 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...be simplified by placing the product of the means equal to the product of the extremes. 390. Cor. I. The mean proportional' between two numbers is equal to the square root of their product. 391. Cor. n. If two proportions have any three terms of one equal respectively to the three corresponding... | |
 | Frederick Howland Somerville - Algebra - 1913 - 458 pages
...Then b = Voci Proof : a : 6 = 6 : c. By Art. 371, 62 = ac. Extracting square root, b - Vac. That is : The mean proportional between two numbers is equal to the square root of their product. 374. Given ad - bc. Then a:bTO-c:d. Proof : ad = be. Dividing by bd, 5 = 5. bd That is : If the product... | |
 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 250 pages
...proportion f = -J by alternation, inversion, composition, division, composition and division. 386. THEOREM. The mean proportional between two numbers is equal to the square root of their product. For let - = -, then 62 = «c. Why? .-. b = . ' 7» /> ' /«c. c 387. EXERCISES 1. Find the value of... | |
 | William Betz - Geometry - 1916 - 536 pages
...principle enables us to find any term of a proportion, if the other three are given. 359. Theorem II. The mean proportional between two numbers is equal to the square root of their product. For if a : b = b : c, then b1 = ac. Therefore b — Vac. 360. Theorem III. If the product of a pair... | |
 | Elmer Adelbert Lyman, Albertus Darnell - Algebra - 1917 - 520 pages
...fractions gives 42 = 2 • 8 or 4 = V2 • 8. This example illustrates the following property : II. A mean proportional between two numbers is equal to the square root of their product. PROOF. Let a, b, aad с be such numbers that a = b b с' b2 = ас. (Clearing of fractions.) .-. b... | |
 | Arthur Schultze - Algebra - 1919 - 618 pages
...is equal to the product of the extremes. Let a : b = с : d, ' HClearing of fractions, ad = be. 182. The mean proportional between two numbers is equal to the square root of their product. Let the proportion be a : b = b : c. Then Ь2 = ас. (§181.) Hence b = Vac. 183. If the product of... | |
 | Julius Lederer Neufeld - Algebra - 1920 - 412 pages
...the extremes, If a:b=c:d The,, | = | Clearing of fractions, ad = be. If a : b = b : c, Then 62 = ac A mean proportional between two numbers is equal to the square root of their product. Principle 2. — // the product of two numbers is equal to the product of two other numbers, either... | |
 | William Raymond Longley, Harry Brooks Marsh - Algebra - 1926 - 608 pages
...geometric series with a constant ratio. Hence „ Cr _ 0 -a-~ G' G2 = ab. 1П G = Väb. The geometric mean between two numbers is equal to the square root of their product. 209. Problems. In most problems having to do with geometric series, five quantities are involved, a,... | |
 | Arthur McCracken Harding, George Walker Mullins - Algebra - 1928 - 344 pages
...any proportion the terms are in proportion by inversion. (5) If a/b = b/c, then b = -¡¡ac. Thus, the mean proportional between two numbers is equal to the square root of their product. (6) Suppose a/b = c/d. Adding 1 to both members of the equation gives (a + b)/b = (c + d)/d. Thus,... | |
 | Daniel Barnard Hagar - Arithmetic - 1871 - 352 pages
...between -1/36 = 6 tlle extremes of a proportion is one of the equal means of the proportion (Art. 547), the mean proportional between two numbers is equal to the square root of the product of those numbers. The product of 4 by 9 is 36, and the square root of 36 is 6, the mean... | |
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V9 x 25 sq. ft. = 15 sq. ft. NOTE. — The mean proportional between two numbers is equal to the square root of their product. 13. Find the volume of the frustum of a square pyramid, its upper base containing 64 square inches, and its lower base 196 square... 
