| Robert Potts - Geometry - 1876 - 446 pages
...less, that is, ' when the greater 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."** IV. Magnitudes are said to have a ratio to one another, when the less can be multiplied so as to exceed... | |
| George Elliot Voyle, G. de Saint-Clair-Stevenson - English language - 1876 - 676 pages
...property under their charge, if committed through carelessness, &c. Batió — In mathematics, the **mutual relation of two magnitudes of the same kind to one another, in respect of quantity.** Ratios are divided into arithmetical and geometrical. An arithmetical ratio consists in the difference... | |
| Āryabhaṭa - 1878
...the less, that ia, when the greater contains the less a certain number of times exactly. XXIX. The **mutual relation of two magnitudes of the same kind to one another, in respect of quantity,** is called their ratio. XXX. The first of four magnitudes is said to have the same ratio to the second,... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...by the less; that is, when the greater contains the less a certain number of times exactly. 3. Ratio **is a mutual relation of two magnitudes of the same...ratio to one another, when the less can be multiplied** go as to exceed the other. 5. The first of four magnitudes is said to hare the same ratio to the second,... | |
| Euclides - 1881
...expressed, like many others, in commensurate terms; for their common measure, or common unit is unknown. IV. **Magnitudes are said to have a ratio to one another, when the less can** he multiplied so as to exceed the other. This definition is intended as a test of the likeness or similarity... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 426 pages
...by the less; that is, when the greater contains the less a certain number of times exactly. 3. Ratio **is a mutual relation of two magnitudes of the same...exceed the other. 5. The first of four magnitudes is** said to have the same ratio to the second, that the third has to the fourth, when any equimultiples... | |
| Leonard Marshall - 1883
...circumference of each wheel? V.— RATIO, PROPORTION, AND VARIATION. 1. Ratio is defined by Euclid as the **mutual relation of two magnitudes of the same kind to one another in respect of quantity** (see Bk. V. Def. iii.). In Algebra the ratio of a : b is measured by the . , .. antecedent aj ., .... | |
| Alexander Mackenzie - 1884
...established between things which are not of the same kind. Euclid's definition is as follows : — " Ratio **is a mutual relation of two magnitudes of the same kind to one another in respect of quantity."** " Magnitudes which have the same ratio are called proportionals. When four magnitudes are proportionals... | |
| Alexander Mackenzie, Alexander Macgregor, Alexander Macbain - Clans - 1884
...established between things which are not of the same kind. Euclid's definition is as follows:—" Ratio **is a mutual relation of two magnitudes of the same kind to one another in respect of quantity."** " Magnitudes which have the same ratio are called proportionals. When four magnitudes are proportionals... | |
| Euclides - 1884
...are multiples that contain these magnitudes, respectively, the same number of times. 4. Ratio is a **relation of two magnitudes of the same kind to one another, in respect of** quantuplicity (a word which refers to the number of times or parts of a time that the one is contained... | |
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