 | Dennis M'Curdy - 1846 - 168 σελίδες
...Magnitudes of the same kind only, or having some common property ^ can have a ratio to one another. 5. The first of four magnitudes has the same ratio to the second which the third has to the fourth, when equimultiples of the first and third, also of the second and fourth, being taken ; if the multiple... | |
 | Euclides - 1846 - 292 σελίδες
...that EF is the same multiple of B which GH ts of B. Wherefore, If the first %c. QED PROP. IV. THBOR. If the first of four magnitudes has the same ratio to the second which the i ' ird has to the fourth, and if of the first and third there be taken any equimultiples whatever,... | |
 | Euclides - 1848 - 52 σελίδες
...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 the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
 | Euclides - 1853 - 176 σελίδες
...with the sixth, is of the fourth d. 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 - 1853 - 334 σελίδες
...must be of the same kind. But there 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 - 400 σελίδες
...the less can be multiplied so as to exceed the other. 5. 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... | |
 | Euclides - 1855 - 230 σελίδες
...four magnitudes are proportionals. Idem ' If four magnitudes of the same kind be proportionals. Idem If the first of four magnitudes has the same ratio to the second which the third has to the fourth. Idem. Idem And if the first be greater than the third. r They are proportionals also \ when taken inversely.... | |
 | Euclides - 1855 - 270 σελίδες
...and, as necessary to complete the demonstration oi some subsequent propositions. PROP. A. THEOREM. If the first of four magnitudes has the same ratio to the second, which the third has to the fourth; and if the first be greater than the second, the third is also greater than the fourth; if equal, equal;... | |
 | John Hind - 1856 - 346 σελίδες
...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... | |
 | 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... | |
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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... 
