| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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