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" Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes. "
Elements of Geometry: Containing the Principal Propositions in the First Six ... - Página 213
por Euclid - 1789 - 272 páginas
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A Short History of Science

William Thompson Sedgwick, Harry Walter Tyler - 1917 - 474 páginas
...on the basis of the theorem : If two unequal magnitudes are given, and if one takes from the greater more than its half, and from the remainder more than its half and so on, one arrives sooner or later at a remainder which is less than the smaller given magnitude. Books...
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The Evolution of the Euclidean Elements: A Study of the Theory of ...

W.R. Knorr - 1975 - 374 páginas
...last is proved via a noted convergence principle (X,l): if from a given magnitude there is removed more than its half, and from the remainder more than its half, and so on, the remainder eventually becomes smaller than any preassigned finite magnitude. It is interesting...
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Nature Mathematized: Historical and Philosophical Case Studies in Classical ...

International Conference on the History and Philosophy of Science (3, 1980, Montréal) - 1983 - 325 páginas
...to paraphrase Euclid, we can say that given two unequal quantities, from the greater we can subtract more than its half, and from the remainder more than its half, such that a quantity smaller than a given smaller quantity is always reached (Elements X. prop I)....
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