| 1816
...flumes in 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 foundation... | |
| 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... | |
| Peter Nicholson - 1825 - 372 páginas
...book, and is necessary to 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 its half, and** so on : There shall at length remain a magnitude Itss than the least of the proposed magnitudes. Let... | |
| Robert Simson - 1827 - 513 páginas
...the circle 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 more than its half, and** so on, there shall at length remain a magnitude less than the least of the proposed magnitudes. Let... | |
| Euclid - 1835 - 513 páginas
...circle 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 more than its half, and** so on, there shall at length remain a magnitude less than the least of the proposed magnitudes. Let... | |
| John Playfair - 1836 - 114 páginas
...proposed 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 ; there shall at length remain a magnitude less than C. For C may be multiplied, so as at length... | |
| Euclid, James Thomson - 1837 - 390 páginas
...Wherefore, if there be two triangular prisms, &c. BOOK XII. LEMMA I.* 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 : there will at length remain a magnitude less than the least of the proposed magnitudes. Let... | |
| Euclid - 1838 - 416 páginas
...proposed 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** D than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied,... | |
| James Wood - 1841 - 305 páginas
...manner, when с is the dividend, more than its half is taken away, and so on ; but if from any quantity **there be taken more than its half, and from the remainder more than its half, and** so on, there will, at length, remain a quantity less than any that can be asigned (Eue. x. I.) [109.... | |
| Euclides - 1841 - 351 páginas
...&c. QED THE ELEMENTS OF EUCLID. BOOK XII. LEMMA I. 1 I f from the greater of ttno unequal magnitude*, **there be taken more than its half, and from the remainder more than** Us half; and 10 on: there shall at length remain a magnitude less than the least of the proposed magnitudes.... | |
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