 | Euclides - 1814 - 560 pagine
...therefore E is to G, so is c F to H. Therefore, if the first, &c. QED See N. C0R. Likewise, if the first has the same ratio to the second, which the third has to the fourth, then also any equimultiples whatever of the first and third have the same ra- Boox V. tio to the second... | |
 | Charles Butler - 1814 - 540 pagine
...comparison of one number to another is called their ratio ; and when of four giren numbers the first has the same ratio to the second which the third has to the fourth, these four numbers are said to be proportionals. Hence it appears, that ratio is the comparison of... | |
 | Euclides - 1816 - 588 pagine
...the less can be multiplied so as to exceed the other. y. 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... | |
 | Sir John Leslie - 1817 - 456 pagine
...in the reduction of equations. According to Euclid, " 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 - 1819 - 354 pagine
...also mB = mnC, and by hypothesis A = mB, therefore A— m«C. Therefore, &c. Q,. ED 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 whaterer be taken of the first and third, and any whatever of the second and... | |
 | John Mason Good - 1819 - 800 pagine
...the other uf the I'nuiih. Prop. IV. Theor. If the first of four magnitude« ha» the same ratio lo the second which the third has to the fourth; then any equimultiples whatever of the first and third sh.ill have the sain« ratio to any equimultiples of the second and fourth, viz. the equimultiple of... | |
 | John Playfair - 1819 - 350 pagine
...mnC, and by hypothesis A = mB, therefore A~mn C. Therefore, &c. Q, ED PROP. IV. THEOR. If thefirst 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 thefirst and third, and any whatever of the second and... | |
 | Euclid, Robert Simson - 1821 - 514 pagine
...third, together with the sixth, is of the fourth D. If, therefore, the first, &c. QED PROP. IV. THEOR. IF the first of four magnitudes has the same ratio...same ratio to any equimultiples of the second and fourlji, viz. ' the equimultiple of the first shall have the > 'same ratio to that of the second, which... | |
 | Euclid - 1822 - 222 pagine
...controversy among geometers. Euclid defines them thus: The Jirst 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 Jirst and third being taken, and any equi-multiples whatsoever... | |
 | George Crabb - 1823 - 704 pagine
...15 to 5, which is expressed thus : as 6 : 2 : : 15 : 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 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... 
