| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...fourth D. If, therefore, the first, etc. QED PROPOSITION IV. THEOB. If the first of four magnitudes has **the same ratio to the second which the third has to the fourth,** then any equimultiples •whatever of the first and third shall have the same ratio to any equimultiples... | |
| Euclides - Geometry - 1853 - 334 pages
...is no necessity for all four to be of the same kind. OBS. 3. When the first of four magnitudes has **the same ratio to the second which the third has to the fourth,** the third clearly has the same ratio to the fourth which the first has to the second. Such will appear... | |
| Euclides - Geometry - 1853 - 176 pages
...If, therefore, the first, &c. QED PROPOSITION IV. — THEOREM. If the first of four magnitudes has **the same ratio to the second which the third has to the** fowrth ; then any equimultiples whatever of tlie first and third shall have the same ratio to any equimultiples... | |
| Euclides - 1855 - 270 pages
...magnitude, they cannot be said to be of the same Hud, and so cannot have any ratio to each other. V. **The first of four magnitudes is said to have the same ratio to the** «cond, which the third has to the fourth, when any equimultiples whatsoever of the first and third... | |
| Euclides - 1855 - 230 pages
...b = 6, which is the first case in Euclid. 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,... | |
| John Hind - 1856 - 346 pages
...is stated in the fifth Book of Euclid's Elements, that "Proportion is the Similitude of Ratios ; and **the first of four magnitudes is said to have the same...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 - 346 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 - 400 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... | |
| Euclid - 1859 - 150 pages
...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... | |
| Eucleides - 1860 - 396 pages
...the 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,... | |
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