...means are equal, as in the proportion a : b = b : c, we have 6 a = ac, whence 6 = \/ac ; that is, a mean proportional between two numbers is equal to the square root of their product. 6. Conversely, if the product of two numbers is equal to the product of two others, either two may...

...divide by the first, to find the fourth term, or the answer. In arithmetic, too, we are told that " the mean proportional between two numbers is equal to the square root of their product." The reason we may perceive from the following proportion : a : b : : b : c Here b is what is termed...

...proportional between the extremes of a proportion is one of the equal means of the proportion (Art. 346), the mean proportional between two numbers is equal to the square root of their product. Hence, Л/816 X 97J = -v/79560 = 282.0638+, Ans. 75. r Ib. = 12 oz. ; 12 oz. : oz. = $- : x , Ans'...

...proportion a : b = b : c, we have 6* = ac, whence b = y^ac; that is, a mean proportional (II., 36) between two numbers is equal to the square root of their product. 6. Conversely, if the product of two numbers is equal to the product of two others, either two may...

...proportion a : b = b : c, we have 6 2 == ac, whence b = y^ac; that is, a mean proportional (II., 36) between two numbers is equal to the square root of their product. 6, Conversely, if the product of two numbers is equal to the product of two others, either two may...

...: с Let e : 6 :: b : c. Therefore I., ft2 = ac. Extract the square root, b = ^/a c. Hence, III. A mean proportional between two numbers is equal to the square root of their product. Let a:b::c:d. Therefore I., ad — be. ab Divide bv с d, - = -• с d IV. If four numbers are in...

...square of the mean proportional between two numbers is equal to the product of the numbers. Hence, the mean proportional between two numbers is equal to the square root of their product. EXAMPLES. 270. 1. Find a fourth proportional to 7, 10, and 21." By Art. 268, the required fourth proportional...

...first = 3 X 3 sq. ft. ; of second, 5 x 5 sq. ft. ; of third, 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,...

...the proportion a : b = b : c, we have & = ac, whence 6 = \/ac; that is, a mean proportional (II., 36) between two numbers is equal to the square root of their product. 6. Conversely, if the product of two numbers is equal to the product of two others, either two may...

...: Ъ :: Ь : с. 4 Therefore I., l'¿ = nc. Extract the square root, Ъ = -у/а с. Hence, III. A mean proportional between two numbers is equal to the square root of their product. Let a : 6 : : с : d. Therefore I., ad = be. а Ъ Divide by с d, - = -5 • IV. If four numbers are,...