| John Hind - 1856
...Elements, that "Proportion is the Similitude of Ratios ; and 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, and any equimultiples whatever of the second said fourth... | |
| John Playfair - Euclid's Elements - 1856 - 318 pages
...therefore A=mnC /(, tj',;t<f'£ PROP. IV. THEOR. /, / 2. // //>5 If the first of four magnitudes has thr, **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... | |
| James Bates Thomson - Arithmetic - 1858 - 384 pages
...answer is greater than the third term, arises from the fact, that theßrst türm of a proportion has **the same ratio to the second, which the third has to the** /он г £Л or answer ; consequently, if the answer is greater than the third term, the second term... | |
| Euclides - 1859
...àiroiovovv ToXXaя-Xaíriaff/iov, rev áurоv i'Ctí Xóyov Xq^öivra raráXXqXa. If the first has **the same ratio to the second which the third has to the fourth;** any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of... | |
| Robert Potts - Geometry, Plane - 1860 - 361 pages
...is to G, so is F to H. (v. def. 5.) Therefore, if the first, &c. QED Cos, 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... | |
| Eucleides - 1860
...first case in Euclid. G. (c) V. 2. PROPOSITION A. THEOREM. — If the first of four magnitudes have **the same ratio to the second which the third has to the fourth,** then, if the first be greater than the second, the third is also greater than the fourth ; and if equal,... | |
| Euclides - 1861
...the same ratio, as Ato I}; ie A : B = C : x. PROP. A, — THEOR. If the first of four magnitudes has **the same ratio to the second which the third has to the fourth;** then if the first be greater than the second the third is greater than the fourth ; and if equal, equal... | |
| Robert Fowler - 1861
...those m = 16 j cases. PROPOKTION. 133. Def. — If there be four quantities, such that the first has **the same ratio to the second which the third has to the fourth,** then the four quantities are said to be proportionals. Thus if а, Ъ, с, d be the four quantities,... | |
| George Sturton Ward - Geometry, Algebraic - 1862 - 79 pages
...and therefore e ; / : ; g : A. Therefore, if the first, &c.— QED COR. 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 have the same ratio to the second and... | |
| Euclides - 1863
...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...whatsoever of the first and third being taken, and** auy equimultiples whatsoever of the second and fourth; if the multiple of the first b« IMS than that... | |
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