| Euclides - 1865
...a magnitude less than the least of the proposed magnitudes. Let AB and C be two unequal magnitudes, **of which AB is the greater. If from AB there be taken...and from the remainder more than its half, and so on** ; Then there shall at length remain a magnitude less than C. AD FG BCB CONSTRUCTION For C may be multiplied... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...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...there shall at length remain a magnitude less than** the smaller of the proposed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...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...there shall at length remain a magnitude less than** the smaller of the proposed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the... | |
| Robert Potts - 1868 - 410 sider
...in the other. BOOK XIL LEMMA I. Jf from the greater of two unequal majnituJes, there be taken mart **than its half, and from the remainder more than its half; and** to on: there shall at length remain a magnitude leu than the least of the proposed magnitudes. (Book... | |
| Euclides, James Hamblin Smith - 1872 - 349 sider
...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 A ; and divide... | |
| Euclides - 1874
...than the least of the proposed magnitudes. ^ Let AB and C be two unequal magnitudes, of the same kind, **of which AB is the greater. If from AB there be taken...and from the remainder more than its half, and so on** ; Then there will at length remain a magnitude less than C. Construction. For C may be multiplied so... | |
| Robert Potts - 1876 - 403 sider
...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...there shall at length remain a magnitude less than** the least of the proposed magnitudes. Let then the segments EK, KF, FL, LG, GM, MH, HN, NE be those... | |
| Isaac Todhunter - 1880 - 400 sider
...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
...propositions of this Book. LEMMA I. If from the greater of two unequal magnitudes of the tame kind, **there be taken more than its half, and from the remainder more than its half; and** to on : there will at length remain a magnitude less than the least of the proposed magnitudes. Let... | |
| Walter William Rouse Ball - 1901 - 527 sider
...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 proposition... | |
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