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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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The college Euclid: comprising the first six and the parts of the eleventh ...

Euclides - 1865
...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...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
...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...there shall at length remain a magnitude less than the smaller of the proposed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 sider
...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...there shall at length remain a magnitude less than the smaller of the proposed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the...
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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
...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 A ; and divide...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...than the least of the proposed magnitudes. ^ Let AB and C be two unequal magnitudes, of the same kind, of which AB is the greater. If from AB there be taken...and from the remainder more than its half, and so on ; Then there will at length remain a magnitude less than C. Construction. For C may be multiplied so...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 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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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 sider
...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
...propositions of this Book. LEMMA I. If from the greater of two unequal magnitudes of the tame kind, there be taken more than its half, and from the remainder more than its half; and to on : there will at length remain a magnitude less than the least of the proposed magnitudes. Let...
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A Short Account of the History of Mathematics

Walter William Rouse Ball - 1901 - 527 sider
...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 proposition...
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