 | Euclides - 1846 - 292 sider
...has a greater ratio to B than E has to F. Wherefore, If the first tsc. QED Con. Also, if the first have a greater ratio to the second than the third has to the fourth, but the third the same ratio to the fourth which the fifth has to the sixth, it may be shewn, in like... | |
 | Thomas Gaskin - 1847 - 301 sider
...second, but the multiple of the third not greater than the multiple of the fourth ; hence the first has a greater ratio to the second than the third has to the fourth. 3. Euclid, Prop. 19, Book i. If A : B :: B : C, then the ratio of A to C is that compounded of the... | |
 | Euclides - 1848 - 52 sider
...shall also have to the second a greater ratio than the fifth has to the sixth. COR. And if the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth; it may be demonstrated,... | |
 | Royal Military Academy, Woolwich - 1853 - 400 sider
...ratios to the sum of the consequents will be respectively greater or less than that other ratio. 7. If the first of four magnitudes have a greater ratio to the second than the third has to the fourth ; then, (a) The second will have to the first a less ratio than the fourth to the third : — (6) The... | |
 | Euclides - 1853 - 334 sider
...two extremes, and the second and third the two means. vn. The first of four magnitudes is defined to have a greater ratio to the second than the third has to the fourth (or, what is the same thing, the third to have a less ratio to the fourth than the first has to the... | |
 | Euclides - 1853 - 176 sider
...greater ratio to b than e has to f (v. def. 7). Wherefore, if the first, &c. QED COR. And if the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth ; it may be demonstrated,... | |
 | Euclides - 1855 - 270 sider
...ratio to B, than E has to F (V. Def. 7). Wherefore, if the first, &c. QED COROLLARY. — If the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth ; it may be demonstrated,... | |
 | Euclides - 1855 - 230 sider
...fourth, but the third to the fourth a greater ratio than the fifth has to the sixth. If the first has a greater ratio to the second than the third has to the fourth, but the third the same ratio to the fourth which the fifth has to the sixth. If any number of magnitudes... | |
 | Robert Potts - 1860 - 380 sider
...greater ratio to B, than E has to F. (v. def. 7.) Wherefore, if the first, &c. QED CoR. And if the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth ; it may be demonstrated,... | |
 | Eucleides - 1860 - 396 sider
...fourth, but the third to the fourth a greater ratio than the fifth has to the sixth. If the first has a greater ratio to the second than the third has to the fourth, but the third the same ratio to the fourth which the fifth has to the sixth. If any number of magnitudes... | |
| |
And if the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth... 
