 | Euclides - 1865 - 402 σελίδες
...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... | |
 | Robert Potts - 1865 - 528 σελίδες
...Mathematical Honours at Cambridge. BOOK XII. LEMMA L 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. (Book x. Prop. 1.) Let AB and C be two unequal magnitudes, of... | |
 | Euclid, Isaac Todhunter - 1867 - 426 σελίδες
...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 - 424 σελίδες
...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 - 434 σελίδες
...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 - 376 σελίδες
...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 - 342 σελίδες
...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 - 446 σελίδες
...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 - 426 σελίδες
...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 - 236 σελίδες
...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... | |
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Let AB and C be two unequal magnitudes, 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... 
