Mathematics: The Man-Made Universe (Dover Books on

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It is simplest to think of mathematics as the catalogue of all possible patterns. ... But the change, though steadily and rapidly progressive, has, nevertheless, been gradual; and like those who drift down the stream of a deep and smooth river, we are not aware of the progress we have made, until we fix our eye on the now distant point from which we have been drifted.---Such of the present generation as can recollect the last twenty or twenty-five years of the eighteenth century, will be fully sensible of the truth of this statement especially if their acquaintance and connexions lay among those who, in my younger time, were facetiously called ``folks of the old leaven,'' who still cherished a lingering, though hopeless, attachment to the house of Stuart.
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Smithsonian Contributions to Astrophysics. Volume 5. Number

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This will be an exciting weekend that will provide something for everyone. Much nearer to the mouth of the cave, he heard the notes of a lively Gaelic song, guided by which, in a sunny recess, shaded by a glittering birch-tree, and carpeted with a bank of firm white sand, he found the damsel of the cavern, whose lay had already reached him, busy, to the best of her power, in arranging to advantage a morning repast of milk, eggs, barley-bread, fresh butter, and honey-comb.
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Elements of Number Theory (Dover Phoenix Editions)

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This means that an inconsistent arithmetic is coherent and complete. The spiritual pride, which in mine Host of the Candlestick mantled in a sort of supercilious hypocrisy, was in this man's face elevated and yet darkened by genuine and undoubting fanaticism. The School of Mathematics and Statistics is just one of 25 areas covering 11 disciplines. Evan, upon are not allowed to keep half-a-score of muskets, whether for defence or rescue.'' ``With his tail on!'' echoed Edward in some surprise. ``Yes---that is, with all his usual followers, when he visits those of the same rank.
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Lectures on N_X(p) (Research Notes in Mathematics)

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In The Thermophysics of Porous Media, the author shows that physical consistency requires a… Interfacial phenomena driven by heat or mass transfer are widespread in science and various branches of engineering. But after a short conflict between his eager desire to believe she was in his neighbourhood, guarding, like an angel of mercy, the couch of his sickness, Waverley was compelled to conclude that his conjecture was altogether improbable; since, to suppose she had left the comparatively safe situation at Glennaquoich to descend into the Low Country, now the seat of civil war, and to inhabit such a lurking-place as this, was a thing hardly to be imagined.
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Selected Papers (Springer Collected Works in Mathematics)

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But notwithstanding that the Presbyterians had the persecution in Charles II. and his brother's time, to exasperate them, there was little mischief done beyond the kind of petty violence mentioned * in the text. Specifically, it says that because the addition of new auxiliary hypotheses, e.g. conditionals involving �if�then� statements, would enable each of two distinct theories on the same scientific or mathematical topic to accommodate any new piece of evidence, no physical observation could ever decide between them.
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Psychological Science, Research, Theory, & Application in

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The Baron stared, and said his son and he would certainly ride by Little Veolan, and pay their compliments to the Bailie, but could not think of bringing with them the ``haill comitatus nuptialis, or matrimonial procession.'' He added, ``that, as he understood that the barony had been sold by its unworthy possessor, he was glad to see his old friend Duncan had regained his situation under the new Dominus, or proprietor.'' The Bailie ducked, bowed, and fidgeted, and then again insisted upon his invitation; until the Baron, though rather piqued at the pertinacity of his instances, could not nevertheless refuse to consent, without making evident sensations which he was anxious to conceal.
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Psychological Science Research, Theory, & Application in

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Nevertheless, followers of Brouwer have continued to develop intuitionistic mathematics onto the present day (Troelstra & van Dalen 1988). She allowed that the northern part of the island contained some ancient families, but they were all Whigs and Presbyterians except the Highlanders; and respecting them she must needs say, there could be no great delicacy among the ladies, where the gentlemen's usual attire was, as she had been assured, to say the least, very singular, and not at all decorous.
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The Golden Ratio: The Story of Phi, the Extraordinary Number

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All works of art are constructed according to the rules which geometry involves; and we find the same laws observed in the works of nature. On the subject of general relativity and covering special relativity as well, there is a magnum opus, perhaps even a 44 magnum opus. The Universal Turing Machine, which began as an abstract idea, later laid the groundwork for the development of the modern computer. It was the function of intuition to create new forms; it was the acknowledged right of logic to accept or reject these new forms, in whose birth in had no part. ...the children had to live, so while waiting for logic to sanctify their existence, they throve and multiplied.
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European Journal of Political Theory: Volume 2 Number 1

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Their motions appeared spontaneous and confused, but the result was order and regularity; so that a general must have praised the conclusion, though a martinet might have ridiculed the method by which it was attained. When Waverley again entered upon the subject which he had most at heart, the situation, namely, of his father and his uncle, Colonel Talbot seemed now rather desirous to alleviate than to aggravate his anxiety. And the theory of the real numbers and functions on them is all that is needed to formulate Newtonian mechanics.
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Recent Progress in Analytical Number Theory, Two-Volume Set:

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Various reports were, of course circulated in various ways; some founded on an accurate rehearsal of what may have been partly real, some on circumstances having no concern whatever with the subject, and others on the invention of some importunate persons, who might perhaps imagine, that the readiest mode of forcing the author to disclose himself, was to assign some dishonourable and discreditable cause for his silence. This, as he afterwards learned, proceeded from Gilfillan's party, who had now assembled, the stragglers in front and rear having joined the others.
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