 | Euclides, James Hamblin Smith - 1872 - 376 σελίδες
...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 - 1874 - 80 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 1876 - 446 σελίδες
...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 - 1880 - 426 σελίδες
...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 σελίδες
...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 - 1881 - 236 σελίδες
...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... | |
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THEOREM. lf 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 have to the second a greater ratio than the fifth, has to the... 
