 | Euclides - 1848 - عدد الصفحات: 52
...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... | |
 | Euclides - 1853 - عدد الصفحات: 334
...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... | |
 | Royal Military Academy, Woolwich - 1853 - عدد الصفحات: 400
...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 - 1853 - عدد الصفحات: 176
...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 - عدد الصفحات: 270
...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 - عدد الصفحات: 230
...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 - عدد الصفحات: 346
...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 - عدد الصفحات: 346
...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 - عدد الصفحات: 400
...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 - عدد الصفحات: 150
...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... | |
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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... 
