 | Eucleides - 1860 - 396 σελίδες
...employed by Euclid in the fifth book, and by it we are enabled to ascertain their relative value. 2. A greater magnitude is said to be a multiple of a...contains the less a certain number of times exactly. SCHOLIUM. It is necessary to observe the distinction between the expressions "measures" and "is contained... | |
 | Robert Potts - 1860 - 380 σελίδες
...greater; that is, 'when the less is contained a certain number of times exactly in the greater.' II. A greater magnitude is said to be a multiple of a...contains the less a certain number of times exactly.' m. " Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity."... | |
 | Euclides - 1860 - 288 σελίδες
...measure, are called commensurable lines : those that have no common measure, incommensurable lines. 4. A greater magnitude is said to be a multiple of a...contains the less a certain number of times exactly. 5. Equimultiples of magnitudes are multiples that contain these magnitudes, respectively, the same... | |
 | John Playfair - 1860 - 334 σελίδες
...greater, that is, when the less is contained a certain number of times, exactly, in the greater. 2. A greater magnitude is said to be a multiple of a less, when tho greater is measured by the less, that is, when the greater contains the less a certain number of... | |
 | Euclides - 1861 - 464 σελίδες
...magnitudes of which the same or equal magnitudes are equimultiples are equal to one another. Def. 2, V. — A greater magnitude is said to be a multiple of a less, when the greater is measured by the less. CASE I. — Let the number of magnitudes in each set be two. Let AB, CD, &c., be equims. of, E, F,... | |
 | George Sturton Ward - 1862 - 104 σελίδες
...in the greater." lf«ia=5ora— -, m being any whole number, a is m said to be a. part of Ъ. II. a. A greater magnitude is said to be a multiple of a...contains the less a certain number of times exactly." If a = m Ъ, m being any whole number, a is said to be a multiple of Ъ. II. /3. Magnitudes which contain... | |
 | Euclides - 1863 - 122 σελίδες
...when the less is contained a certain number of times exactly iu the greater. n. A greater magnitnde is said to be a multiple of a less, when the greater...by the less; that is, when the greater contains the lees a certain number of times exactly. III. The mutual relation of two magnitudes of the same kind... | |
 | Euclides - 1864 - 448 σελίδες
...contained a certain number of times exactly in the greater.' II. A greater magnitude is said to he a multiple of a less, when the greater is measured...magnitudes of the same kind to one another, in respect of quantity." IV. Magnitudes are said to have a ratio to one another, when the less can be multiplied... | |
 | Euclides - 1865 - 402 σελίδες
...the greater; that is, when the less is contained a certain number of times exactly in the greater. n. A greater magnitude is said to be a multiple of a...contains the less a certain number of times exactly. in. Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity.... | |
 | Robert Potts - 1865 - 528 σελίδες
...greater ; that is, ' when the less is contained u certain number of times exactly in the greater.' II. A greater magnitude is said to be a multiple of a...less, that is, ' when the greater contains the less a certaia number of times exactly.' in. " Ratio is a mutual relation of two magnitudes of the same kind... | |
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A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater; that is, ' when the less is contained a certain number of times 
