 ... 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 - 316 sider
...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 - 332 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 - 168 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 - 546 sider
...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 - 382 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 - 444 sider
...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 - 292 sider
...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 - 334 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 - 52 sider
...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 - 270 sider
...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... | |
| |
