 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...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... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...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... | |
 | Euclid - Geometry - 1838 - 470 pages
...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,... | |
 | Euclides - Geometry - 1841 - 378 pages
...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... | |
 | James Wood - Algebra - 1841 - 492 pages
...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... | |
 | Euclides - 1842 - 316 pages
...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... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...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... | |
 | Philip Kelland - Algebra - 1843 - 168 pages
...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... | |
 | Euclides, James Thomson - Geometry - 1845 - 382 pages
...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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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... 
