| 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... | |
| 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... | |
| W. R. Shea - 1983 - 325 sider
...to paraphrase Euclid, we can say that given two unequal quantities, from the greater we can subtract **more than its half, and from the remainder more than its half,** such that a quantity smaller than a given smaller quantity is always reached (Elements X. prop I).... | |
| 1894
...Euclid's Tenth Book: If fron the greater of two unequal magnitudes there be taken more than its half, arm **from the remainder more than its half, and so on, there shall at length remain** magnitude less than the smaller of the proposed magnitudes. Here the smaller of the proposed magnitudes... | |
| Popular educator - 1860
...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. For if AB and с be the two proposed magnitudes, of which А... | |
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