A Treatise on Fluxions: In Two Volumes, Volume 1

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W. Baynes and W. Davis, 1801 - Calculus - 412 pages
 

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Page 46 - If by this inquiry into the nature of the understanding I can discover the powers thereof, how far they reach, to what things they are in any degree proportionate, and where they fail us, I suppose it may be of use to prevail with the busy mind of man to be more cautious in meddling with things exceeding its comprehension, to stop when it is at the utmost extent of its tether, and to sit down in a quiet ignorance of those things which, upon examination, are found to be beyond the reach...
Page xv - Berkeley, bishop of Cloyne, published a piece called "The Analyst ;" in which he took occasion, from some disputes that had arisen concerning the grounds of the fluxionary method, to explode the method itself, and also to charge mathematicians in general with infidelity in religion. Maclaurin thought himself included in this charge, and began an answer to Berkeley's book: but, as he proceeded, so many discoveries, so many new theories and problems occurred to him, that, instead of a vindicatory pamphlet,...
Page x - ... several expressions, which, though convenient, might be liable to exceptions, and, perhaps, occasion disputes. I have always represented fluxions of all orders by finite quantities, the supposition of an infinitely little magnitude being too bold a postulatum for such a science as geometry. But, because the method of infinitesimals is much in use, and is valued for its conciseness, 1 thought it was requisite to account explicitly for the truth, and perfect accuracy, of the conclusions that are...
Page xvi - In the mean time, he was continually gratifying the public with some performance or observation of his own, many of which were published in the fifth and sixth volumes of the " Medical Essays,
Page 56 - ... flowing quantities." For example: I don't here consider Mathematical Quantities as composed of Parts extremely small, but as generated by a continual motion. Lines are described, and by describing are generated, not by any apposition of Parts, but by a continual motion of Points. Surfaces are generated by the motion of Lines, Solids by the motion of Surfaces, Angles by the Rotation of their Legs, Time by a continual flux...
Page xviii - Maclaurin was a very good as well as a very great man, and worthy of love as well as admiration. His peculiar merit as a philosopher was, that all his studies were accommodated to general utility ; and we find, in many places of his works, an application even of the most abstruse theories, to the perfecting of mechanical arts.
Page xix - Account of sir Isaac Newton's Philosophical discoveries." His "Algebra," though not finished by himself, is yet allowed to be excellent in its kind ; containing, in no large volume, a complete elementary treatise of that science, as far as it has hitherto been carried ; besides some neat analytical papers on curve lines. His "Account of sir Isaac Newton's Philosophy" was occasioned by the following circumstances : sir Isaac dying in the beginning of 1728, his nephew, Mr.
Page xvii - ... before he could finish the memorials he proposed to send, the premium was limited to the discovery of a North-West passage : and he used to regret, that the word West was inserted, because he thought that passage, if at all to be found, must lie not far from the pole. In 1745, having been very active in fortifying the city of Edinburgh against the rebel army, he was obliged to fly to the north of England ; where he was invited by Herring, then archbishop of York, to reside with him during his...
Page xv - These being of different standing and proficiency, he was obliged to divide them into four or five classes, in each of which he employed a full hour every day, from the first of Nov. to the first of June. In the first class he taught the first six books of " Euclid's Elements," plain trigonometry, practical geometry, the elements of fortification, and an introduction to algebra.
Page xiv - Newton, and other eminent men ; at which time also he was admitted a member of the Royal Society : and in another journey, in 1721, he contracted an intimacy with Martin Folkes, Esq. the President of it, which continued during his whole life.

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