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" ... 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. "
The Element of Geometry - Side 87
av John Playfair - 1836 - 114 sider
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...be two unequal magnitudes, of the same kind, 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 ; Then there will at length remain a magnitude less than C. Construction. For C may be multiplied so...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1876
...space S ; because, by the preceding Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more than...magnitudes. Let then the segments EK, KF, FL, LG, GM, MH, UN, NE be those that remain, and are together less than the excess of the circle EG above S : therefore...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 sider
...Prop. I.) Let A Band Cbe two unequal magnitudes, of which A7ii* the greater. If from AB there be taken more than its half, and from the remainder more than...there shall at length remain a magnitude less than C. D I A I K F H For C may be multiplied so as at length to become greater than AB* Let it be so multiplied,...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 sider
...magnitudes. Lot 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...there shall at length remain a magnitude less than C. For C may be multiplied so as at length to become greater than AB. Let it bo so multiplied, and...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...this Book. LEMMA I. If from the greater of two unequal magnitudes of the tame kind, there be taken more than its half, and from the remainder more than its half; and to on : there will at length remain a magnitude less than the least of the proposed magnitudes. Let...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 400 sider
...magnitudes. Let AB and C be two unequal magnitiides, of which AB is the greater : if from AB there be taken more than its half, and from the remainder more than...there shall at length remain a magnitude less than C. For C may be multiplied so as at length to become greater than AB. Let it be so multiplied, and...
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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 Account of the History of Mathematics

Walter William Rouse Ball - 1901 - 527 sider
...there be 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 was placed by Euclid as the first proposition of the tenth book of his Elfmentx, but...
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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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