 PRINCIPLE 7. — If four numbers are in proportion, the. difference between the terms of the first ratio is to either term of the first ratio as the difference between the terms of the second ratio is to the corresponding term of the second ratio ; that...  Advanced Algebra for Colleges and Schools - Page 331by William James Milne - 1902 - 608 pagesFull view - About this book
 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...+ d: d or a+4:a::c+d:r. 4. If four quantities are in proportion, they arc so by division ; that is. If a : b : : с : d, then, a — b : b : : с — d : d or a — b : a : : с — d : с. 5. Equimultiples of two quantities are pro : y, in the constant ratio... | |
 | James Haddon - Algebra - 1871 - 244 pages
...and, multiplying by-, we have 0 MC ab - = -., .: a : с :: о : d. с d This is called alternando. 6. If a : b : : с : d, then a + b : b : : с + d : d. (Euclid, Book V. Prop. 18.) For z- = -, and, adding 1 to each side, у .-. a + 6 : 6 : : e + d : d.... | |
 | Charles Scott Venable - Algebra - 1880 - 168 pages
...: b : : с + d : d. Also, since — = — . it is clear that а с a + b : a : : с + d : с. 125. If a : b : : с : d, then a — b : b : : с — d : d. ft 1' First, -j- — -j , and subtracting 1 from both sides of и d this equation, we have - - 1 -... | |
 | William James Milne - Algebra - 1881 - 360 pages
...proportion, the sum of the terms of the first ratio is to either term of the first ratio as t)ie sum of the terms of the second ratio is to the corresponding term of tlie second ratio. Thus, when a:b :: c:d, a-\-b:b :: c-\-d:d and a-\-b:a :: c-\-d:c. When the sum of... | |
 | James Morford Taylor - Algebra - 1889 - 340 pages
...then a : с = b : d. (iii.) Composition : If я. : b — с : d, then a + b : b — с + d : d. (iv.) Division : If a : b = с : d, then a — b : b = с - d : d. (v.) Composition and Division : If a : b = с : d, then a + b:a — b = с + d : с — d. These propositions... | |
 | James Morford Taylor - Algebra - 1889 - 340 pages
...с = b : d. (iii.) Composition : If a : b = с : d, then a + b : b — с + d : d. (iv.) Dimsion : If a : b = с : d, then a — b : b = с — d : d. (v.) Composition and Division : If a : b = с : d, then a+b:a — b = с + d : с — d. These propositions... | |
 | George Irving Hopkins - 1891 - 210 pages
...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 the difference of the terms... | |
 | William James Milne - Algebra - 1892 - 370 pages
...PRINCIPLE 7. — If four quantities are in proportion, the difference between the terms of the first ratio is to either term of the first ratio as the difference between the term* of the second ratio is to the corresponding term of the second ratio. Thus, when a:b::c:d, a... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1897 - 548 pages
...= с : d, then a + b:b = cf d:d [Composition.] For n b that is, О (л or a + b :b = с + d: d. (4) If a : b = с : d, then a — b : b = с — d: d. [Division.] For - = - ; therefore --!=--!; öd bd thati* a-b_c-d. tnat is, — - — — — ——... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...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. When the difference of... | |
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