...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,...

...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,...

...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,...

...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,...

...and b. If a:b = b: c = c:d, then b and с are called the two mean proportionals between a and d. 334. The mean proportional between two numbers is equal to the square root of their product. Proof. If a : b = b : c, then o2 = etc, or b = Vac. Exercise 121. From each of the following products...

...^ л/2. 9. Insert 4 geometrical means between x and — y. 373. PRINCIPLE. — The geometrical mean between two numbers is equal to the square root of their product. The above principle may be established as follows : Let a and 6 represent any two numbers, and G their...

...a2 : b2. , , ab с а а а Also, Ix-xj = Ixi;xT' b с dbb Ь a a3 ä = ü.-. a : d = as : b3. 247. The mean proportional between two numbers is equal to the square root of their product. For, if a : Ь = Ь : с, a 6 then - = -, Ь с and Ь2 = ас. .-. b = Väc. 248. The products of...

...(or mean). Dem. Let y = v Thena<¿ = 6<?. Why? bd And a=^,b = ^,e = ^,d = ^ Why? deba 304. COR. 2. A mean proportional between two numbers ,is equal to the square root of their product. Dem. Let - = -• Then x = Va3. xa For z2 = ad. Why ? 305. Prop. 2. If four numbers are in proportion,...

...aaa Also, T:X.XJ = IXÎXT1 b с d - b 6 a a' 'T - = — . d b2 ... a : d = a2 : bs. 247. 771e mea2 proportional between two numbers is equal to the square root of their product. For, if a : b = b : c, then "=Л b с .41d b2 _ „c. .'. b = Vac. 248. The products of the correspondiny...