| Euclid, John Playfair - 1826 - 320 sider
...magnitudes, of whieh 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.** A For C may be multiplied so as, at length, to beeome greater than AB. Let DE, therefore, be a multiple... | |
| Robert Simson - 1827 - 513 sider
...EFGH above the 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...there shall at length remain a magnitude less than** the least of the proposed magnitudes. Let then the segments EK, KF, FL, LG, GM, MH, HN, NE, be those... | |
| John Playfair - 1832 - 333 sider
...magnitudes, of which AB is the greater. If from AB there be taken away its half, D and from the remainder **its half, and so on; there •"• shall at length...than C. For C may be multiplied so as, at length, to** be- , come greater than AB. Let DE, therefore, be a J multiple of C, which is .greater than AB, and... | |
| John Playfair - 1833 - 333 sider
...greater; If from AB there be taken away its half, and from the remainder its half, and so on ; there A **shall at length remain a magnitude less than C. For...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,... | |
| 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 a magnitude less than** the least of the proposed magnitudes. A. IHB D For if AB and C be the two proposed magnitudes, of which... | |
| Euclides - 1834
...unequal magnitudes, there be taken SeeN. more than its half, and from the remainder more than its hay, **and so on ; there shall at length remain a magnitude less than** the least of the proposed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the greater... | |
| John Playfair - 1835 - 316 sider
...there be taken away its half, and from the remainder its half, and so on ; there shall at length » D **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 of C, which is greater than AB, and let it Kf -JIT contain the parts DF,... | |
| Euclid - 1835 - 513 sider
...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** Sec N. than its half, and from the remainder more than its half, and so on ; there shall at length... | |
| John Playfair - 1836 - 114 sider
...was to be done. PROP. VI. THEOR. If from the greater of two unequal magnitudes, there be taken mere **than its half, and from the remainder more than its half, and so on : there** shallot length remain a magnitude less than the least of the proposed magnitudes. Let AB and C be two... | |
| John Playfair - 1837 - 318 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...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,... | |
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