| Jeremiah Day - Algebra - 1814 - 303 pages
...quantities are proportional. If the products are not equal, the quantities are not proportional. 379. **In mathematical investigations, when the relations...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,... | |
| Jeremiah Day - Algebra - 1831 - 332 pages
...d, the order of these four quantities may be varied, in any way which will leave ad=bc. Hence, 379. **In mathematical investigations, when the relations...of the means equal to the product of the extremes.** 380. If four quantities are proportional, THE ORDER op THE MEANS, OR OF THE EXTREMES, OR OF THE TERMS... | |
| Jeremiah Day - 1832
...quantities are proportional. If the products are not equal, the quantities arc not proportional. 379. **In mathematical investigations, when the relations...quantities may be varied, in any way which will leave** ad— be. Hence, 380. If four quantities are proportional, THE ORDER OF THE MEANS, OR OF THE EXTREMES,... | |
| Silas Totten - Algebra - 1836 - 304 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 - 192 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 - 332 pages
...demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leasre **the product of the means equal to the product of the...products, will not destroy the proportion. Thus, if a** : 6 : : c : d, the order of these four quantities may be varied, in any way which will leave ad=bc.... | |
| Jeremiah Day - Algebra - 1842 - 332 pages
...proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of ihe **ratios; or which will leave the product of the means...products, will not destroy the proportion. Thus, if** o: 6:: c: d, the order of these four quantities may be varied, in any way which will leave ad=bc. Hence,... | |
| Jeremiah Day, James Bates Thomson - Algebra - 1844 - 252 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... | |
| Horatio Nelson Robinson - Arithmetic - 1845 - 288 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 - 294 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... | |
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