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" Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB 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 C. For C may be multiplied, so... "
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... - Side 244
av Euclid, Isaac Todhunter - 1883 - 400 sider
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A Short Account of the History of Mathematics

Walter William Rouse Ball - 1901 - 527 sider
..." ; which depends on the proposition that " if from the greater of two unequal magnitudes there tie taken more than its half, and from the remainder more than its half, and so on, there will at length remain a magnitude less than the least of the proposed magnitudes." This proposition...
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A Short History of Science

William Thompson Sedgwick, Harry Walter Tyler - 1917 - 474 sider
...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 XI,...
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The Evolution of the Euclidean Elements: A Study of the Theory of ...

W.R. Knorr - 1975 - 374 sider
...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 to...
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Nature Mathematized: Historical and Philosophical Case Studies in Classical ...

W. R. Shea - 1983 - 325 sider
...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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The American Mathematical Monthly: Devoted to the Interests of ..., Volumer 1-2

1894
...Euclid's Tenth Book: If fron the greater of two unequal magnitudes there be taken more than its half, arm from the remainder more than its half, and so on, there shall at length remain magnitude less than the smaller of the proposed magnitudes. Here the smaller of the proposed magnitudes...
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The popular educator, Volum 2

Popular educator - 1860
...greater of two proposed magnitudes be taken not less than its half, and from the remainder not less than its half, and so on ; there shall at length remain a magnitude less than the least of the proposed magnitudes. For if AB and с be the two proposed magnitudes, of which А...
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