion that the body really wanted to go straight but some mysterious agent made it go crooked is picturesque but unscientific.
Paraphasing Newton’s First Law of Motion. In a Gifford Lecture delivered at the University of Edinburgh (1927), 'Gravitation: The Law', The Nature of the Physical World (1928), 124.
Science quotes on:  |  Body (243)  |  Continue (63)  |  Far (154)  |  First Law Of Motion (3)  |  Motion (158)  |  Sir Isaac Newton (327)  |  Rest (93)  |  State (136)  |  Uniform (17)

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.
In poem, 'The Kiss Precise', Nature (20 Jun 1936), 137, 1021, as quoted, cited, explained and illustrated in Martin Gardner, The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems (2001), 139-141.
Science quotes on:  |  Bend (12)  |  Centre (27)  |  Circle (55)  |  Concave (3)  |  Dead (57)  |  Distance (76)  |  Dumb (9)  |  Euclid (52)  |  Half (56)  |  Intrigue (2)  |  Inverse (6)  |  Kiss (4)  |  Leave (127)  |  Minus (5)  |  Need (283)  |  Rule Of Thumb (3)  |  Sign (56)  |  Small (161)  |  Square (23)  |  Sum (41)  |  Zero (19)

In Euclid each proposition stands by itself; its connection with others is never indicated; the leading ideas contained in its proof are not stated; general principles do not exist. In modern methods, on the other hand, the greatest importance is attached to the leading thoughts which pervade the whole; and general principles, which bring whole groups of theorems under one aspect, are given rather than separate propositions. The whole tendency is toward generalization. A straight line is considered as given in its entirety, extending both ways to infinity, while Euclid is very careful never to admit anything but finite quantities. The treatment of the infinite is in fact another fundamental difference between the two methods. Euclid avoids it, in modern mathematics it is systematically introduced, for only thus is generality obtained.
In 'Geometry', Encyclopedia Britannica (9th edition).
Science quotes on:  |  Admit (44)  |  Aspect (57)  |  Attach (13)  |  Avoid (52)  |  Both (81)  |  Bring (90)  |  Careful (24)  |  Connection (107)  |  Consider (80)  |  Contain (67)  |  Difference (246)  |  Entirety (4)  |  Euclid (52)  |  Exist (147)  |  Extend (41)  |  Fact (725)  |  Finite (31)  |  Fundamental (158)  |  General (156)  |  Generality (34)  |  Generalization (41)  |  Give (200)  |  Great (524)  |  Group (72)  |  Idea (577)  |  Importance (216)  |  Indicate (18)  |  Infinite (128)  |  Infinity (72)  |  Introduce (41)  |  Lead (158)  |  Method (230)  |  Modern (159)  |  Modern Mathematics (36)  |  Obtain (45)  |  On The Other Hand (32)  |  Pervade (9)  |  Principle (285)  |  Proof (243)  |  Proposition (80)  |  Quantity (64)  |  Separate (69)  |  Stand (107)  |  State (136)  |  Systematically (7)  |  Tendency (54)  |  Theorem (88)  |  Thought (536)  |  Toward (45)  |  Treatment (100)  |  Whole (189)

It has been asserted … that the power of observation is not developed by mathematical studies; while the truth is, that; from the most elementary mathematical notion that arises in the mind of a child to the farthest verge to which mathematical investigation has been pushed and applied, this power is in constant exercise. By observation, as here used, can only be meant the fixing of the attention upon objects (physical or mental) so as to note distinctive peculiarities—to recognize resemblances, differences, and other relations. Now the first mental act of the child recognizing the distinction between one and more than one, between one and two, two and three, etc., is exactly this. So, again, the first geometrical notions are as pure an exercise of this power as can be given. To know a straight line, to distinguish it from a curve; to recognize a triangle and distinguish the several forms—what are these, and all perception of form, but a series of observations? Nor is it alone in securing these fundamental conceptions of number and form that observation plays so important a part. The very genius of the common geometry as a method of reasoning—a system of investigation—is, that it is but a series of observations. The figure being before the eye in actual representation, or before the mind in conception, is so closely scrutinized, that all its distinctive features are perceived; auxiliary lines are drawn (the imagination leading in this), and a new series of inspections is made; and thus, by means of direct, simple observations, the investigation proceeds. So characteristic of common geometry is this method of investigation, that Comte, perhaps the ablest of all writers upon the philosophy of mathematics, is disposed to class geometry, as to its method, with the natural sciences, being based upon observation. Moreover, when we consider applied mathematics, we need only to notice that the exercise of this faculty is so essential, that the basis of all such reasoning, the very material with which we build, have received the name observations. Thus we might proceed to consider the whole range of the human faculties, and find for the most of them ample scope for exercise in mathematical studies. Certainly, the memory will not be found to be neglected. The very first steps in number—counting, the multiplication table, etc., make heavy demands on this power; while the higher branches require the memorizing of formulas which are simply appalling to the uninitiated. So the imagination, the creative faculty of the mind, has constant exercise in all original mathematical investigations, from the solution of the simplest problems to the discovery of the most recondite principle; for it is not by sure, consecutive steps, as many suppose, that we advance from the known to the unknown. The imagination, not the logical faculty, leads in this advance. In fact, practical observation is often in advance of logical exposition. Thus, in the discovery of truth, the imagination habitually presents hypotheses, and observation supplies facts, which it may require ages for the tardy reason to connect logically with the known. Of this truth, mathematics, as well as all other sciences, affords abundant illustrations. So remarkably true is this, that today it is seriously questioned by the majority of thinkers, whether the sublimest branch of mathematics,—the infinitesimal calculus—has anything more than an empirical foundation, mathematicians themselves not being agreed as to its logical basis. That the imagination, and not the logical faculty, leads in all original investigation, no one who has ever succeeded in producing an original demonstration of one of the simpler propositions of geometry, can have any doubt. Nor are induction, analogy, the scrutinization of premises or the search for them, or the balancing of probabilities, spheres of mental operations foreign to mathematics. No one, indeed, can claim preeminence for mathematical studies in all these departments of intellectual culture, but it may, perhaps, be claimed that scarcely any department of science affords discipline to so great a number of faculties, and that none presents so complete a gradation in the exercise of these faculties, from the first principles of the science to the farthest extent of its applications, as mathematics.
In 'Mathematics', in Henry Kiddle and Alexander J. Schem, The Cyclopedia of Education, (1877.) As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 27-29.
Science quotes on:  |  Analogy (56)  |  Applied Mathematics (15)  |  Attention (115)  |  Auguste Comte (20)  |  Count (48)  |  Curve (32)  |  Discovery (676)  |  Distinguish (61)  |  Empirical (27)  |  Formula (79)  |  Foundation (105)  |  Genius (243)  |  Geometry (215)  |  Hypothesis (249)  |  Illustration (28)  |  Imagination (268)  |  Inspection (6)  |  Intellectual (120)  |  Investigation (175)  |  Logic (247)  |  Memorize (4)  |  Memory (105)  |  Multiplication Table (10)  |  Nature Of Mathematics (77)  |  Observation (445)  |  Perception (61)  |  Problem (490)  |  Representation (35)  |  Scrutinize (5)  |  Solution (211)  |  Triangle (10)

Law 2: A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Axioms, or Laws of Motion, Law 2, 416.
Science quotes on:  |  Force (249)  |  Law Of Motion (13)  |  Proportion (70)

Lawyers have to make a living and can only do so by inducing people to believe that a straight line is crooked. This accounts for their penchant for politics, where they can usually find everything crooked enough to delight their hearts.
As quoted in Harry Black, Canada and the Nobel Prize: Biographies, Portraits and Fascinating Facts (2002), 19.
Science quotes on:  |  Belief (503)  |  Crooked (3)  |  Delight (64)  |  Heart (139)  |  Lawyer (21)  |  Politics (95)

Our knowledge of stars and interstellar matter must be based primarily on the electromagnetic radiation which reaches us. Nature has thoughtfully provided us with a universe in which radiant energy of almost all wave lengths travels in straight lines over enormous distances with usually rather negligible absorption.
In 'Flying Telescopes', Bulletin of the Atomic Scientists (May 1961), Vol. 17, No. 5, 191.
Science quotes on:  |  Absorption (8)  |  Astronomy (203)  |  Distance (76)  |  Electromagnetic Radiation (2)  |  Enormous (41)  |  Interstellar (6)  |  Knowledge (1293)  |  Matter (340)  |  Nature (1211)  |  Negligible (3)  |  Star (336)  |  Thoughtful (10)  |  Travel (61)  |  Universe (683)  |  Wavelength (6)

Some of the men stood talking in this room, and at the right of the door a little knot had formed round a small table, the center of which was the mathematics student, who was eagerly talking. He had made the assertion that one could draw through a given point more than one parallel to a straight line; Frau Hagenström had cried out that this was impossible, and he had gone on to prove it so conclusively that his hearers were constrained to behave as though they understood.
In Little Herr Friedemann (1961), 25.
Science quotes on:  |  Assertion (32)  |  Behave (17)  |  Conclusive (7)  |  Constrain (8)  |  Draw (55)  |  Eager (15)  |  Given (5)  |  Impossible (108)  |  Mathematics (1149)  |  Parallel (17)  |  Point (122)  |  Prove (108)  |  Student (201)  |  Understand (326)

The path isn’t a straight line; it’s a spiral. You continually come back to things you thought you understood and see deeper truths.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 246
Science quotes on:  |  Back (104)  |  Continually (16)  |  Deep (121)  |  Path (84)  |  See (369)  |  Spiral (14)  |  Thought (536)  |  Truth (914)  |  Understand (326)

To work our railways, even to their present extent, there must be at least 5,000 locomotive engines; and supposing an engine with its tender to measure only 35 feet, it will be seen, that the whole number required to work our railway system would extend, in one straight line, over 30 miles, or the whole distance from London to Chatham.
From 'Railway System and its Results' (Jan 1856) read to the Institution of Civil Engineers, reprinted in Samuel Smiles, Life of George Stephenson (1857), 512.
Science quotes on:  |  Locomotive (8)  |  Mile (39)  |  Railroad (27)

What distinguishes the straight line and circle more than anything else, and properly separates them for the purpose of elementary geometry? Their self-similarity. Every inch of a straight line coincides with every other inch, and of a circle with every other of the same circle. Where, then, did Euclid fail? In not introducing the third curve, which has the same property—the screw. The right line, the circle, the screw—the representations of translation, rotation, and the two combined—ought to have been the instruments of geometry. With a screw we should never have heard of the impossibility of trisecting an angle, squaring the circle, etc.
From Letter (15 Feb 1852) to W.R. Hamilton, collected in Robert Perceval Graves, Life of W.R. Hamilton (1889), Vol. 3, 343.
Science quotes on:  |  Angle (19)  |  Circle (55)  |  Coincide (5)  |  Combine (34)  |  Curve (32)  |  Distinguish (61)  |  Elementary (45)  |  Euclid (52)  |  Fail (58)  |  Geometry (215)  |  Impossible (108)  |  Instrument (92)  |  Introduce (41)  |  Line (89)  |  Property (123)  |  Representation (35)  |  Rotation (7)  |  Screw (7)  |  Similar (35)  |  Square (23)  |  Translation (15)

When I was eight, I played Little League. I was on first; I stole third; I went straight across. Earlier that week, I learned that the shortest distance between two points was a direct line. I took advantage of that knowledge.
In Comic Relief (1996).
Science quotes on:  |  Advantage (73)  |  Geometry (215)  |  Joke (73)  |  Knowledge (1293)  |  Point (122)  |  Shortest Distance (2)  |  Steal (13)

When the boy begins to understand that the visible point is preceded by an invisible point, that the shortest distance between two points is conceived as a straight line before it is ever drawn with the pencil on paper, he experiences a feeling of pride, of satisfaction. And justly so, for the fountain of all thought has been opened to him, the difference between the ideal and the real, potentia et actu, has become clear to him; henceforth the philosopher can reveal him nothing new, as a geometrician he has discovered the basis of all thought.
In Sprüche in Reimen. Sprüche in Prosa. Ethisches (1850), Vol. 3, 214. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 67. From the original German, “Wenn der knabe zu begreifen anfängt, daß einem sichtbaren Punkte ein unsichtbarer vorhergehen müsse, daß der nächste Weg zwischen zwei Punkten schon als Linie gedacht werde, ehe sie mit dem Bleistift aufs Papier gezogen wird, so fühlt er einen gewissen Stolz, ein Behagen. Und nicht mit Unrecht; denn ihm ist die Quelle alles Denkens aufgeschlossen, Idee und Verwirklichtes, potentia et actu, ist ihm klargeworden; der Philosoph entdeckt ihm nichts Neues; dem Geometer war von seiner Seite der Grund alles Denkens aufgegangen.” The Latin phrase, “potentia et actu” means “potentiality and actuality”.
Science quotes on:  |  Basis (89)  |  Begin (106)  |  Boy (46)  |  Clear (97)  |  Conceive (36)  |  Difference (246)  |  Discover (196)  |  Draw (55)  |  Experience (338)  |  Fountain (16)  |  Geometer (22)  |  Ideal (69)  |  Invisible (38)  |  Justly (6)  |  New (483)  |  Nothing (385)  |  Open (66)  |  Paper (82)  |  Pencil (17)  |  Philosopher (164)  |  Point (122)  |  Precede (20)  |  Pride (64)  |  Real (148)  |  Reveal (50)  |  Satisfaction (56)  |  Shortest Distance (2)  |  Thought (536)  |  Understand (326)  |  Visible (37)


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 |

- 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



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