| Euclid, Isaac Todhunter - 1867 - 400 páginas
...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... | |
| Robert Potts - 1868 - 410 páginas
...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 - 1872 - 349 páginas
...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
...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 - 1876 - 403 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... | |
| Isaac Todhunter - 1880 - 400 páginas
...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 - 1881
...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 - 1883 - 400 páginas
...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 - 1901 - 527 páginas
..."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... | |
| Walter William Rouse Ball - 1901 - 527 páginas
..." ; 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... | |
| |