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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: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804
...fpace S. becaufe, 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 its half, and fo on, there fhall at length remain a magnitude lefs than the lead of the propofecl magnitudes. Let...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 sider
...magnitudes. D 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...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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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
...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...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 multi- **' plied,...
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A pocket encyclopædia, or library of general knowledge, Volumer 1-4

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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Pocket Encyclopedia: Or, A Dictionary of Arts, Sciences, and Polite ..., Volum 1

Edward Augustus Kendall - 1811
...the 1st proposition of lunik 10, which is, that if from the greater of. t\vo. 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 those proposed. On this foundation...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volum 5

John Mason Good - 1813
...some of the propositions of this book. If from the greater of two unequal magnitudes, there be taken more than its half, and from the remainder more than...magnitude less than the least of the proposed magnitudes. Prop. I. Theor. Similar polygons inscribed in circles, are to one another as the squares of their diameter«....
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...magnitudes. 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, aod so on; there shall at length remain * magnitude less than C. A For C may be multiplied so as at...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sider
...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 its half, and so on, there shiill at length remain a magnitude less than the least of the proposed magnitudes. Let then the segments...
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