 | Eucleides - 1860 - 396 pagina’s
...book, and by it we are enabled to ascertain their relative value. 2. A greater magnitude is said to be a multiple of a less, when the greater is measured...contains the less a certain number of times exactly. SCHOLIUM. It is necessary to observe the distinction between the expressions "measures" and "is contained... | |
 | John Playfair - 1860 - 334 pagina’s
...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...contains the less a certain number of times exactly.' 4. Magnitudes are said to be of the same kind, when the less can be multiplied so as to exceed the... | |
 | Euclides - 1861 - 464 pagina’s
...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 pagina’s
...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 less when the greater is measured...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 pagina’s
...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 is measured...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 - 1865 - 402 pagina’s
...is contained a certain number of times exactly in the greater. n. A greater magnitude is said to be a multiple of a less, when the greater is measured...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 pagina’s
...contained u certain number of times exactly in the greater.' II. A greater magnitude is said to be a multiple of a less, when the greater is measured...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... | |
 | William Harding Girdlestone - 1867 - 368 pagina’s
...be attributed to the imperfect translation of Euclid's definition of Ratio, Book v., Definition 3. " Ratio is a mutual relation of two magnitudes of the...same kind to one another, in respect of quantity.„ Here we may ask what is the difference between the words magnitude and quantity ? Are they not in reality... | |
 | William Thomas Brande, George William Cox - 1867 - 1090 pagina’s
...majority. Ratio (Lat.). In Geometry, this word is defined by Euclid (Elrmenis, book v. del'. 3) to be ' a mutual relation of two magnitudes of the same kind to one another in respect of quantity' This definition has been much criticised. Dr. Barrow (J.ectimies Math.), who calls it a metaphysical... | |
 | Euclid, Isaac Todhunter - 1867 - 426 pagina’s
...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 the greater is measured by the less; that ia, when the greater contains the less a certain number of times exactly. 3. Ratio is a mutual relation... | |
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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 exactly in the greater. 
