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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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 320 sider
...magnitudes, of whieh 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. A For C may be multiplied so as, at length, to beeome greater than AB. Let DE, therefore, be a multiple...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 sider
...EFGH above the 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...there shall at length remain a magnitude less than the least of the proposed magnitudes. Let then the segments EK, KF, FL, LG, GM, MH, HN, NE, be those...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 sider
...magnitudes, of which AB is the greater. If from AB there be taken away its half, D and from the remainder its half, and so on; there •"• shall at length...than C. For C may be multiplied so as, at length, to be- , come greater than AB. Let DE, therefore, be a J multiple of C, which is .greater than AB, and...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 333 sider
...greater; If from AB there be taken away its half, and from the remainder its half, and so on ; there A shall at length remain a magnitude less than C. For...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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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 a magnitude less than the least of the proposed magnitudes. A. IHB D For if AB and C be the two proposed magnitudes, of which...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...unequal magnitudes, there be taken SeeN. more than its half, and from the remainder more than its hay, and so on ; there shall at length remain a magnitude less than the least of the proposed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the greater...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 sider
...there be taken away its half, and from the remainder its half, and so on ; there shall at length » D 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 of C, which is greater than AB, and let it Kf -JIT contain the parts DF,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 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 Sec N. than its half, and from the remainder more than its half, and so on ; there shall at length...
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The Element of Geometry

John Playfair - 1836 - 114 sider
...was to be done. PROP. VI. THEOR. If from the greater of two unequal magnitudes, there be taken mere than its half, and from the remainder more than its half, and so on : there shallot length remain a magnitude less than the least of the proposed magnitudes. Let AB and C be two...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 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...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,...
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