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" For all the fruitful uses of imaginaries, in Geometry, are those which begin and end with real quantities, and use imaginaries only for the intermediate steps. Now in all such cases, we have a real spatial interpretation at the beginning and end of our... "
An Essay on the Foundations of Geometry - Page 45
by Bertrand Russell - 1897 - 201 pages
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An Essay on the Foundations of Geometry

Bertrand Russell - Geometry - 1897 - 221 pages
...correlate, and can be supposed to possess one only by a convenient fiction. 43. The fact that the fiction is convenient, however, may be thought to indicate that...algebraical quantities, and may perform any operations which are algebraically permissible. If the quantities with which we end are capable of spatial interpretation,...
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Memorabilia Mathematica; Or, The Philomath's Quotation-book

Robert Edouard Moritz - Mathematics - 1914 - 436 pages
...are the most powerful instruments. — HILL, THOMAS. North American Review, Vol. 85, p. 285. 1736. All the fruitful uses of imaginaries, in Geometry,...important; in the intermediate links, we are dealing in purely algebraic manner with purely algebraic quantities, and may perform any operations which are...
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Memorabilia Mathematica: Or, The Philomath's Quotation-book

Robert Édouard Moritz - Mathematics - 1914 - 436 pages
...these are the most powerful instruments.—HILL, THOMAS. North American Review, Vol. 85, p. 235. 1735. All the fruitful uses of imaginaries, in Geometry,...important; in the intermediate links, we are dealing in purely algebraic manner with purely algebraic quantities, and may perform any operations which are...
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Lectures on the Philosophy of Mathematics

James Byrnie Shaw - Mathematics - 1918 - 222 pages
...Maxwell." We may repeat the opinion of the philosopher Russell,3 on the imaginary and. on related objects: All the fruitful uses of imaginaries, in Geometry,...and end with real quantities, and use imaginaries 1 Life of Hamilton, Vol. 3, p. 493. 2 Life of Lord Kelvin, p. 1138. 3 Foundations of Geometry (1897),...
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An Essay on the Foundations of Geometry

A. W. Russell - 2017 - 240 pages
...correlate, and can be supposed to possess one only by a convenient fiction. 43. The fact that the fiction is convenient, however, may be thought to indicate that...algebraical quantities, and may perform any operations which are algebraically permissible. If the quantities with which we end are capable of spatial interpretation,...
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