... 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
| 1816
...the proof of prop. i. book x. which imports, that if, from the grc.Uer of two quantities, be taken **more than its half, and from the remainder more than its half, and** fo continually, there will, at length, remain a quantity Icfs than either of thole propofed. On th;s... | |
| John Playfair - 1819 - 333 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... | |
| John Playfair - 1819 - 317 sider
...unequal magnitudes there be taken away its half, and from the remainder its half : and so on; Tliere will **at length remain a magnitude less than the least of the proposed magnitudes.** A H Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken away... | |
| Euclid, Robert Simson - 1821 - 516 sider
...space 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...the circle EFGH above S: therefore the rest of the** circlt-, viz, the polygon EKFLGMHN, is greater than the space S. Describe likewise in thecircle ABCD... | |
| 1823
...the proof of Prob. I. book x. which imports, 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 those proposed. On this foundation... | |
| Peter Nicholson - 1825 - 372 sider
...tome of the propositions of lias book. If from the greater afino unequal magnitudes, there be taken **more than its half, and from the remainder more than...and so on : There shall at length remain a magnitude** Itss than the least of the proposed magnitudes. Let AB and С be two unequal magnitudes, of which AB... | |
| Euclid, John Playfair - 1826 - 320 sider
...unequal magnitudes there be taken away its half, and from the remainder 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 unequal magnitudes, of whieh AB is the greater. If from AB there be taken away its... | |
| Robert Simson - 1827 - 513 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 multi- K plied,... | |
| Euclid, Robert Simson - 1829 - 516 sider
...and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than , v **its half, and from the remainder more than its half,...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... | |
| Thomas Perronet Thompson - 1833 - 150 sider
...greater of two proposed magnitudes be taken not less than its half, and from the remainder not less **than its half, and so on ; there shall at length remain...magnitude less than the least of the proposed magnitudes.** A. IHB D For if AB and C be the two proposed magnitudes, of which AB is the See Note. greater, then... | |
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