 | George Lees - 1826 - 276 σελίδες
...square of the mean. For, if a '. b '. '. b '. c, then (No. 1 08.) ac = 62. Hence, a mean proportional between two quantities is equal to the square root of their product. For, let a; be a mean proportional between a and c, so that a '. x '. '. x '. c, then! is a? = ao,... | |
 | John Playfair - 1829 - 210 σελίδες
...the mean. If A : B : : B : C, then AC=B3. 28. Cor. B=v/ AC, that is, a geometrical mean proportional between two quantities is equal to the square root of their product. • . 29. If any three terms of a proportion be given, the fourth term may be found. Let x be the unknown... | |
 | John Radford Young - 1839 - 332 σελίδες
...of terms be odd, the product of the extremes is equal to the square of the middle term ; and hence a geometrical mean between two quantities is equal to the square root of their product. 2. The last term in any geometrical series is equal to the product of the first term, and that power of... | |
 | Horatio Nelson Robinson - 1864 - 444 σελίδες
...ScilOLlUM. — Taking the square root of the last equation, we have b = Vac ; hence, The mean proportional between two quantities is equal to the square root of their product. PROPOSITION XIV. — If three quantities be in continued proportion, the first is to the third, as... | |
 | Horatio Nelson Robinson - 1866 - 328 σελίδες
...Extracting the square root of the last equation, ve have _ 6 = •Sac ; hence, The mean proportional between two quantities is equal to the square root of their product 24* PROPORTION. PROPOSITION VI. 368. Quantities which are proportional to the same quantities are proportional... | |
 | Daniel Barnard Hagar - 1873 - 278 σελίδες
...by division, a = — / d = — ; 6 = — , andc = — . dacb TJieorem TV. 334. The mean proportional between two quantities is equal to the square root of their product. Let a:b::b:c. By Theorem I, 62 = ac/ Extracting square root, b = j/aef. Theorem V. 335. If four quantities... | |
 | Joseph Ficklin - 1874 - 446 σελίδες
...as in the proportion a : Ъ = b : c, we have b9 = ac, whence b = \^ac; that is, a mean proportional between two quantities is equal to the square root of their product. Let аа = Ъс . . . (1); then, dividing both members by cd, - = -j, or a:c = b:d . . . (2). С (i... | |
 | Horatio Nelson Robinson - 1874 - 340 σελίδες
...Extracting the square root of the last equation, we have 6 = v/ас ; hence, The mean proportional between two quantities is equal to the square root of their product. 24* PROPOSITION VI. 368. Quantities which are proportional to the same quantities are proportional... | |
 | George Albert Wentworth - 1877 - 436 σελίδες
...- ; and ™ may be taken to represent the value of -. 6 nb PROPOSITION II. 260. A mean proportional between two quantities is equal to the square root of their product. In the proportion a : b : : b : с, b2 = а с, § 259 (the product of the extremes is equal to the... | |
 | William Henry Harrison Phillips - 1878 - 236 σελίδες
...product of the means. If A : B = B : C, we have B2 = AC, or, B = V5^C ; that is, the mean proportional between two quantities is equal to the square root of their product. EXERCISE 1. Find the mean proportional between 6 and 24 ; between 5 and 10. SCHOLIUM. It is important... | |
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The mean proportional between two quantities is equal to the square root of their product. 
