 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...right angles. AVherefore, every solid angle &Q. QED BOOK XII. 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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...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... | |
 | Robert Potts - 1868 - 434 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, James Hamblin Smith - Geometry - 1872 - 376 pages
...magnitudes. Let A and B be two unequal magnitudes of the same kind, of which A is the greater. Then if from A there be taken more than its half, and from the remainder more than its half, and so on ; there must at length remain a magnitude less than B. Take a multiple of B, as mB, greater than... | |
 | Euclides - 1874 - 342 pages
...the circle EFGH above the space S. For, by the foregoing 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 - Geometry - 1876 - 446 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... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...right angles. Wherefore, every solid angle &c. QED 'BOOK XII. LEMMA. If from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more t/ian its half, and so on, there shall at length remain a magnitude less than the smaller of the proposed... | |
 | Euclides - Euclid's Elements - 1881 - 236 pages
...excess of the circle EFGH abo?e the space S. For (XII. Lemma 1) il from the greater of two unequal A 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 - Euclid's Elements - 1883 - 428 pages
...proposed 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 its half, and so on, there shall at length remain a magnitude less than C. For C may be multiplied so as at length... | |
 | Walter William Rouse Ball - Mathematics - 1901 - 580 pages
..."method of exhaustions " ; which depends on the proposition that " 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." This... | |
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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. 
