 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
 | John Bonnycastle - 1848 - 334 pages
...the duplicate ratio of a : b. PEOP. V. If four quantities be continued proportionals, thefirst has to the fourth the triplicate ratio of that which it has to the second. Let a : 6 : : b : с, and b:c::c:d; then a, b, c, d are continued proportionals, and since а b , b с ,... | |
 | Euclides - 1848 - 52 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.... | |
 | Euclides - Geometry - 1853 - 176 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.... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 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, etc., increasing the denomination still by unity, in any number of proportionals.... | |
 | Euclides - 1855 - 270 pages
...ia called duplicate ratio. 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.... | |
 | Euclides - 1855 - 230 pages
...that which it has to the 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, (fee., increasing the denomination still by unity, in any number of proportionals.... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...(225.) If three quantities are in continued proportion, the first will have to the third the duplicate ratio of that which it has to the second. Let a : b : : b : c. Then a : c : : a' : &'. For since a : b : : b : c, by Art. 212, ac=b*. Multiplying each... | |
 | Elias Loomis - Algebra - 1858 - 394 pages
...that is, a'Xc=aXb\ Resolving this equation into a proportion by Art. 213, we have a : c : : a' : V. (226.) If four quantities are in continued proportion,...the fourth the triplicate ratio of that which it has tc, the second. Let a, b, c, d be four quantities in continued proportion, so that a : b :: b : c :... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 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.... | |
 | James Elliot - 1860 - 252 pages
...ratio of 20 to 45 ? DEF. 7. When four quantities are in continued proportion, the first is said to have to the fourth the Triplicate Ratio of that which it has to the second ; and the first is said to have to the second the Subtriplicate Ratio of that which it has to the fourth.... | |
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