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

Euclid, James Thomson - 1837 - 390 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...the remainder more than its half, and so on ; there will at length remain a magnitude less than C. For C may be multiplied so as at length to become greater...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...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 away its half, and from the remainder its half, and so on, there shall at length remain a magnitude...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 sider
...magnitude less than the least of the proposed magnitudes.* K H Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken...magnitude less than C. For C may be multiplied, so at length to become greater than AB. Let it be so multiplied, and let DE its multiple be greater than...
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The Elements of Euclid

Euclid - 1838 - 416 sider
...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 than its half, and from the remainder more D than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied,...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 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 than its half, and from the remainder , j> more than its half, and so on; there shall at length remain a magnitude less than C. For C may...
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The elements of algebra

James Wood - 1841 - 287 sider
...manner, when с is the dividend, more than its half is taken away, and so on ; but if from any quantity there be taken more than its half, and from the remainder more than its half, and so on, there will, at length, remain a quantity less than any that can be asigned (Eue. x. I.) [109. In practice...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...PROP. A. IF from the greater of two unequal magnitudes there be taken its half, and from the remainder its half, and so on : there shall at length remain a magnitude less than the least of the proposed magnitudes, how small soever it may be. Let A, B, c, D, &c. be a series of...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 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 away its half, and from the remainder its half, and so on ; there shall at length remain a magnitude...
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Lectures on the Principles of Demonstrative Mathematics

Philip Kelland - 1843 - 147 sider
...difference between any two unequal magnitudes being diminished by more than its half, and the remainder by more than its half, and so on ; there shall at length remain a magnitude less than any that may be assigned." It is by this process that Archimedes demonstrates the equality of the area...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 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...the remainder more than its half, and so on ; there will at length remain a magnitude less than C. For C may be multiplied so as at length to become greater...
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