| James Hamblin Smith - Algebra - 1882 - 414 pages
...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...the fourth, when any equimultiples whatsoever of the** f1rst and third being taken and any equimultiples whatsoever of the second and fourth : " If the multiple... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...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,** that the third has to the fourth, when any equimultiples whatever of the first and the third being... | |
| Euclides - 1885 - 340 pages
...ratio and its reciprocal is unity." v. The first of four magnitudes has to the second the same ratio **which the third has to the fourth, when any equimultiples...equimultiples whatsoever of the second and fourth, if,** according as the multiple of the first is greater than, equal to, or less than the multiple of the... | |
| Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...ratio and its reciprocal is unity." v. The first of four magnitudes has to the second the same ratio **which the third has to the fourth, when any equimultiples...equimultiples whatsoever of the second and fourth, if,** according as the multiple of the first is greater than, equal to, or less than the multiple of the... | |
| Howard Candler - 1885 - 116 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...the third has to the fourth, when, any equimultiples** whatever being taken of the ist and 3rd, and any equimultiples whatever of the 2nd and 4th, if the... | |
| William Steadman Aldis - Algebra - 1887 - 616 pages
...f3,ft This condition is evidently equivalent to the definition 5 of the Fifth Book of Euclid, viz.— **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 whatever of the first and third being taken,... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 538 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 ' same ratio ' to the second** that the third has to the fourth, when, any equimultiples whatever of the first and third being taken,... | |
| Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 165 pages
...following manner : — The first of four magnitudes is said to have the same ratio to the second, as **the third has to the fourth, when any equimultiples...equimultiples whatsoever of the second and fourth** being taken; if the multiple of the first be less than that of the second, the multiple of the third... | |
| Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 190 pages
...Art. 67. Def. 13. EUCLID'S TEST FOR EQUAL RATIOS. Euclid states this Test in the following manner: — **The first of four magnitudes is said to have the same ratio to the second,** as the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,... | |
| Joseph Battell - Force and energy - 1903 - 722 pages
...must contain 2, 3 X 3, or 9 times. See Axiom 6. PROPOSITION IV. ' If the first of four magnitudes has **the same ratio to the second which the third has to the fourth,** and if any equimultiple whatever is taken of the first and third, and any whatever of the second and... | |
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