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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, with many additional propositions, and explanatory ...

Euclides - 1855
...Multiples of Magnitudes. HYPOTHESES. 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. If one magnitude be the same multiple of another, which a part taken from the first is of a part taken...
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The Popular Educator, Volum 2

1856
...magnitudes be taken not less than its half, and from the remainder not less than its half, and ••« on ; there shall at length remain a magnitude less than the least of the proposed magnitudes. For if AB and с be the two proposed magnitudes, of which А в is the greater, then because (by Cor....
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860
...V. 1. . . V. c. (p. 34). HYPOTHESES. 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. If one magnitude be the same multiple of another, which a part taken from the first is of a part taken...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...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. (Const.) For C may be multiplied so as at length to become greater than AB. Let it be so multiplied,...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...(Book x. Prop. I.) Cbe 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. K F H GiFor <7may be multiplied so as at length to become grea Let it be so multiplied, and let...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...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, and so on ; Then there shall at length remain a magnitude less than C. AD FG BCB CONSTRUCTION For C may be multiplied...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 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 multiplied, and...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 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 ^ n to become greater than AB. Let it be so multiplied,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 sider
...in the other. BOOK XIL LEMMA I. Jf from the greater of two unequal majnituJes, there be taken mart than its half, and from the remainder more than its half; and to on: there shall at length remain a magnitude leu than the least of the proposed magnitudes. (Book...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 sider
...together. BOOK XII. LEMMA. If from, the greater of two unequal magnitudes of the same kind there be taken more than its half, and from the remainder more than its half, and so on, there must at length remain a magnitude less than the smaller of the proposed magnitudes. Let A and B be...
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