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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 First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 páginas
...1) the prisms are equal. Wherefore, &c. BOOK XII. LEMMA I.* — 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 [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...proportional to the cubes of their homologous edges. BOOK XII. LEMMA I. 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. (Book...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845
...given line. For it has been shown in the proposition that this is equivalent to taking away from EC more than its half, and from the remainder more than its half, and so on continually ; .-. (Prop. 73, Cor.) the quantity ultimately left is less than any given quantity....
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...shall be equal to one another. BOOK XII. PROPOSITIONS. LEMMA I. IP 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. (Book...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...side of the hexagon. T. Of the 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...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...propositions of this Book. LEMMA I. 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 will at length remain a magnitude less than the least of the proposed magnitudes. Let...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860
...GHKLMN. THE ELEMENTS OF EUCLID. BOOK XII. ' LEMMA I. THEOREM. — 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. DEMONSTRATION....
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...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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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...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 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 - 1867 - 400 páginas
...four right angles. Wherefore, every solid angle &c. QED XIL 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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