 | John Playfair - 1806 - 320 Seiten
...hypothesis A=mB, therefore A=mnC. Therefore, &c. QED PROP. IV. THEOR. IF the first of four magnitudes have 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... | |
 | Sir John Leslie - 1809 - 522 Seiten
...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...being taken, and any equimultiples whatsoever of the aecmxd and fourth ; if the multiple of the first be less than that of the second, the multiple of the... | |
 | Euclid - 1810 - 554 Seiten
...therefore E is to G, so isc F to H. Therefore, if the first, &c. QED C0R. Likewise, if the first have the same ratio to the second, which the third has to the fourth, then also any equimultiple!; 1 3. 5. b Hypoth. KEA GM L' FCDHN whatever of the first and third have... | |
 | Charles Butler - 1814 - 540 Seiten
...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... | |
 | Charles Hutton - 1815 - 686 Seiten
...of the third is also equal to that of the fourth ; or if when the multiple of the first is greater than that of the second, the multiple of the third is also greater than that of the fourth : then, the first X)f the four magnitudes shall be to the second as... | |
 | Euclides - 1816 - 588 Seiten
...fourth D. 1f, therefore, the first, &c. QED A CD 2.5. BouK V. See N. If the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any equimultiples whatever of the first and third shall have the same ratio to any equimultir... | |
 | John Playfair - 1819 - 350 Seiten
...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 Seiten
...third is also equal to that of the fourth; or, if the multiple of the * SBP note. first be greater than that of the second, the multiple of the third is also greater than that of the fourth. VL Magnitudes which haye the same ratio are called proportionals.... | |
 | Euclid - 1822 - 222 Seiten
...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...fourth, when any equi-multiples whatsoever of the Jirst and third being taken, and any equi-multiples whatsoever of the second and fourth being taken,... | |
 | George Crabb - 1823 - 704 Seiten
...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 multiple of the first be less than that of the third, the multiple of the second is also less than that of the fourth ;• if equal, equal ; and if... | |
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If the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth... 
