The Compete Works of Lyof N. Tolstoï
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| Hersteller: | Forgotten Books (Tolstoï, Lyof N.) |
| Stand: | 2015-08-04 03:50:33 |
Produktbeschreibung
Excerpt from The Compete Works of Lyof N. Tolstoï: War and Peace, V-Vi The human intellect cannot grasp the idea of absolutely uninterrupted motion. Man can begin to understand the laws of any kind of motion only when he takes into consideration arbitrarily selected units of such motion. But at the same time from this arbitrary division of unbroken motion into measurable units flows the greater part of human errors. Takes, for instance, the called "sophism" of the ancients, to prove that Achilles would never overtake a tortoise which had the starts of him, even through Achilles ran ten times more swiftly than the tortoise. As soon as Achilles had passed over the distance between them, the tortoise would have advanced one-tenth of that distance; Achilles runs that tenth, the tortoise advances a hundredth, and soon ad infinitum. This problem seemed to the ancients unsolvable. The fallacy of the reasoning that Achilles would never overtake the tortoise arose from this: simply, that intermitted units of motions were arbitrary taken for granted, whereas the motion of Achilles and the tortoise were continuous. By assuming ever smaller and smaller units motion, we only approach the settlement of this question, we never really attain to it. Only by assuming infinitesimal quantities, and the progression up to one-tenth, and by taking the sum of this geometrical progression, can we attain the solution of the question. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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