| John Playfair - Euclid's Elements - 1842 - 317 pages
...mB=mnC, and by hypothesis A=mB, therefore A=wmC PROP. IV. THEOR. If the first of four magnitudes has **the same ratio to the second which the third has to the fourth,** and if any equimultiples whatever be taken of the first and third, and any whatever of the second and... | |
| George Peacock - Algebra - 1842
...of the second, the multiple of the thii will be equal to that of the fourth : and if the multiple of **first be less than that of the second, the multiple of the** will be less than that of the fourth. It is this proposition which is deduced as a necessary consequence... | |
| Scottish school-book assoc - 1845
...geometrical magnitudes, and therefore it is necessary to substitute another, which is as follows: — Def. **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, James Thomson - Geometry - 1845 - 352 pages
...whatever of G, H: therefore (V. def. 5) as E : G : : F : H. Therefore, &c. Cor. Likewise, if the first **have the same ratio to the second, which the third has to the fourth,** then also any like multiples whatever of the first and third have the same ratio to the second and... | |
| Euclides - 1845
...is to G, so is F to H. (v. def. 5.) Therefore, if the first, &c. QED COB. Likewise, if the first has **the same ratio to the second, which the third has to the fourth,** then also any equimultiples whatever of the first and third shall have the*same ratio to the second... | |
| Euclid - Geometry - 1845 - 199 pages
...ratio to the second, than the fifth has to the sixth. PROPOSITION XIV. THEOR. — If the first has **the same ratio to the second which the third has to the fourth;** then, if the first be greater than the third, the second shall be greater than the fourth ; and if... | |
| Dennis M'Curdy - Geometry - 1846 - 138 pages
...multiple, &c. QED Recite (a) definitions 1, 2, A of b 5 -B D-0 H4 Th. If the first of four magnitudes **have the same ratio to the second which the third has to the fourth** ; then any equimultiples of the antecedents shall have the same ratio as any equimultiples of the consequents.... | |
| Dennis M'Curdy - Geometry - 1846 - 138 pages
...having some common property ^ can have a ratio to one another. 5. The first of four magnitudes has **the same ratio to the second which the third has to the fourth, when** equimultiples of the first and third, also of the second and fourth, being taken ; if the multiple... | |
| Euclides - 1846
...has a greater ratio to the second than the fifth has to the sixth. PROP. XIV. THEOR. If the first has **the same ratio to the second which the third has to the fourth,** then, if the first be greater than the third, the second shall be greater than the fourth, and if equal,... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 317 pages
...two numbers. Let A=mB, and B=nC ; then A=mnC. PROP. IV. THEOR. If the first of four magnitudes has **the same ratio to the second which the third has to the fourth,** and if any equimultiples whatever be taken of the first and third, and any whatever of the second and... | |
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