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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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Encyclopaedia Perthensis; Or Universal Dictionary of the Arts ..., Volum 9

1816
...the proof of prop. i. book x. which imports, that if, from the grc.Uer of two quantities, be taken more than its half, and from the remainder more than its half, and fo continually, there will, at length, remain a quantity Icfs than either of thole propofed. On th;s...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 sider
...magnitudes, of which AB is the greater. If from AB there be taken away its half, and from the remainder its half, and so on ; 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 DE, therefore, be a multiple...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 sider
...unequal magnitudes there be taken away its half, and from the remainder its half : and so on; Tliere will at length remain a magnitude less than the least of the proposed magnitudes. A H Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken away...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 516 sider
...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...the circle EFGH above S: therefore the rest of the circlt-, viz, the polygon EKFLGMHN, is greater than the space S. Describe likewise in thecircle ABCD...
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Encyclopaedia Britannica; Or A Dictionary of Arts, Sciences, and ..., Volum 8

1823
...the proof of Prob. I. book x. which imports, 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 those proposed. On this foundation...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 sider
...tome of the propositions of lias book. If from the greater afino unequal magnitudes, there be taken more than its half, and from the remainder more than...and so on : There shall at length remain a magnitude Itss than the least of the proposed magnitudes. Let AB and С be two unequal magnitudes, of which AB...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 320 sider
...unequal magnitudes there be taken away its half, and from the remainder its half: and so on ; There will at length remain a magnitude less than. the least of the proposed magnitudes. Let AB and C be two unequal magnitudes, of whieh AB is the greater. If from AB there be taken away its...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 sider
...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...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- K plied,...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1829 - 516 sider
...and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than , v its half, and from the remainder more than its half,...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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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 150 sider
...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...magnitude less than the least of the proposed magnitudes. A. IHB D For if AB and C be the two proposed magnitudes, of which AB is the See Note. greater, then...
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