| Euclid, James Thomson - 1845 - 352 páginas
...1) the prisms are equal. Wherefore, &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... | |
| Euclides - 1845
...proportional to the cubes of their homologous edges. 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 shall at length remain a magnitude less than the least of the proposed magnitudes. (Book... | |
| Scottish school-book assoc - 1845
...given line. For it has been shown in the proposition that this is equivalent to taking away from EC **more than its half, and from the remainder more than its half, and** so on continually ; .-. (Prop. 73, Cor.) the quantity ultimately left is less than any given quantity.... | |
| Euclides - 1848
...shall be equal to one another. BOOK XII. PROPOSITIONS. LEMMA I. IP 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. (Book... | |
| Euclides - 1855
...side of the hexagon. T. Of the Multiples of Magnitudes. HYPOTHESES. 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. If one magnitude be the same multiple of another, which a part taken from the first is of a... | |
| Euclides - 1855
...propositions of this Book. LEMMA I. If from the greater of two unequal magnitudes of the same kind, **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... | |
| Eucleides - 1860
...GHKLMN. THE ELEMENTS OF EUCLID. BOOK XII. ' LEMMA I. THEOREM. — 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. DEMONSTRATION.... | |
| Euclides - 1864
...circle EFGH above the space 8; 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... | |
| Euclides - 1865
...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 will at length remain a magnitude less than the least of the proposed magnitudes. Let... | |
| Euclid, Isaac Todhunter - 1867 - 400 páginas
...four right angles. Wherefore, every solid angle &c. QED XIL 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 smaller of the proposed magnitudes. Let... | |
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