...+ 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...

...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....

...: 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 -...

...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...

...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...

...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...

...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...

...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...

...= 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, — - — — — ——...

...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...