| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...proposition may be easily extended to any number of magnitudes. QED PROPOSITION XXII. (Eucl. v. 24.) **If the first have to the second the same ratio which the third has to the fourth,** and the fifth have to the second the same ratio which the sixth has to the fourth, then the first and... | |
| Euclid, Lewis Carroll - Euclid's Elements - 1874 - 80 pages
...the sign + , the other has the sign — .] PROP. A. If the first have to the second the same ratio as **the third has to the fourth : then, if the first be greater than the** second, the third is greater than the fourth ; if equal, equal ; if less, less. [If the first (a) have... | |
| Charles Lutwidge Dodgson - 1874 - 96 pages
...the sign + , the other has the sign — .] PROP. A. If the first have to the second the same ratio as **the third has to the fourth : then, if the first be greater than the** second, the third is greater than the fourth ; if equal, equal ; if less, less. [If the first (a) have... | |
| Euclides - 1874 - 342 pages
...together (V. Def. 5). Wherefore, if any number, &c. Q ED PROPOSITION 13. — Theorem. If the first has **to the second the same ratio which the third has to the fourth,** but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also... | |
| Euclides, James Hamblin SMITH - 1876 - 382 pages
...proposition may be easily extended to any number of magnitudes. 0. ED PROPOSITION XXII. (Eucl. v. 24.) // **the first have to the second the same ratio which the third has to the fourth,** and the fifth have to the second the same ratio which the sixth has to the fourth, then the first and... | |
| Richard Wormell - 1876 - 268 pages
...II. Ratios that are equal to the same ratio are equal to one another. .. .. 191 13. If the first has **to the second the same ratio which the third has to the fourth,** but the third to the fourth a greater ratio than the fifth to the sixth, the first shall have to the... | |
| Robert Potts - Geometry - 1876 - 446 pages
...magnitudes. Therefore, if there be any number, &c. QED PROPOSITION XXIV. THEOREM. If the first hat **to the second the same ratio which the third has to the fourth** ; and the fifth to the second the same ratio which the sixth has to the fourth; the first and fifth... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...whatever be the number of magnitudes. Wherefore, ifthere^be any number &c. QED PROPOSITION 24. THEOREM. **If the first have to the second the same ratio which the third has to the fourth,** and the ffth have to the second the same ratio which the sixth has to the fourth, then the first and... | |
| Sandhurst roy. military coll - 1880 - 68 pages
...CROSS, SW 1880. L 8. What test does Euclid give to determine when the first of four magnitudes has **to the second the same ratio which the third has to the fourth** ? Prove that in equal circles, angles whether at the centres or at the circumferences have the same... | |
| Euclides - Euclid's Elements - 1881 - 236 pages
...have the same ratio to any equimultiples whatever of the second and fourth. Let A the first, have to B **the second, the same ratio which the third ''" has to the fourth** D, and of A and C let E and F be any equimultiples whatever. Then E shall be to B as F to D. Take of... | |
| |