 | Alexander Ingram - Trigonometry - 1799 - 374 pages
...a magnitude lefs than the leall of the propofed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken...half, and from the remainder more than its half, and fo on ; there fhall at length remain a magnitude lefs than C. For C may be multiplied fo, as at length... | |
 | John Bonnycastle - Euclid's Elements - 1803 - 470 pages
...propofed magnitudes, K. • Let AB and C be any two magnitudes, of which AB is the greater ; then, if from AB there be taken more than its half; and from the remainder more than its half ; and fo on : there will at length remain a magnitude lefs than C. For fince AB and C are each finite magnitudes,... | |
 | John Bonnycastle - 1803 - 306 pages
...magnitudes, Let AB and C be any two magnitudes, of which AB is the greater; then, if from AB there betaken more than./ its half ; and from the remainder more than its half ; and fo on : there will at length remain a magnitude lefs than C. For fince AB and c are each finite magnitudes,... | |
 | Robert Simson - Trigonometry - 1804 - 530 pages
...a magnitude lefs than the leaft of the propofed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the greater. if from AB there be taken more T^ than its half, and from the remainder more A •*.•' than its half, and fo on ; there fhall at... | |
 | Robert Simson - Trigonometry - 1806 - 546 pages
...^*v*-^ to some of the propositions of this book. SseN. IF from the greater of two unequal magnitudes there be taken more than its half, and from the remainder...there shall at length remain a magnitude less than the least of the proposed magnitudes. D Let AB and C be two unequal magnitudes, of which AB is the... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...its half be taken away, and from the remainder its half, D and so on, there will at length remain a A magnitude less than C. For C may be multiplied so as, at length, to become greater than AB. Let DE, therefore, be a multiple of C, which is greater than AB, and let it contain the parts DF, FG, GE... | |
 | 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
...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 rj than its half, and from the remainder more than its half, and so on ; there shall at length remain... | |
 | 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... | |
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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... 
