 | Euclides - 1816 - 588 pages
...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 shiill at length remain a magnitude less than the least of the proposed magnitudes. Let... | |
 | Encyclopedias and dictionaries - 1823 - 858 pages
...the proof of Prob. I. book x. which imports, that if, from the greater of two quantities, you take more than its half, and from the remainder more than its half, and so continually, there will, at length, remain a quantity less than either of those proposed. On this... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...least of the proposed magnitudes. Let AB and С be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from v the remainder more than its half, and so on; jj. there shall at length remain a magnitude less "•... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...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 than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied so as at length... | |
 | Euclid - 1835 - 540 pages
...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 shall at length remain a magnitude less than the least of the proposed magnitudes. Let... | |
 | John Playfair - Geometry - 1836 - 148 pages
...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 than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so as at length... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...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 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... | |
 | Euclid - Geometry - 1838 - 470 pages
...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,... | |
 | 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.... | |
 | Euclides - Geometry - 1841 - 378 pages
...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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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 as at length to become greater than AB. 
