| Olinthus Gregory - 1834 - 427 páginas
...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...x 9) = 6. . 3. If a proportion contain an unknown** tern}, such, for example, as 5 : 3 : : 15 : the unknown quantity ; since 5 times the ttnknown quantity... | |
| Olinthus Gregory - 1838 - 427 páginas
...15 are found equal, we may infer the equality of their ratios, or the proportion i = y, or 5 : 3 : : **15:9. So that a proportion may always be constituted...product. Thus, between 4 and 9 the mean proportional is** \/(4 x 9) = 6. 3. If a proportion contain an unknown term, such, for example, as 5 : 3 : : 15 : the... | |
| John Hind - 1840 - 224 páginas
...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... | |
| Davis Wasgatt Clark - 1844 - 346 páginas
...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,... | |
| George Hutton (arithmetic master, King's coll. sch.) - 1844
...= 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,... | |
| Davis Wasgatt Clark - 1846 - 358 páginas
...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,... | |
| James Bates Thomson - 1847 - 422 páginas
...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... | |
| James Bates Thomson - 1847 - 422 páginas
...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—... | |
| James Bates Thomson - 1848 - 422 páginas
...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... | |
| John Hind - 1856
...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... | |
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