| John Playfair - Euclid's Elements - 1806 - 311 pages
...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 - Geometry, Plane - 1809 - 493 pages
...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 - Geometry - 1810 - 518 pages
...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 - Mathematics - 1814
...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 - Astronomy - 1815 - 628 pages
...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 - 528 pages
...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 - Circle-squaring - 1819 - 333 pages
...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 - Geometry - 1821 - 516 pages
...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 - 179 pages
...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,... | |
| James Mitchell - Mathematics - 1823 - 576 pages
...equimultiples whatever of tiie first and third being taken, and any equimultiples whatever of the 2d iind'4lh ; **if the multiple of the first be less than that of the** 2(1, the multiple of the 3d is also less than that of the •!• h ; or if the multiple of the I -i... | |
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