| Euclid, John Playfair - Euclid's Elements - 1846 - 334 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... | |
| Euclides - 1848 - 52 pages
...of the second, and the other of the fourth. PROP. IV. THEOREM. 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... | |
| 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 - 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,... | |
| 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... | |
| 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... | |
| |