 | William Whewell - 1837 - 226 pagine
...*i, *II, *III, IV. Book v. *Definition of Proportion. The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when^ — any eq'wi-multiples whatsoever of the Jirst and third being taken, and any equi-multiples... | |
 | Euclides - 1840 - 192 pagine
...repeated TO times =mnC; whence also mB = mnC ; but A = mB (Hyp.), and therefore 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... | |
 | John Hind - 1840 - 252 pagine
...Elements, that " Proportion is the Similitude of Ratios; and theJirst 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^rst and third being taken, and any equimultiples whatever of... | |
 | Euclides - 1841 - 378 pagine
...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 pagine
...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 pagine
...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 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 - 1842 - 316 pagine
...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... | |
 | Wales Christopher Hotson - 1842 - 306 pagine
...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... | |
 | Euclid, James Thomson - 1845 - 382 pagine
...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... | |
 | Euclides - 1845 - 546 pagine
...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... | |
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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... 
