 | Oliver Byrne - 1841 - 144 σελίδες
...this definition before proceeding further. с 2 PROP. IV. THEO. If the first of four magnitudes have the same ratio to the second, which the third has...whatever of the first and third shall have the same ratio to any equimultiples of the second and fourth ; viz., the equimultiple of the first shall have the... | |
 | Euclides - 1841 - 378 σελίδες
...therefore HD is the same multiple of F, that GB is of E. If, therefore, two magnitudes, &c. QED PROP. A. THEOR. If the first of four magnitudes has the same ratio to the second, which the third hos to the fourth; then, if the first be greater than the second, the third ii also greater than the... | |
 | Oliver Byrne - 1841 - 140 σελίδες
...manner. Euclid expresses this definition as follows : — 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... | |
 | John Playfair - 1842 - 332 σελίδες
...Therefore nC+7tC+&c. repeated m times=mnC ; whence also mB=mnC, and by hypothesis A=mB, therefore A=wmC PROP. IV. THEOR. If the first of four magnitudes has...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... | |
 | Wales Christopher Hotson - 1842 - 306 σελίδες
...Geometrical Definition of Proportion. (Euclid, book v. def. 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 whatsover... | |
 | Euclides - 1842 - 316 σελίδες
...Definition of proportion according to Euclid, (Def. V., Book " 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, James Thomson - 1845 - 382 σελίδες
...of G, H: therefore (V. def. 5) as E : G : : F : H. Therefore, &c. Cor. Likewise, if the first have the same ratio to the second, which the third has to the fourth, then also any like multiples whatever of the first and third have the same ratio to the second and fourth... | |
 | Euclid - 1845 - 218 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 - 1845 - 546 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... | |
 | Euclid, John Playfair - 1846 - 334 σελίδες
...third as often as 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...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... 
