 | Arthur Schultze - Algebra - 1906 - 584 pages
...the product of the extremes. Let a : b = с : d, ?=д. bd Clearing 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 62 = ac. (§181.) Hence b = Väc. 183. If the product of... | |
 | George Albert Wentworth - Algebra - 1906 - 440 pages
...bb a a2 ;=*• .-. a : с = a2 : b2. ab с а а а Also, rx-x3 = rxrxi' 6 с dbbb a a" = 390. The mean proportional between two numbers is equal to the square root of their product. For, if a : b = 6 : c, then b- = ac. (p. 321, §379) .-. b = Vac. 391. TAc products' of the corresponding... | |
 | Webster Wells - Algebra - 1906 - 484 pages
...in any proportion, the means can be written as the extremes, and the extremes as the means. 336. The mean proportional between two numbers is equal to the square root of their product. Let the proportion be a : b = b : c. Then by § 331, b1 = ac, and b = Vac. 337. In any proportion,... | |
 | William James Milne - Algebra - 1908 - 476 pages
...proportion a:m = m:b, m is called a mean proportional between it and b. By Prin. l, m2 = 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.... | |
 | Webster Wells - Geometry, Plane - 1908 - 208 pages
...217. Applying the above theorem to the proportion - = -, we have W = ac, or b = Vac. bc That is, the mean proportional between two numbers is equal to the square root of their product. PROP. II. THEOREM 218. (Converse of Prop. I.) If the product of two numbers is equal to the product... | |
 | Webster Wells - Algebra - 1908 - 456 pages
...in any proportion, the means can be written as the extremes, and the extremes as the means. 144. The mean proportional between two numbers is equal to the square root of their product. Let the proportion be - = - • b с Then, by § 139, 62 = ac, or 6 = Vac. 145. In any proportion,... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...217. Applying the above theorem to the proportion - = -, we have 62 = ac, or b = Vac. bc That is, the mean proportional between two numbers is equal to the square root of their product. PROP. II. THEOREM 218. (Converse of Prop. I.) If the product of two numbers is equal to the product... | |
 | Webster Wells - Geometry - 1908 - 329 pages
...217. Applying the above theorem to the proportion - = - . we have b2 = ac. or b = Vac. bc That is, the mean proportional between two numbers is equal to the square root of their product. PROP. II. THEOREM 218. (Converse of Prop. I.) If the product of two numbers is equal to the product... | |
 | Frederick Howland Somerville - Algebra - 1908 - 428 pages
...Vac. Proof : . a : b = b : c. By Art. 371, b2 = 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 = be. Then a:b = c:d. Proof : ad = be. Dividing by bd, í = í. bd That is : If tl1e... | |
 | James William Nicholson - Algebra - 1909 - 332 pages
...proportion. Let mq = np. tYYl IY\ Divide by nq, — - - ; or m : n = p : q. 300. Mean proportional. The mean proportional between two numbers is equal to the square root of their product. Let a : 6 = b : с. Then, 62 = ac. ... 6=Vac. 301. Principle of alternation. If four numbers are in... | |
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A mean proportional between two numbers is equal to the square root of their product. 
