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" If four numbers are in proportion, they are in proportion by inversion; that is, the second term is to the first as the fourth is to the third. "
First Course in Algebra - Page 264
by William Benjamin Fite - 1913 - 334 pages
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Grammar School Algebra

George Edward Atwood - 1900 - 276 pages
...= b : d .: d : c = 6 : a .-. d : b = c : a Obtain four proportions with a and d as the means. 429. If four numbers are in proportion, they are in proportion by inversion ; that is, the second term is to the first as the fourth is to the third. If a : b = c : d ad = bc...
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An Algebra for High Schools and Academies

Louis Parker Jocelyn - Algebra - 1902 - 460 pages
...the square root of their product. Dem. Let - = -• Then x = Va3. xa For z2 = ad. Why ? 305. Prop. 2. If four numbers are in proportion, they are in proportion by inversion. _ T a <: r,,, bd Dem. Let - = - • 1 hen - = — bd а с For 1-^=1-=--. or od b- = d. а с 306....
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Elementary Algebra

Frederick Howland Somerville - Algebra - 1908 - 428 pages
...c:d. Then b : a = d : c. Proof: о = £. 6 d Then, Whence, d - = ^ . ac Or, 6 : a = d : c. That is : If four numbers are in proportion, they are in proportion by inversion. 376. Given a:b = c:d. Then a:c = b:d. Proof : a _c b~d' Multiplying by Í, о5 = 5«. с be cd Whence,...
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Elementary Algebra: first course

John Charles Stone, James Franklin Millis - Algebra - 1911 - 698 pages
...are in proportion. That is, if ad = b, od SUGGESTION. — Divide both members of ad = be by bd. (3) If four numbers are in proportion, they are in proportion by inversion. That is, if 2 = £, then b- = Í. bd а с SUGGESTION. — Divide 1 = 1 by the members of - = -•...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...to the third term as the second is to the fourth. Thus if a:b = c:d, then a. : c = b : d. Why? 363. If four numbers are in proportion, they are in proportion by inversion; that is, the second term is to the first as the fourth is to the third. Thus if a : b = c : d, then...
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Plane Geometry

William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...the third term as the second is to the fourth. Thus if a :b = c : d, then a : c = b ; d. Why? 363. If four numbers are in proportion, they are in proportion by inversion; that is, the second term is to the first as the fourth is to the third. Thus if a:b = c:d, then b:a=d:c....
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Plane and Solid Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...(2) a mean. Ex. 624. If7* + 8y:12 = 2a; + 3f:3) find the ratio x : y. PROPOSITION III. THEOREM 395. If four numbers are in proportion, they are in proportion by inversion; that is, the second term is to the first as the fourth is to the third. Given a:b=c:d. To prove b:u~d:c....
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First Course in Algebra

William Benjamin Fite - Algebra - 1913 - 304 pages
...proportional to three numbers ? 28. What is meant by saying that a, b, c, and d are proportional ? 29. What is meant by the statement that if four numbers are in proportion they are in proportion by alternation ? 30. What is meant by the statement that if four numbers are in proportion they are in...
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Elementary Algebra Revised

Frederick Howland Somerville - Algebra - 1913 - 458 pages
...= d:e. Proof: ? = °. Then, 1 .,- ? = 1 -s-5. bd Whence, - = - • ac Or, 6 : a = d : c. That is : If four numbers are in proportion, they are in proportion by inversion. 376. Given a:b = c:d. Then a:c = b:d. Proof : If four numbers are in proportion, they are in proportion...
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A Review of Algebra

Romeyn Henry Rivenburg - Algebra - 1914 - 92 pages
...; the' sum of the first 5 terms is 25. Find the common difference. 8. Explain the terms, and prove that if four numbers are in proportion, they are in proportion by alternation, by inversion, and by composition. Find x when 3 + ж_40 + ж3 9. Find the value of ж...
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