When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c., increasing the denomination still by unity, in any number of proportionals. A Treatise on Algebra - Page 213by Elias Loomis - 1846 - 346 pagesFull view - About this book
| Eucleides - 1860 - 396 pages
...is EX to PL, and PL to KO: but if four magnitudes be continual proportionals, the first is said to have to the fourth, the triplicate ratio of that which it has to the second (e) ; therefore the solid AB has to the solid KO, the triplicate ratio of that which AB has to EX :... | |
| Euclides - 1861 - 464 pages
...proposition« 19 and 20, bk. vi. XI. — When four magnitudes are continual proportionals, the first is said to have to the fourth, the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c., increasing the denomination still by unity in any number of proportionals.... | |
| George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...Introduction, pp. 21 and 22. XI. "When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c., increasing the denomination still by unity, in any number of proportionals.... | |
| Euclides - 1863 - 122 pages
...which it has to the second. XI. When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on; quadruplicate, &c., increasing the denomination still by unity in any number of proportionals.... | |
| Euclides - 1864 - 448 pages
...which it has to the second. XL When four magnitudes are continual proportionals, the first is said to have to the fourth, the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c., increasing the denomination still b]T unity, in any number of proportionals.... | |
| Robert Potts - 1865 - 528 pages
...which it has to the second. XI. When four magnitudes are continual proportionals, the first is said to have to the fourth, the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c. increasing the denomination still by unity, in any number of proportionals.... | |
| Euclides - 1865 - 402 pages
...which it has to the second. XL When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c., increasing the denomination still by unity, in any number of proportionals.... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...the first and the third.] 1 1. When four magnitudes are continued proportionals, the first is said to have to the fourth, -the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c. increasing the denomination still by unity, in any number of proportionals.... | |
| Robert Potts - 1868 - 434 pages
...which it has to the second. XT. When four magnitudes are continual proportionals, the first is said to have to the fourth, the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c., increasing the denomination still by unity, in any number of proportionals.... | |
| Euclides - 1874 - 342 pages
...which it has to the second. 11. When four magnitudes are continual proportionals, the first is said to have to the fourth, the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c., increasing the denomination still by unity, in any number of proportionals.... | |
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