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" 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 shall at length remain a magnitude less than the least of the proposed magnitudes. "
Elements of Geometry: Containing the Principal Propositions in the First Six ... - Página 213
por Euclid - 1789 - 272 páginas
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 páginas
...right angles. AVherefore, every solid angle &Q. QED BOOK XII. 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 shall at length remain a magnitude less than the smaller of the proposed magnitudes. Let...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 páginas
...circle EFGH above the space 8; 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 shall at length remain a magnitude less than the least of the proposed magnitudes. Let...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 páginas
...magnitudes. Let A and B be two unequal magnitudes of the same kind, of which A is the greater. Then if from A 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 B. Take a multiple of B, as mB, greater than...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...the circle EFGH above the space S. For, by the foregoing 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 will at length remain a magnitude less than the least of the proposed magnitudes. Let...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 páginas
...circle 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 more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes. Let...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 páginas
...right angles. Wherefore, every solid angle &c. QED 'BOOK XII. LEMMA. If from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more t/ian its half, and so on, there shall at length remain a magnitude less than the smaller of the proposed...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...excess of the circle EFGH abo?e the space S. For (XII. Lemma 1) il from the greater of two unequal A magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there will at length remain a magnitude less than the least of the proposed magnitudes. Let...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 400 páginas
...proposed magnitudes. Let AB and C be two unequal magnitiides, 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 as at length...
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A Short Account of the History of Mathematics

Walter William Rouse Ball - 1901 - 527 páginas
..."method of exhaustions " ; which depends on the proposition that " 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 will at length remain a magnitude less than the least of the proposed magnitudes." This...
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A Short Account of the History of Mathematics

Walter William Rouse Ball - 1901 - 527 páginas
..." ; which depends on the proposition that " if from the greater of two unequal magnitudes there tie taken more than its half, and from the remainder more than its half, and so on, there will at length remain a magnitude less than the least of the proposed magnitudes." This...
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