 | Euclides - 1853 - 176 σελίδες
...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 σελίδες
...other in 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 σελίδες
...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 σελίδες
...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 - 1856 - 346 σελίδες
...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 - 1858 - 400 σελίδες
...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 σελίδες
...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 σελίδες
...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,... | |
 | Robert Potts - 1860 - 380 σελίδες
...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... | |
 | Euclides - 1861 - 464 σελίδες
...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... | |
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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, and any equimultiples whatsoever of the second and fourth ; if the multiple... 
