 When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have...  Manual of Euclid: Books IV, V, VI. - Page 29by Euclid - 1868Full view - About this book
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...greater than the multiple of the second, but the multiple of the third ,is not greater than the multiple of the fourth, then the first is said to have to the...second a greater ratio than the third has to the fourth ; and the third is said to have to the fourth a less ratio than the first has to the second. 8. Analogy,... | |
 | Robert Potts - 1868 - 434 pages
...is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth : and, on the contrary, the third is said to have to the fourth a less... | |
 | Archibald Sandeman - Algebra - 1868 - 486 pages
...CONTINUEDLY PROPORTIONATE or IN A CONTINUED PROPORTIONALITY. 246. Def. The first of four magnitudes is said to have to the second a GREATER RATIO than the third has to the fourth when the first is greater than some fraction of the second but the third is not greater than the same... | |
 | Edward Wyndham Tarn - Curves, Plane - 1871 - 244 pages
...multiple of the second, the multiple of the third is also greater, equal to, or less than the multiple of the fourth ; then the first is said to have to the second the same ratio or proportion as the third has to the fourth. Magnitudes which have the same ratio to... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...multiple of the second, but the multiple of the third is not greater than [or is less than] the multiple of the fourth, then the first is said to have to the...a greater ratio, than the third has to the fourth. NOTE 6. The meaning of Def. vn. may be expressed, after taking the scales of multiples as in the explanation... | |
 | Euclid, Lewis Carroll - Euclid's Elements - 1874 - 80 pages
...greater than the multiple of .the second, but the multiple of the third is not greater than the multiple of the fourth, then the first is said to have to the...second a greater ratio than the third has to the fourth ; and the third is said to have to the fourth a less ratio than the first has to the second. VIII.... | |
 | Charles Lutwidge Dodgson - 1874 - 96 pages
...greater than the multiple of the second, but the multiple of the third is not greater than the multiple of the fourth, then the first is said to have to the...second a greater ratio than the third has to the fourth ; and the third is said to have to the fourth a less ratio than the first has to the second. VIII.... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...of the first is greater than that of the second, but the multiple of the third is not greater than that of the fourth; then the first is said to have to the second a greater ratio than the third to the fourth ; or, which is the same thing, the ratio of the third to the fourth is said to be less... | |
 | Euclides - 1874 - 342 pages
...is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth ; and, on the contrary, the third is said to have to the fourth a less... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth : and, on the contrary, the third is said to have to the fourth a less... | |
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