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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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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 351 sider
...a magnitude lefs than the leall of the propofed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken...half, and from the remainder more than its half, and fo on ; there fhall at length remain a magnitude lefs than C. For C may be multiplied fo, as at length...
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

John Bonnycastle - 1803 - 279 sider
...propofed magnitudes, K. • Let AB and C be any two magnitudes, of which AB is the greater ; then, if from AB there be taken more than its half; and from the remainder more than its half ; and fo on : there will at length remain a magnitude lefs than C. For fince AB and C are each finite magnitudes,...
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

John Bonnycastle - 1803 - 279 sider
...magnitudes, Let AB and C be any two magnitudes, of which AB is the greater; then, if from AB there betaken more than./ its half ; and from the remainder more than its half ; and fo on : there will at length remain a magnitude lefs than C. For fince AB and c are each finite magnitudes,...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804
...a magnitude lefs than the leaft of the propofed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the greater. if from AB there be taken more T^ than its half, and from the remainder more A •*.•' than its half, and fo on ; there fhall at...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 sider
...^*v*-^ to some of the propositions of this book. SseN. IF from the greater of two unequal magnitudes there be taken more than its half, and from the remainder...there shall at length remain a magnitude less than the least of the proposed magnitudes. D Let AB and C be two unequal magnitudes, of which AB is the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 sider
...its half be taken away, and from the remainder its half, D and so on, there will at length remain a A magnitude less than C. For C may be multiplied so as, at length, to become greater than AB. Let DE, therefore, be a multiple of C, which is greater than AB, and let it contain the parts DF, FG, GE...
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The British encyclopedia, or, Dictionary of arts and sciences, Volum 3

William Nicholson - 1809
...proof of the 1st proposition of book 10, which is, that if from the creator of two quantities, yon take more than its half, and from the remainder more than its half, and so continually, there will, at length, remain a quantity less than either of those proposed. On this foundation...
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The British Encyclopedia, Or Dictionary of Arts and Sciences ..., Volum 3

William Nicholson - 1809
...proof of the 1st proposition of book 10, which is, mat if from the greater of two quantities, yon take more than its half, and from the remainder more than its half, and so continually, there wi&, at length, remain a quantity less than either of those proposed. On this foundation...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 sider
...a magnitude less than the least of the proposed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more rj than its half, and from the remainder more than its half, and so on ; there shall at length remain...
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A pocket encyclopædia, or library of general knowledge, Volum 2

Edward Augustus Kendall - 1811
...proof of the 1st proposition of book 10, which is, that if from the greater of two quantities, you take more than its half, and from the remainder more than its half, and so continually, there will at length remain a quantity less than either of thoca proposed. On this foundation...
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