| Euclid - Geometry - 1853 - 136 pages
...and mean ratio." For the segment BH is to the segment AH as AH is to the whole line AB; and in such a **proportion the product of the extremes equals the product of the means,** or in this instance the rectangle under AB and BH is equal to the square on AH, which is proposition... | |
| Charles Auguste A. Briot - 1863 - 376 pages
...extremities, are called the extremes ; the two others, placed in the middle, are called the means. In every **proportion, the product of the extremes equals the product of the means.** Be they the two equal ratios or the proportion — a _ c_ 1 ~ d' If we multiply by d the two terms... | |
| Thomas Kimber - Mathematics - 1865 - 192 pages
...8 : 12 : : 2 : 3, where 8 and 3 are called the extreme, and 12 2 the mean terms. • 102. In every **proportion, the product of the extremes equals the product of the means** ; thus, if 8 : 12 : : 2 : 3, then 8X3 8 2 = 12 x 2 ; for if — - = - and both fractions be brought... | |
| John Homer French - Arithmetic - 1869 - 335 pages
...compound and a simple ratio, or of two compound ratios ; as, 5:9) „ , 5:9) (5:2 537. Since in a simple **proportion the product of the extremes equals the product of the means** (see 532, 1.) ; and since a compound ratio is reduced to a simple one, by multiplying all the antecedents... | |
| Edward Olney - Algebra - 1873 - 354 pages
...ratio. Thus if a : Ъ : : b : с : : с : d : : d : e, we have a continued proportion. 61. Prop. 1. — **In any proportion the product of the extremes equals the product of the means.** DEM. — If я : Ъ : : e : d then ad = be. For a : b : : с : d is the same as - = -, which l> d cleared... | |
| Henry Major - 1875 - 308 pages
...to 1 0 ; which may be written 4 : 8 : : 5 : 10. These are called proportionals. SIMPLE PROPORTION. **In any proportion the product of the extremes equals the product of the means,** or the first and fourth terms multiplied equals the second and third multiplied together. 147 In the... | |
| Milton Browning Goff - Arithmetic - 1876 - 462 pages
...2O da. JI for ( ) da. We have now to find the number of days in the Sec. cause. And since this is a **proportion, the product of the extremes equals the product of the means,** and we therefore can readily fill the blank ( ) by Rule I, or II. (281). PR OBLJSHTS. 1. If 6 men build... | |
| Edward Olney - Algebra - 1877 - 390 pages
...ratio. Thus if a : b : : b : c : : c : d : : d : e, we have a continued proportion. 65. Prop. 1. In a **proportion the product of the extremes equals the product of the means.** DEM. — If o : b : : c : d then ad = 6c. For a : 6 : : c : d is the same flt C as r = -a which cleared... | |
| 1877 - 188 pages
...read, 8 : 12 : : 2 : 3, where 8 and 3 are called the extreme, and 12 2 the mean terms. 102. In every **proportion, the product of the extremes equals the product of the means** ; thus, if 8 : 12 : : 2 : 3, then 8X3 8 2 = 12x2; for if - • = — and both fractions be brought... | |
| Edward Olney - 1878 - 362 pages
...ratio. Tims if a : b : : Ъ : с : : с : d : : d : e, we have a continued proportion. 61. Prop. 1. — **In any proportion the product of the extremes equals the product of the means.** DEM. — If a : b : : с : d then ad = be. For a : b : : e : d is the same as r = -, which ti a cleared... | |
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