 | Pierce Morton - 1830 - 584 σελίδες
...magnitude of the other ; and conversely (ax. 1, 2, 3, 4).* ' " The first of fonr magnitudes is enid to bare the same ratio to the second, wh'ich the third has to the fourth, when any equimultiples whatsoever of the fir>t aiid third being taken, ¡ind any equimultiples whatsoever... | |
 | Euclid - 1833 - 216 σελίδες
...controversy among geometers. Euclid defines them thus : The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equi-multiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
 | Euclides - 1834 - 518 σελίδες
...of the fourth D. If, therefore, the first, &c. <?. ED PROPOSITION IV. See N. THEOR. — If the Jtrsl of four magnitudes has the same ratio to the second...the fourth, then any equimultiples whatever of the Jirst and third, shall have the same ratio to any equimultiples of the second and fourth ; viz, " the... | |
 | James Ryan, Robert Adrain - 1835 - 388 σελίδες
...proportion, and are not wanted in the method of demonstration adopted in this essay. PROP. IV. THEOR. If the first of four magnitudes has the same ratio...ratio to any equimultiples of the second and fourth ; that is, the equimultiple of the first shall be to that of the second as the equimultiple of the... | |
 | Euclid - 1835 - 540 σελίδες
...as E is to G, so is c F to H. Therefore, " if the first," &c. QED See N. Cou. Likewise, if the first has the same ratio to the second, which the third has to the fourth, then also any equimultiples LFCDH whatever of the first and third have the same ratio to the second Book... | |
 | John Playfair - 1835 - 336 σελίδες
...times = mnC ; whence also mB=mnC, and by hypothesis A=mB, therefore A=m»C, PROP. IV. THEOR. - • " If the first of four magnitudes has the same ratio to the second lohich the third has to the fourth, and if any equimultiples whatever be taken of the first and third,... | |
 | 1836 - 488 σελίδες
...the first will contain the third as oft as there are units in the product of these two numbers. IV. 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 tcriken of the first and third, and any whatever of the second... | |
 | John Playfair - 1837 - 332 σελίδες
...repeated m times=77mC; whence also 7nB=77inC, and by hypothesis A=mB, therefore A=7nnC. 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... | |
 | Euclid, James Thomson - 1837 - 410 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... | |
 | William Whewell - 1837 - 226 σελίδες
...*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... | |
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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... 
