| Robert Potts - Algebra - 1879
...VII., 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,... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...of E. Wherefore, if two magnitudes &c. QED PROPOSITION A. THEOREM. If the first of four magnitudes **have the same ratio to the second that the third has to the fourth,** then, if thejftrtt be greater than the second, the third thatt also be greater than the fourth, and... | |
| George Albert Wentworth - Geometry, Plane - 1881 - 250 pages
...a ± ? a : b ± ?-b : : a : b. Ч 1 QED 272. DEP. 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,... | |
| Euclides - 1881
...they cannot be said to be of the same kind, and so cannot have any ratio to each other. T. The Brst **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,... | |
| James Hamblin Smith - 1883
...representing the ratios must be equal. Euclid's test is given in Book v. Def. 5, where it stands thus : \ " **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... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 400 pages
...of E. Wherefore, if two magnitudes &c. QKD PROPOSITION A. THEOREM. 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 shall also be greater than the fourth, and... | |
| Euclides - 1884
...of the fourth, equal to it, or less. 6. Magnitudes are said to be proportionals when the first has **the same ratio to the second that the third has to the fourth;** and the third to the fourth the same ratio which the fifth has to the sixth ; and so on, whatever be... | |
| Howard Candler - Algebra - 1885 - 94 pages
...fourth, that is, д, l>, c, d are said to be proportionals if — = b а The geometrical definition is 2. **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 being taken of the ist and 3rd,... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...number of metres may make, a greater length can always be found containing an exact number of yards. 5. **The first of four magnitudes is said to have the '...any equimultiples whatever of the second and fourth,** the multiple of the third is greater than, equal to, or less than that of the fourth, according as... | |
| Euclid - Geometry - 1890 - 400 pages
...greater than, equal to, or less than the multiple of the fourth — under those conditions, the first **is said to have the same ratio to the second that the third has to the fourth** ; and the four magnitudes are called proportionals. And, conversely, if four magnitudes are proportionals,... | |
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