 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...  An elementary course of practical mathematics - Page 39by James Elliot - 1850Full view - About this book
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...multiple of the third is less than that of the fourth, then the first of the original four magnitudes is said to have to the second the same ratio which the third has to the fourth. NOTE 4. — To make Def. v. clearer we give the following illustration. Suppose A, B, C, D to be four... | |
 | 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... | |
 | 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
...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... | |
 | Euclides - 1884 - 434 pages
...of B and B + D + F; .-. A : B = A + O + E : B + D + FV Def. 5 PROPOSITION 13. THEOREM. If the first have 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... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...theorem : — " The product of a ratio and its reciprocal is unity." v. The first of four magnitudes has to the second the same ratio which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
 | Euclides - 1885 - 340 pages
...: — •" The product of a ratio and its reciprocal is unity." v. The first of four magnitudes has to the second the same ratio which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
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