"Theorem" Quotes from Famous Books
 ... to prove the above-mentioned theorem respecting motion must be made thus: Take two balls of equal weight and shape and let them fall from a great height so that when they start falling they touch one another, and let the investigator stand on the ground ...
— Thoughts on Art and Life • Leonardo da Vinci
... that I have seen you, for many is the whipping I have had for your book of Algebra." Now I never was capable of committing such an unheard-of enormity as being the cause of flagellation to any man by simple or quadratic equations; and it must have been the binomial theorem which had tickled his catastrophe, for it was my father's treatise which had penetrated into the new world of ...
— Canada and the Canadians - Volume I • Sir Richard Henry Bonnycastle
... to whom geometry owes this magnificent theorem, had engraved on his tomb, as one of his proudest titles to fame, the generating spiral and its double, begotten of the unwinding of the thread. An inscription proclaimed, 'Eadem mutata resurgo: I rise again like unto myself.' Geometry would find it difficult to better this splendid flight ...
— The Life of the Spider • J. Henri Fabre
... years ago this chimera became an actual existence, and today it is furnishing a new world to physics, in which mechanics may become geometry, time be co-ordinated with space, and every geometric theorem in the world is a physical theorem in the experimental world in study in the laboratory. Startling indeed it is to the scientist to be told that an artificial dream-world of the mathematician is more real than that he sees with his ...
— Architecture and Democracy • Claude Fayette Bragdon
... if the choice were necessary, which cannot be, I might sacrifice you. There is this duality in man's nature. The ambition of his intellect, the passion, it may be, to force upon the world some vision of his imagination or some theorem of his brain, works in him side by side with his personal being, and the two are never quite fused. Can you not recall a score of examples in history of men who have led this dual existence? You reviewed for me Bismarck's Love Letters and were yourself struck by this sharp ...
— The Jessica Letters: An Editor's Romance • Paul Elmer More
... Jimsy's own version of it. She always kept his letter for the last, childishly, on the nursery theorem of "First the worst, second the same, last the best of all ...
— Play the Game! • Ruth Comfort Mitchell
... Euclid seemed childishly easy, and was thrown aside, but the Descartes baffled him for a time. However, he set to it again and again and before long mastered it. He threw himself heart and soul into mathematics, and very soon made some remarkable discoveries. First he discovered the binomial theorem: familiar now to all who have done any algebra, unintelligible to others, and therefore I say nothing about it. By the age of twenty-one or two he had begun his great mathematical discovery of infinite series and fluxions—now known by the name of the Differential Calculus. ...
— Pioneers of Science • Oliver Lodge
... as difficult as that," said Donald. "While you're talking about peculiar things, I'll tell you one. In class I came right up against Oka Sayye on the solution of a theorem in trigonometry. We both had the answer, the correct answer, but we had arrived at it by widely different routes, and it was up to me to prove that my line of reasoning was more lucid, more natural, the inevitable one by which the solution should be reached. We got so ...
— Her Father's Daughter • Gene Stratton-Porter
... horrible suppressions of states, which, since that time, have struck many a noble nation, and have annulled their certificate of birth, so to speak. All contemporary social crimes have their origin in the partition of Poland. The partition of Poland is a theorem of which all present political outrages are the corollaries. There has not been a despot, nor a traitor for nearly a century back, who has not signed, approved, counter-signed, and copied, ne variatur, the partition of Poland. When the record of modern treasons was examined, that was ...
— Les Miserables - Complete in Five Volumes • Victor Hugo
... kingdoms, making war by land and sea, ringing great bells, waving great banners, they, too—these insolent, boisterous burghers—accomplish their work. Thus, the mighty power of the purse develops itself and municipal liberty becomes a substantial fact. A fact, not a principle; for the old theorem of sovereignty remains undisputed as ever. Neither the nation, in mass, nor the citizens, in class, lay claim to human rights. All upper attributes—legislative, judicial, administrative—remain in the land-master's breast alone. It is an absurdity, ...
— The Rise of the Dutch Republic, 1555-1566 • John Lothrop Motley
... party feeling seems, as far as we can judge, to be still in the future. If we want studies that will, while they last, thoroughly divert the mind from the prejudices of party, science is even better than ancient history; there are no party cries connected with the Binomial Theorem. ...
— Practical Essays • Alexander Bain
... what Mr. Philip said, because it isn't true." She wagged a pedagogic finger at herself. "See here! Think of it in terms of Euclid. If you do a faulty proof by superposition and haven't remembered the theorem rightly, you can go on saying, 'Lay AB along DE' till all's blue and you'll never make C coincide with F. In the same way Mr. Philip can blether to his silly heart's content and he'll never prove that I'm a bold girl. Me, Ellen ...
— The Judge • Rebecca West
... admit, he says, that the direction and the velocity of every atom of matter in the universe (including cerebral matter, i.e., the brain, which is a material thing) are strictly determined, it would not at all follow from the acceptance of this theorem that our mental life is subject to the same necessity. For that to be the case, we should have to show absolutely that a strictly determined psychical state corresponds to a definite cerebral state. This, as we have seen, has not been proved. It is admitted that to some ...
— Bergson and His Philosophy • J. Alexander Gunn
... eternal. It was just as true at the dawn of creation that the square described on the hypotenuse of a right-angle triangle is equal to the square described on the other two sides, as it was when Pythagoras enunciated the theorem. "Thou shall not kill," is a law written by the Divine hand amid tempest and fire, but it stands. "Thou shalt love thy neighbor as thyself," rings from the portals of heaven through the gates of humanity and its command will not go unheeded. They are ...
— The Jericho Road • W. Bion Adkins
... itself obligatory; and when a person is asked to believe that this morality derives its obligation from some general principle round which custom has not thrown the same halo, the assertion is to him a paradox; the supposed corollaries seem to have a more binding force than the original theorem; the superstructure seems to stand better without, than with, what is represented as its foundation. He says to himself, I feel that I am bound not to rob or murder, betray or deceive; but why am I bound to promote the general happiness? If my own happiness lies in something ...
— Utilitarianism • John Stuart Mill
... to us, why is faith in God and in His providence not then weakened in the religious man? Why, on the contrary, does he cling to it more and more? The reason is, because such a faith is not a cold theorem, against which some doubt may eventually arise, but a truth rooted in the love inherent in our nature; and consequently it acquires vigour with the growth of love, and its power cannot be extinguished but when we cease to love. So, also, the other impulses to heroism and ...
— A Guide for the Religious Instruction of Jewish Youth • Isaac Samuele Reggio
... Dawn? How if it never break? How if this West by other Wests is pieced, And these by vacant Wests on Wests increased — One Pain of Space, with hollow ache on ache Throbbing and ceasing not for Christ's own sake? — Big perilous theorem, hard for king and priest: 'Pursue the West but long enough, 'tis East!' Oh, if this watery world no turning take! Oh, if for all my logic, all my dreams, Provings of that which is by that which seems, Fears, hopes, chills, heats, hastes, patiences, droughts, tears, Wife-grievings, slights on ...
— The Poems of Sidney Lanier • Sidney Lanier
... been an extraordinary one. He is a man of good birth and excellent education, endowed by nature with a phenomenal mathematical faculty. At the age of twenty-one he wrote a treatise upon the Binomial Theorem, which has had a European vogue. On the strength of it he won the Mathematical Chair at one of our smaller universities, and had, to all appearances, a most brilliant career before him. But the man had hereditary tendencies of the most diabolical kind. A criminal strain ran in his ...
— Memoirs of Sherlock Holmes • Sir Arthur Conan Doyle
... of classification; it is the finding of resemblance between the phenomenon in question and other phenomena. In Mathematics, the explanation of a theorem is the same as its proof, and consists in showing that it repeats, under different conditions, the definitions and axioms already assumed and the theorems already demonstrated. In Logic, the major premise of every syllogism is an explanation of the conclusion; for the minor premise ...
— Logic - Deductive and Inductive • Carveth Read
... indebted than to any other men of genius from the time of Bacon. The discoveries of Newton are scarcely without a parallel, and he is generally regarded as the greatest mathematical intellect that England has produced. To him the world is indebted for the binomial theorem, discovered at the age of twenty-two; for the invention of fluxions; for the demonstration of the law of gravitation; and for the discovery of the different refrangibility of rays of light. His treatise on Optics and his Principia, ...
— A Modern History, From the Time of Luther to the Fall of Napoleon - For the Use of Schools and Colleges • John Lord
... demonstrate a general theorem, we must give the rule as applied to a particular case; but if we wish to demonstrate a particular case, we must begin with the general rule. For we always find the thing obscure which we wish to prove, and that clear which we use for the proof; ...
— Pascal's Pensees • Blaise Pascal
... birds. When he first brought me a bird, I told him that it was wrong, and tried to convince him, while he was eating it, that he was doing wrong; for he is a reasonable cat, and understands pretty much everything except the binomial theorem and the time down the cycloidal arc. But with no effect. The killing of birds went on to my great regret ...
— Little Masterpieces of American Wit and Humor - Volume I • Various
... is found for the man, or man rises to find his own; until the great impetus in our national life is toward the end of developing the intrinsic values of each child, and fitting the task to it; so long as trade masters the many, and the minds of the majority are attracted toward the simple theorem of making cheap and forcing sales, or buying cheap and selling dear; so long as the child is competitively educated in great classes, and the pride of life is in possession of material things, instead of the eternal things—just so long will we have ...
— Child and Country - A Book of the Younger Generation • Will Levington Comfort
... Marxians. Their Socialism is as little Marxian as Russian. When Marx and Engels forecasted the establishment of proletarian dictatorship it was part of their theorem that economic evolution would have reduced practically all the masses to a proletarian state; that industrial and commercial concentration would have reached such a stage of development that there would be on the one side a small class of owners, and, on the other side, the proletariat. ...
— Bolshevism - The Enemy of Political and Industrial Democracy • John Spargo
... common, everyday language, may be shown by another mathematical illustration. Every student of Algebra learns the binomial theorem, or expression for the square of the sum of two quantities; but he does not reflect upon it, illustrate it, or perceive {39} its every-day applications, and if asked to give the square of 21, will fail to see that he should be able to give the answer instantly without ...
— How to Study • George Fillmore Swain
... In Pascal, for instance, in the persuasive writers generally, how difficult to define the point where, from time to time, argument which, if it is to be worth anything at all, must consist of facts or groups of facts, becomes a pleading—a theorem no longer, but essentially an appeal to the reader to catch the writer's spirit, to think with him, if one can or will—an expression no longer of fact but of his sense of it, his peculiar intuition of a world, prospective, or discerned ...
— Appreciations, with an Essay on Style • Walter Horatio Pater
... short consideration which, independently of every other, convinces me that there is no solid foundation in Mr. Hume's conclusion, is the following. When a theorem is proposed to a mathematician, the first thing he does with it is to try it upon a simple case, and if it produce a false result, he is sure that there must be some mistake in the demonstration. Now to proceed in this way with what may be called Mr. Hume's theorem. If twelve men, whose probity ...
— Evidences of Christianity • William Paley
... the positive, which is destined finally to prevail, by the universal recognition that all phaemomena without exception are governed by invariable laws, with which no volitions, either natural or supernatural, interfere. This general theorem is completed by the addition, that the theological mode of thought has three stages, Fetichism, Polytheism, and Monotheism: the successive transitions being prepared, and indeed caused, by the gradual ...
— Auguste Comte and Positivism • John-Stuart Mill
... is clearly impossible. The conclusion of a geometrical theorem is a truth for all time. There is no difference here between a complicated theorem, having many conditions, and a simpler theorem with fewer. It is indeed easier for a few than for many conditions to be all present together: but ...
— Moral Philosophy • Joseph Rickaby, S. J.
... where my unmilitary glance could trace no regularity, the young lieutenant was perfectly at home. He fathomed the meaning of every ditch, and formed an entire plan of the fortress from its half-obliterated lines. His description of Ticonderoga would be as accurate as a geometrical theorem, and as barren of the poetry that has clustered round its decay. I viewed Ticonderoga as a place of ancient strength, in ruins for half a century: where the flags of three nations had successively waved, and none waved now; where armies had struggled, ...
— Old Ticonderoga, A Picture of The Past - (From: "The Snow Image and Other Twice-Told Tales") • Nathaniel Hawthorne
... follow can be got out of premisses, simply because you show what would follow if you had the required knowledge. When the attempt is made, as it seems to me to be made sometimes, to deduce economical laws from some law of human desire—as from the simple theorem that equal increments of a commodity imply diminishing amounts of utility—I should reply not only that the numerical data are vaguely defined and incapable of being accurately stated, but that the attempt must be illusory because the conclusions are not ...
— Social Rights and Duties, Volume I (of 2) - Addresses to Ethical Societies • Sir Leslie Stephen
... brother—his "after clap"—as Archie B. called him. He was timid, uncertain, pious and given to tears—"bo'hn on a wet Friday"—as Archie B. had often said. He was always the effect of Archie B.'s cause, the illustration of his theorem, the solution of his problem of mischief, the penalty ...
— The Bishop of Cottontown - A Story of the Southern Cotton Mills • John Trotwood Moore
... 'objections,' as he puts it, are only 'difficulties'; they make it hard to understand the theory, but are no more reasons for rejecting it than would be the difficulty which a non-mathematical mind finds in understanding the differential calculus for rejecting 'Taylor's theorem.' And, so far, the difference is rather in the process than the conclusion. Newman believes in God on the testimony of an inner voice, so conclusive and imperative that he can dismiss all apparently contradictory facts, ...
— The Life of Sir James Fitzjames Stephen, Bart., K.C.S.I. - A Judge of the High Court of Justice • Sir Leslie Stephen
... never mind! Come, it's time for me to learn my lessons. See here, what I've got to do," said Tom, drawing Maggie towards him and showing her his theorem, while she pushed her hair behind her ears, and prepared herself to prove her capability of helping him in Euclid. She began to read with full confidence in her own powers; but presently, becoming quite bewildered, her face flushed with irritation. ...
— The Ontario Readers: Fourth Book • Various
... can be, fulfilled; and as to faith, it is simply a vice. So far from taking anything on trust, you must refuse to accept any statement whatsoever till it is proved so plainly you can't help believing it whether you like it or not; just as a theorem in—" ...
— Cecilia de Noel • Lanoe Falconer
... she said, and called her mate, "Sweet Theorem, be with me at this hour. How oft together in a dear debate We two bore witness to our Sovereign's power. But he is dead and henceforth all our days Are wrapped in gloom, And we who never ceased to sing his praise May weep our lord, ...
— The Vagabond and Other Poems from Punch • R. C. Lehmann
... of the child for the parent is a tame and essentially selfish emotion, absolutely powerless when it comes into competition with the passions which are concerned with the transmission of the vital flame. This theorem having been stated, what is the first obligatory scene? Evidently one in which a mother shall refuse a second marriage, with a man whom she loves, because it would injure the prospects and wound the feelings of her adored daughter. Then, when the adored daughter ...
— Play-Making - A Manual of Craftsmanship • William Archer
... on the nest, then the baby sparrows but one day old. If any one thinks it easy to find and photograph birds' nests in the heart of the ancient wood on Athabascan banks in mosquito time he has "another guess coming." The mosquito here is not a joke, not a theorem, but a stinging entity. During the five days we are at Fort McMurray the potatoes in Miss Gordon's garden have grown as many inches, literally an inch a day. Wood violets, wild roses, false Solomon-seal, and the wild sarsaparilla are everywhere; the ...
— The New North • Agnes Deans Cameron
... Barnes's shop nor to the Marshalls for nearly a month. One Sunday morning he was poring over the Moreh Nevochim, for it had proved too powerful a temptation for him, and he fell upon the theorem that without God the Universe could not continue to exist, for God is its Form. It was one of those sayings which may be nothing or much to the reader. Whether it be nothing or much depends upon the ...
— Clara Hopgood • Mark Rutherford
... complimented by Ptolemy, who, however, after much thought and research, decided that he could not accept it as final. His own theory was that the Milky Way was an emigration of lightning bugs; and he supported and reinforced this theorem by the well-known fact that the locusts ...
— Innocents abroad • Mark Twain
... curious prohibition against eating beans; the Hesiodic-Pythagorean [Greek: pros elion me omichein]; the vow of silence, like that taken by the Hindu muni; the doctrine of five elements (aether as fifth); above all, the so-called Pythagorean Theorem, developed in the mathematical Culvas[u]tras[29] of India; the irrrational number [square root symbol]2; then the whole character of the religious-philosophical fraternity, which is exactly analogous to the Indic orders of the time; ...
— The Religions of India - Handbooks On The History Of Religions, Volume 1, Edited By Morris Jastrow • Edward Washburn Hopkins
... either as complementary or as prolongations, range themselves. In pure mathematics we have the Infinitesimal Calculus discovered simultaneously by Leibnitz and Newton, mechanics reduced by d'Alembert to a single theorem, and that superb collection of theories which, elaborated by the Bernouillis, Euler, Clairaut, d'Alembert, Taylor and Maclaurin, is finally completed at the end of the century by Monge, Lagrange, and Laplace.[3102] In astronomy, the series of calculations and observations ...
— The Origins of Contemporary France, Volume 1 (of 6) - The Ancient Regime • Hippolyte A. Taine
... thinking deals more with relations and meanings than with particular objects, images naturally play a smaller part in reasoning than in memory and imagination. Yet they have their place here as well. Students of geometry or trigonometry often have difficulty in understanding a theorem until they succeed in visualizing the surface or solid involved. Thinking in the field of astronomy, mechanics, and many other sciences is assisted at certain points by the ability to form clear and ...
— The Mind and Its Education • George Herbert Betts
... interesting standpoint. In arithmetic, where the sum of the squares of the two sides of a right-angled triangle is illustrated by an example and later on in geometry the same proposition is taken up in a different way and proved as a universal theorem, new and interesting light is thrown upon an old problem of arithmetic. In United States history, after the Revolution has been studied, the biography of a man like Samuel Adams throws much additional and vivid light upon the events and actors in Boston and ...
— The Elements of General Method - Based on the Principles of Herbart • Charles A. McMurry
... paid for by British commodities, therefore, the purchase of Foreign commodities encourages British industry as much as the purchase of British commodities" (Principles of Political Economy, p. 152). The important exception to this theorem arising from the nature of the commodities exported and imported has been already dealt with. Let us examine the vital principle of the theorem. "The capital," says Adam Smith, "which is employed ...
— The History of the Great Irish Famine of 1847 (3rd ed.) (1902) - With Notices Of Earlier Irish Famines • John O'Rourke
... of emotional reaction. If he went to the theatre, which he did out of habit, he could find no pleasure there. The thought of his house of his home, of his wife, and of his absent children moved him as little, he said, as a theorem of Euclid."[76] ...
— The Varieties of Religious Experience • William James
... Dawn? my Dawn? How if it never break? How if this West by other Wests is pierced. And these by vacant Wests and Wests increased— One pain of space, with hollow ache on ache, Throbbing and ceasing not for Christ's own sake? Big, perilous theorem, hard for king and priest; 'Pursue the West but long enough, 'tis East!' Oh, if this watery world no turning take; Oh, if for all my logic, all my dreams, Provings of that which is by that which seems, Fears, hopes, ...
— Christopher Columbus and His Monument Columbia • Various
... Mrs. Whitland mourned him in all sincerity. She was also relieved. One-half of the burden which lay upon her had been lifted; the second half was wrestling with the binomial theorem at Cheltenham College. ...
— Bones in London • Edgar Wallace
... not arranged in strict order of difficulty. And the fact that they have interested and given pleasure to man for untold ages is no doubt due in some measure to the appeal they make to the eye as well as to the brain. Sometimes an algebraical formula or theorem seems to give pleasure to the mathematician's eye, but it is probably only an intellectual pleasure. But there can be no doubt that in the case of certain geometrical problems, notably dissection or superposition puzzles, the aesthetic faculty ...
— Amusements in Mathematics • Henry Ernest Dudeney
... this is one: Two figures being given, to describe a third, which shall be equal to one and similar to the other. And it is reported that Pythagoras, upon the discovery of this problem, offered a sacrifice to the gods; for this is a much more exquisite theorem than that which lays down, that the square of the hypothenuse in a right-angled triangle is equal to the squares of the two sides. Right, said Diogenianus, but what is this to the present question? You will easily ...
— Essays and Miscellanies - The Complete Works Volume 3 • Plutarch
... differences of method and form, which may exist between poet and philosopher, is signally illustrated by the relation between Goethe and Spinoza. What Goethe saw and felt, Spinoza proved and defined. The universal and eternal substance was to Spinoza, as philosopher, a theorem, and to Goethe, as poet, a perception and an emotion. Goethe writes to Jacobi that when philosophy "lays itself out for division," he cannot get on with it, but when it "confirms our original feeling as though we were one with nature," it is welcome to him. In the ...
— The Approach to Philosophy • Ralph Barton Perry |
