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abstract Address British Association Advancement of Science algebra American Mathematical Society analysis application Archimedes arithmetic astronomy axioms beauty Boston Budget of Paradoxes Bulletin American Mathematical C. J. Lectures calculus chap circle Collected Mathematical Papers conception deduction definite demonstration Descartes discovery elementary elements equations Essays Euclid faculty Gauss geometry History of Mathematics human mind ideas imagination infinite infinitesimal calculus intuition invention investigations Jahresbericht der Deutschen knowledge language laws Leibnitz Leipzig logical Lord Kelvin magnitude mathe mathematician Mathematics London Mathematics New York Mathematik matics means method metic modern Morgan natural philosophy nature Newton Non-Euclidean geometry notion observation Paradoxes London phenomena physical Plato Positive Philosophy Martineau Presidential Address British principles problems propositions pure mathematics Pythagoras quantity Quaternions reason relations scientific sect space student Sylvester symbols Teaching of Mathematics theorem theory things thought tion true truth understanding universal Universal Algebra Werke Kehrbach
Page 334 - Great fleas have little fleas upon their backs to bite 'em, | And little fleas have lesser fleas, and so ad infinitum.
Page 180 - Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
Page 168 - I do not know what I may appear to the world ; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.
Page 188 - As Ovid be an outcast quite abjur'd : Balk" logic with acquaintance that you have, And practise rhetoric in your common talk : Music and poesy use to quicken you ; The mathematics, and the metaphysics, Fall to them, as you find your stomach serves you: No profit grows where is no pleasure ta'en ; — In brief, sir, study what you most affect.
Page 242 - Go, wondrous creature! mount where Science guides; Go, measure earth, weigh air, and state the tides; Instruct the planets in what orbs to run, Correct old Time, and regulate the sun; Go, soar with Plato to th...
Page 368 - In the first course there was a shoulder of mutton, cut into an equilateral triangle, a piece of beef into a rhomboides, and a pudding into a cycloid.
Page 54 - Just so it is in the mind ; would you have a man reason well, you must use him to it betimes, exercise his mind in observing the connection of ideas and following them in train. Nothing does this better than mathematics, which therefore I think should be taught all those who have the time and opportunity, not so much to' make them mathematicians as to make them reasonable creatures...
Page 326 - Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it— an intelligence sufficiently vast to submit these data to analysis — it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom...
Page 187 - For we do not listen with the best regard to the verses of a man who is only a poet, nor to his problems if he is only an algebraist ; but if a man is at once acquainted with the geometric foundations of things and with their festal splendor, his poetry is exact and his arithmetic musical.