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Page 683 - It is like a grain of mustard seed, which a man took, and cast into his garden; and it grew, and waxed a great tree; and the fowls of the air lodged in the branches of it.
Page 352 - The above method can easily be extended to the case of solids ; we may suppose them to be made up of heavy parallel planes : if we can show that the centres of gravity of these all lie along a line, we know that the centre of gravity of the solid...
Page 657 - I should rejoice to see mathematics taught with that life and animation which the presence and example of her young and buoyant sister could not fail to impart, short roads preferred to long ones, Euclid honourably shelved or buried "deeper than did ever plummet sound...
Page 521 - ... way. The interval between the two is as wide as between empiricism and science, as between the understanding and the reason; or as between the finite and the infinite.
Page 659 - Space is the Grand Continuum from which, as from an inexhaustible reservoir, all the fertilizing ideas of modern analysis are derived; and as Brindley, the engineer, once allowed before a parliamentary committee that, in his opinion, rivers were made to feed navigable canals, I feel almost tempted to say that one principal reason for the existence of space, or at least one principal function which it discharges, is that of feeding mathematical invention.
Page 683 - is like a grain of mustardseed which a man took and cast into his garden.
Page 409 - ... observation has led to a long train of reflections, which will be found embodied in the 3rd part of the memoir. (27) This, in fact, is identical in substance with the noted problem of determining the chance that two straight lines drawn on a black board will cross. Mr Cayley, of whom it may be so truly said, whether the matter he takes in hand be great or small, " nihil tetigit quod non ornavit," .suggests the following independent proof of this.
Page 657 - Euclid honorably shelved or buried "deeper than did ever plummet sound" out of the school-boy's reach, morphology introduced into the elements of Algebra — projection, correlation, and motion accepted as aids to geometry — the mind of the student quickened and elevated and his faith awakened by early initiation into the ruling ideas of polarity, continuity, infinity, and familiarization with the doctrine of the imaginary and inconceivable. It is this living interest in the subject which is so...
Page 659 - ... confidently look forward to a time when they shall form but one body with one soul. Geometry formerly was the chief borrower from arithmetic and algebra, but it has since repaid its obligations with abundant usury; and if I were asked to name, in one word, the pole-star round which the mathematical firmament revolves, the central idea which pervades as a hidden spirit the whole corpus of mathematical doctrine, I should point to Continuity as contained in our notions of space, and say, it is this,...
Page 657 - is that study which knows nothing of observation, nothing of induction, nothing of experiment, nothing of causation"? I, of course, am not so absurd as to maintain that the habit of observation of external nature will be best or in any degree cultivated by the study of mathematics, at all events as that study is at present conducted; and no one can desire more earnestly than myself to see natural and experimental science introduced into our schools as a primary and indispensable branch of education...

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