... 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 - Side 87av John Playfair - 1836 - 114 siderUten tilgangsbegrensning - Om denne boken
| 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...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 magnitudes such that в is half of A,... | |
| John Playfair - 1842 - 317 sider
...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 less than** C. For C may be multiplied so as, at length, to become greater than AB. Let DE, therefore, be a -g\... | |
| 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... | |
| Euclides - 1845
...Prop. 1.) 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. BCE For C may be multiplied so as at length to become greater than AB. Let it be so multiplied,... | |
| Euclid, James Thomson - 1845 - 352 sider
...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 to become greater... | |
| Scottish school-book assoc - 1845
...given line. For it has been shown in the proposition that this is equivalent to taking away from EC **more than its half, and from the remainder more than its half, and so on** continually ; .-. (Prop. 73, Cor.) the quantity ultimately left is less than any given quantity. PROPOSITION... | |
| Euclides - 1846
...given magnitude there be taken a greater than its half, and from the remainder a magnitude greater **than its half, and so on, there shall at length remain a magnitude less than** any other given magnitude less than the former. Let AB and C be the two given magnitudes, of which... | |
| Euclid, John Playfair - 1846 - 317 sider
...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 less than** C. For C may be multiplied so as, at length, to become greater than AB. Let DE, therefore, be a multiple... | |
| Euclides - 1848
...another. BOOK XII. PROPOSITIONS. LEMMA I. IP 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.** (Book x. Prop, i.) PROP. I. THEOREM. Similar polygons inscribed in circles, are to one another as the... | |
| Euclides - 1855
...this Book. LEMMA I. If from the greater of two unequal magnitudes of the same kind, 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 the least of the proposed magnitudes. Let AB and C be two... | |
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