 | Euclides - 1845 - 546 pages
...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... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...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... | |
 | Scottish school-book assoc - 1845 - 444 pages
...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 - 52 pages
...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 - 230 pages
...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 - 270 pages
...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 - 396 pages
...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 - 448 pages
...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 - 402 pages
...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... | |
 | Robert Potts - 1865 - 528 pages
...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... | |
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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. 
