... 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 - 1874
...be two unequal magnitudes, of the same kind, 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 will at length remain a magnitude less than C. Construction. For C may be multiplied so... | |
| Euclides - 1876
...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...magnitudes. Let then the segments EK, KF, FL, LG, GM, MH,** UN, NE be those that remain, and are together less than the excess of the circle EG above S : therefore... | |
| Robert Potts - 1876 - 403 sider
...Prop. I.) Let A Band Cbe two unequal magnitudes, of which A7ii* 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. D I A I K F H For C may be multiplied so as at length to become greater than AB* Let it be so multiplied,... | |
| Isaac Todhunter - 1880 - 400 sider
...magnitudes. Lot 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 bo so multiplied, and... | |
| Euclides - 1881
...this Book. LEMMA I. If from the greater of two unequal magnitudes of the tame kind, there be taken **more than its half, and from the remainder more than its half; and** to on : there will at length remain a magnitude less than the least of the proposed magnitudes. Let... | |
| Euclid, Isaac Todhunter - 1883 - 400 sider
...magnitudes. Let AB and C be two unequal magnitiides, 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... | |
| Walter William Rouse Ball - 1901 - 527 sider
...which depends on the proposition that " if from the greater of two unequal magnitudes there tie 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." This proposition... | |
| Walter William Rouse Ball - 1901 - 527 sider
...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."** This proposition was placed by Euclid as the first proposition of the tenth book of his Elfmentx, but... | |
| William Thompson Sedgwick, Harry Walter Tyler - 1917 - 474 sider
...on the basis of the theorem : If two unequal magnitudes are given, and if one takes from the greater **more than its half, and from the remainder more than its half and so on,** one arrives sooner or later at a remainder which is less than the smaller given magnitude. Books XI,... | |
| W.R. Knorr - 1975 - 374 sider
...last is proved via a noted convergence principle (X,l): if from a given magnitude there is removed **more than its half, and from the remainder more than its half, and so on,** the remainder eventually becomes smaller than any preassigned finite magnitude. It is interesting to... | |
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