| Euclides - 1863
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 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,... | |
| Evan Wilhelm Evans - Geometry - 1862 - 98 pages
...their homologous sides are proportional. 2. Magnitudes are called proportionals when the first has **the same ratio to the second, that the third has to the fourth,** the fifth to the sixth, etc. The first terms of the several equal ratios are called the antecedents,... | |
| Robert Potts - 1864
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 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,... | |
| Alexander Kennedy Isbister - 1865
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 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,... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...to G as J7 is to H. [V. Definition 5. Wherefore, if the first &c. QEB COROLLARY. Also if the first **have the same ratio to the second that the third has to the fourth,** then any equimultiples whatever of the first and third shall have the same ratio to the second and... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...greater ratio to the second than the fifth has to the sixth. PROPOSITION 14. THEOREM. If the first **have the same ratio to the second that the third has to the fourth,** then if the first be greater than the third the second shall be greater than the fourth; anil if equal,... | |
| Robert Potts - 1868 - 410 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 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,... | |
| Joseph Ray - Arithmetic - 1857 - 320 pages
...PROPORTION. ART. 197. Proportion is an equality of ratios. Four numbers are proportional, when the first has **the same ratio to the second that 'the third has to the fourth.** REVIEW. — 194. How is a ratio affected by multiplying the consequent, or dividing the antecedent?... | |
| 1869
...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... | |
| Algebra - 1870
...representing the ratios must be equal. Euclid's test is given in Book Y. 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... | |
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