... 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 - 1855
...Multiples of Magnitudes. HYPOTHESES. 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.** If one magnitude be the same multiple of another, which a part taken from the first is of a part taken... | |
| 1856
...magnitudes be taken not less than its half, and from the remainder not less than its half, and ••« **on ; there shall at length remain a magnitude less than the least of the proposed magnitudes.** For if AB and с be the two proposed magnitudes, of which А в is the greater, then because (by Cor.... | |
| Eucleides - 1860
...V. 1. . . V. c. (p. 34). HYPOTHESES. 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.** If one magnitude be the same multiple of another, which a part taken from the first is of a part taken... | |
| Euclides - 1860
...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. (Const.) For C may be multiplied so as at length to become greater than AB. Let it be so multiplied,... | |
| Euclides - 1864
...(Book x. Prop. I.) Cbe 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. K F H GiFor <7may be multiplied so as at length to become grea Let it be so multiplied, and let... | |
| Euclides - 1865
...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** ; Then there shall at length remain a magnitude less than C. AD FG BCB CONSTRUCTION For C may be multiplied... | |
| Euclid, Isaac Todhunter - 1867 - 400 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...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... | |
| Euclid, Isaac Todhunter - 1867 - 400 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...there shall at length remain a magnitude less than** C. For C may be multiplied so as at length ^ n to become greater than AB. Let it be so multiplied,... | |
| Robert Potts - 1868 - 410 sider
...in the other. BOOK XIL LEMMA I. Jf from the greater of two unequal majnituJes, there be taken mart **than its half, and from the remainder more than its half; and** to on: there shall at length remain a magnitude leu than the least of the proposed magnitudes. (Book... | |
| Euclides, James Hamblin Smith - 1872 - 349 sider
...together. BOOK XII. LEMMA. 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** must at length remain a magnitude less than the smaller of the proposed magnitudes. Let A and B be... | |
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