 | Euclides - 1845 - 546 pagina’s
...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... | |
 | Euclid - 1845 - 218 pagina’s
...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... | |
 | Euclid, John Playfair - 1846 - 334 pagina’s
...there are units in the product of these 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... | |
 | Dennis M'Curdy - 1846 - 168 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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.... | |
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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... 
