 | Arthur Schultze - 1918 - 336 σελίδες
...equal to the product of the extremes. Let a : b = с : d, Í-ÍClearing of fractions, ad = be. 164. The mean proportional between two numbers is equal to the square root of their product. Let the proportion be •. a : b = b : c. Then 62 = ac._(§ 163.) Hence b .= Vac. 165. If the product... | |
 | William James Milne - 1911 - 332 σελίδες
...m : b, m is called a mean proportional between a and b. By Prin. l, m? = ab ; .-. m = V ab. Hence, a mean proportional between two numbers is equal to the square root of their product. 1. Show that the mean proportional between 3 and 12 is either 6 or — 6. Write both proportions. 2.... | |
 | William Betz, Harrison Emmett Webb - 1912 - 368 σελίδες
...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 b2 = ac. Therefore b = Vac. . 360. Theorem III. If the product of a pair of... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - 1912 - 360 σελίδες
...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 b2 = ae. Therefore b = Vac. 360. Theorem III. If the product of a pair of... | |
 | Clara Avis Hart, Daniel D. Feldman - 1912 - 504 σελίδες
...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 - 1913 - 458 σελίδες
...= 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 - 1915 - 250 σελίδες
...= -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 - 1916 - 536 σελίδες
...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 - 1917 - 520 σελίδες
...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... | |
 | Julius Lederer Neufeld - 1920 - 412 σελίδες
...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... | |
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A mean proportional between two numbers is equal to the square root of their product. 
