 If four numbers are in proportion, the sum of the terms of the first ratio is to either term of the first ratio as the sum of the terms of the second ratio is to the corresponding term of the second ratio ; that is, the numbers are in proportion by Composition.  A Treatise on Algebra - Page 156by Benedict Sestini - 1857 - 216 pagesFull view - About this book
 | William Scott - Algebra - 1844 - 568 pages
...(7f^=rf; consequently a±b : a or b::c±d: cord. but Whence, if a : b : : c : d, the sum of the two terms of the first ratio is to their difference as the sum of the two terms of the second ratio is to their difference, also the sum or the difference of the two terms... | |
 | Benedict J. Sestini - Algebra - 1854 - 156 pages
...difference of the terms of the first ratio is to the difference of the terms of the second. And again : The sum of the terms of the first ratio is to their...terms of the second ratio is to their difference. Product of the 8 114. In the arithmetical proportion, the mean and ex- ' treme terms. sum of the extremes... | |
 | Noble Heath - 1855 - 468 pages
...alternando, p -f- q : p — q : : x -j- y : x — y, that is to say, when four quantities are proportional, the sum of the terms of the first ratio is to their difference, as the sum of the terms of the last ratio to their difference. 412. Again, supposing p greater than q, as (411) p — q : x—y :... | |
 | Noble Heath - Arithmetic - 1856 - 472 pages
...alternando, p -\- q : p — q : : x -j- y : x — y ; that is to say, when four quantities are proportional, the sum of the terms of the first ratio is to their difference, as the sum of the terms of the last ratio to their difference. 412. Again, supposing p greater than q, as (411) p — q: x — y :... | |
 | George Irving Hopkins - Geometry, Plane - 1891 - 204 pages
...corresponding term of that ratio. 286. Magnitudes are said to be in proportion by composition and division when the sum of the terms of the first ratio is to their difference as the sum of the terms of the last ratio is to their like difference. THEOREMS. 287. Equimultiples of two magnitudes are in the same... | |
 | George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...proportion by composition when the sum of the terms of the first ratio is to either term of the first ratio as the sum of the terms of the second ratio is to the corresponding term of that ratio. 285. Magnitudes are said to be in proportion by division when... | |
 | William James Milne - Algebra - 1892 - 370 pages
...quantities are in proportion, the sum of the terms of the first ratio is to either term of the first ratio as the sum of the terms of the second ratio is to the corresponding term of the second ratio. Thus, when a : b : : с : d, a + b : b : : с + d : d and... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...inversion. When the sum of the terms of the first ratio of a proportion is to either term of that ratio as the sum of the terms of the second ratio is to the corresponding term of that ratio, the four quantities are said to be in proportion by composition.... | |
 | George Edward Atwood - 1900 - 276 pages
...are in proportion by composition; that is, the sum of the terms of the first ratio is to either term as the sum of the terms of the second ratio is to the corresponding term. 249 If :o 432. If four numbers are in proportion they are in proportion by... | |
 | William James Milne - Algebra - 1901 - 476 pages
...numbers are in proportion, the sum of the terms of the first ratio is to either term of the first ratio as the sum of the terms of the second ratio is to the corresponding term of the second ratio ; that is, the numbers are in proportion by Composition.... | |
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