| André Darré - 1872
...only one hitherto devised that applies equally to commensurable and incommensurable quantities ; " **the first of four magnitudes is said to have the same...the third has to the fourth, when any equi-multiples** whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...nB as mC is to nD. V. Def. 5. QED PROPOSITION XVIII. (Bucl. v. A.) If the first of four magnitudes **have the same ratio to the second that the third has to the fourth,** then, if the first be greater than the second, the third must be greater than the fourth ; and if equal,... | |
| Euclid's Elements - 1874 - 62 pages
...third is also greater than that of the fourth. The Algebraical Definition answering to this would be ' **The first of four magnitudes is said to have the same ratio to the second** which the third has to the fourth, when the first is the same multiple, part, or fraction of the second... | |
| 1874
...third is also greater than that of the fourth. The Algebraical Definition answering to this would be ' **The first of four magnitudes is said to have the same ratio to the second** which the third has to the fourth, when the first is the same multiple, part, or fraction of the second... | |
| 1874
...: QD as &AQC : .-. &AQC : &BQCas &AQC : &AQD; (v. 3) Euclid's test of proportion is the following : **The first of four magnitudes is said to have the same ratio to the second** which the third has to the fourth, when any equimultiples whatever of the first and third being taken... | |
| James Martin (of the Wedgwood inst, Burslem) - 1874
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 5. **The first of four magnitudes is said to have the same ratio to the second,** which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,... | |
| Robert Potts - Geometry - 1876 - 403 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. x V. **The first of four magnitudes is said to have the same ratio to the second,** which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,... | |
| George Albert Wentworth - Geometry - 1877 - 398 pages
...q/ or ai ~ а : fr i ~ b : : a : b. QED 272. DEF. Euclid's test of a proportion is as follows : — **"The first of four magnitudes is said to have the same ratio to the second** which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,... | |
| Āryabhaṭa - 1878
...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,** which the third has to the fouitl', when any equimultiples whatsoever of the first and third i being... | |
| Robert Potts - Algebra - 1879
...Eue. Vu., def. 20. Hence it follows that a, b, c, d are proportionals by Eue. V., def. 5, namely : — **The first of four magnitudes is said to have the same ratio to the second,** which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,... | |
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