| Jeremiah Day - Algebra - 1827 - 352 pages
...quantities are proportional. If the two products are not equal, the quantities are not proportional. ^A 378. **In mathematical investigations, when the relations...will not destroy the proportion. Thus, if a : b'.** '.c : d, the order of these four quantities may be varied, in any way which will leave ad=bc. Hence,... | |
| Silas Totten - Algebra - 1836 - 332 pages
...fractions being equal, and the denominators the same, the numerators must also be equal ; and hence, **the product of the means equal to the product of the extremes.** (66.) The property of geometrical proportions which has just been proved, is the fundamental principle... | |
| George Willson - Arithmetic - 1838 - 194 pages
...is there between the product of the means, and the product of the extremes of a proportion ? Why is **the product of the means equal to the product of the extremes** ? ' What rule is founded on this equality ? Explain the common method of stating in the Single Rule... | |
| Jeremiah Day - Algebra - 1841 - 354 pages
...given, they are frequently stated in the form of a proportion. But it is commonly necessary that ihis **first proportion should pass through a number of transformations...products, will not destroy the proportion. Thus, if a : b** : : c : d, the order of these four quantities may be varied, in any way which will leave ad=bc. Hence,... | |
| James Bates Thomson - Algebra - 1844 - 272 pages
...proportional. 343. It is evident that the terms of a proportion may undergo any change which will not destroy **the equality of the ratios ; or which will leave the...of the means equal to the product of the extremes.** These changes are numerous, but they may be reduced to a few general principles. CASE I. Changes in... | |
| Admiralty - 1845 - 152 pages
...equation, Divide by 13 .-. ж=12 61. An equation may be formed from 4 proportional quantities, by making **the product of the means equal to the product of the extremes.** Let the proportional quantities be x, y, a, b ; or x : y : : a : b. Vy-J (Art. 15.) .-. bx=ay. (Art.... | |
| Horatio Nelson Robinson - Arithmetic - 1845 - 310 pages
...is there between the product of the means, and the product of the extremes of a proportion ? Why is **the product of the means equal to the product of the extremes** ? What rule is founded on this equality ? Explain the common method of stating in the Single Rule of... | |
| Ormsby MacKnight Mitchel - Algebra - 1845 - 308 pages
...:: D : C; B : D : : A : C, &c. &c. From each of which we may readily derive the equation AD= CB, or **the product of the means equal to the product of the extremes.** Many other properties might be presented, but we limit ourselves to this short discussion, and proceed... | |
| Jeremiah Day - Algebra - 1847 - 358 pages
...quantities are proportional. We have only to multiply the means together, and also the extremes. If the **products are equal, the quantities are proportional....products, will not destroy the proportion. Thus, if a : b** : : c : d, the order of these four quantities may be varied, in any way which will leave ad=bc. Hence,... | |
| James Bates Thomson - Algebra - 1847 - 266 pages
...is evident that the terms of a proportion may undergo any change which will not destroy the equn ity **of the ratios ; or which will leave the product of the means equal to the product of the extremes.** These changes are numerous, but they may be reduced to a few general principles. CASE I. Changes in... | |
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