 | Robert Simson - 1838 - 434 σελίδες
...together with the sixth, is of the fourth D. If, therefore, the first, &c. QED ABGCD PROP. IV. THEOR. IF the first of four magnitudes has the same ratio...ratio to any equimultiples of the second and fourth, viz. ' the equimultiple of the ' first shall have the same ratio to that of the second, which the '... | |
 | Euclides - 1840 - 192 σελίδες
...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 σελίδες
...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... | |
 | 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...ratio to any equimultiples of the second and fourth ; viz., the equimultiple of the first shall have the same ratio to that of the second, which the equimultiple... | |
 | Euclides - 1841 - 378 σελίδες
...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
...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 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... | |
 | 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, 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... | |
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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... 
