 | Euclides - 1855 - 270 pagina’s
...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 pagina’s
...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 pagina’s
...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... | |
 | James Bates Thomson - 1858 - 400 pagina’s
...the answer is greater than the third term, arises from the fact, that theßrst türm of a proportion has the same ratio to the second, which the third has to the /он г £Л or answer ; consequently, if the answer is greater than the third term, the second term... | |
 | Euclid - 1859 - 150 pagina’s
...raö' àiroiovovv ToXXaя-Xaíriaff/iov, rev áurоv i'Ctí Xóyov Xq^öivra raráXXqXa. If the first has the same ratio to the second which the third has to the fourth; any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of... | |
 | Eucleides - 1860 - 396 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. /They are proportionals also X when taken inversely.... | |
 | John Playfair - 1860 - 334 pagina’s
...units in the product of these two numbers. Let A=mB, and B=nC ; then A=mnC. PROP. IV. THEOR. If ike first of four magnitudes has the . same ratio to the second which the third has to thejourth, arid if any equimultiples whatever be taken of the first and third, and any whatever of... | |
 | Robert Potts - 1860 - 380 pagina’s
...same multiple of F, that GB is of E. If, therefore, two magnitudes, &c. QED PROPOSITION A. THEOREM. 1} the first of four magnitudes has the same ratio to the second, which tht third has to the fourth ; then, if the first be greater than the second, the third is also greater... | |
 | Robert Fowler - 1861 - 426 pagina’s
...of those m = 16 j cases. PROPOKTION. 133. Def. — If there be four quantities, such that the first has the same ratio to the second which the third has to the fourth, then the four quantities are said to be proportionals. Thus if а, Ъ, с, d be the four quantities, and... | |
 | Euclides - 1861 - 464 pagina’s
...infinitely large. 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 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... 
