...is equal to the Square ofV the Geometrical Mean between them : and consequently the geometrical mean between two numbers is equal to the Square Root of their product. These terms and the corresponding operations form the substance of the next Chapter, and they have...

...mean. Let - - - - a:b::b:c: Then ?-* b c' Or ac-lf. COR. The mean proportional, or geometrical mean, between two numbers is equal to the square root of their product. Thus, if ac=b\ then 6=v/ac. 366. — (4.) If four numbers be proportional, 1. the order of the extremes,...

...= 32; and in the series 1:2:4:8:16, 1X6 = 2x8 = 4x4= 16 = 4"; hence, a geometrical mean between any two numbers is equal to the square root of their product; thus, a geometrical mean between 2 and 8 = J2 x 8 = */l6 = 4. The most useful problems in geometrical progression,...

...a:b::b:c: Then - " , - - - - a -J>-, bc Or ...... ac=b\ COR. The mean proportional, or geometrical mean, between two numbers is equal to the square root of their product. Thus, if ac = b2, then b=Vac. 366.—(4.) If four numbers be proportional, 1. the order of the extremes,...

...side of a square farm which contains 300 acres ; and how far apart are its opposite corners ? 582. A mean proportional between two numbers is equal to the square root of their product. (Arts. 494, 498. Obs. 2.) Qr*sT.— 5SO. When the bypothenusc and perpendicular are given, how is the...

...side of a square farm which contains 360 acres ; and how far apart are its opposite corners ? 582. A mean proportional between two numbers is equal to the square root of their product. (Arts. 494, 498. Obs. 2.) 5. Find a mean proportional between 2 and 8. Solution. — 8X2=16; and Vl6—...

...side of a square farm which contains 360 acres ; and how far apart are its opposite corners ? 582. A mean proportional between two numbers is equal to the square root of their product. (Arts. 494, 498. Obs. 2.) <lu«rr.— 580. When the hypothenuse and perpendicular are given, how is...

...is equal to the Square of the Geometrical Mean between them : and consequently the geometrical mean between two numbers is equal to the Square Root of their product. These terms and the corresponding operations form the chief substance of the next Chapter, and they...

...found equal, we may infer the equality of their ratios, or the proportion -£ = y, or 5 : 3 : : 15:9. So that a proportion may always be constituted with...example, as 5 : 3 : : 15 : the unknown quantity ; since 5 time? 8 the unknown quantity must be equal to 3x15 or 45, that quantity itself is equal to 45 -=- 5...

...means are equal, as in the proportion a : b = b : c, we have V == ac, whence b = \/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...