 ... 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.  The Element of Geometry - Page 87by John Playfair - 1836 - 114 pagesFull view - About this book
 | Robert Simson - Trigonometry - 1804 - 530 pages
...fpace S. becaufe, 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 fo on, there fhall at length remain a magnitude lefs than the lead of the propofecl magnitudes. Let... | |
 | Robert Simson - Trigonometry - 1806 - 546 pages
...magnitudes. D 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...there shall at length remain a magnitude less than C. For C may be multiplied so as at length to become greater than AB. Let it be so multiplied, and... | |
 | William Nicholson - 1809 - 752 pages
...proof of the 1st proposition of book 10, which is, that if from the creator of two quantities, yon 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 foundation... | |
 | William Nicholson - Natural history - 1809 - 700 pages
...proof of the 1st proposition of book 10, which is, mat if from the greater of two quantities, yon take more than its half, and from the remainder more than its half, and so continually, there wi&, at length, remain a quantity less than either of those proposed. On this foundation... | |
 | Euclid - Geometry - 1810 - 554 pages
...Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more rj than its half, and from the remainder more than its...there shall at length remain a magnitude less than C. For C may be multiplied so, as at length to become greater than AB. Let it be so multi- **' plied,... | |
 | Edward Augustus Kendall - 1811 - 474 pages
...proof of the 1st proposition of book 10, which is, 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 thoca proposed. On this foundation... | |
 | Edward Augustus Kendall - Encyclopedias and dictionaries - 1811 - 962 pages
...the 1st proposition of lunik 10, which is, that if from the greater of. t\vo. 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 foundation... | |
 | John Mason Good - 1813 - 714 pages
...some of the propositions of this book. If from the greater of two unequal magnitudes, there be taken more than its half, and from the remainder more than...magnitude less than the least of the proposed magnitudes. Prop. I. Theor. Similar polygons inscribed in circles, are to one another as the squares of their diameter«.... | |
 | Euclides - 1814 - 560 pages
...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, aod so on; there shall at length remain * magnitude less than C. A For C may be multiplied so as at... | |
 | Euclides - 1816 - 588 pages
...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 then the segments... | |
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