| Jeremiah Day - 1814 - 304 σελίδες
...section, so far as to admit the principle, that " when four quantities are in geometrical proportion, the product of the two extremes is equal to the product of the two means :" a principle which is at the foundation of the Rule of Three in arithmetic. See Webber's... | |
| John Bonnycastle - 1818 - 284 σελίδες
...product of the two extremes is equal to that of the two means. 6 In any continued geometrical series, the product of the two extremes is equal to the product of any two means that are equally distant from them ; or to the square of the mean, when the number of terms is... | |
| Charles Hutton - 1818 - 646 σελίδες
...this is the foundation and reason of the practice in the Rule of Three. THEOREM 2. fn any continued geometrical progression, the product of the two extremes is equal to the product of anjr two means that are equally distant from them, or equal to the square of the middle term when there... | |
| George G. Carey - 1818 - 602 σελίδες
...Example; 4, 8, It), is a geometric»! urogiessmn; therefore, ifix^^S11 3. If it consist of/our term«, the product of the two extremes is equal to the product of the two im-aus Example: 4, 8, Iti, 31, is a geometrical progression; therefore, 32X4— 16x8. 3. In... | |
| William Jillard Hort - 1822 - 308 σελίδες
...terms lying between them are called mean terms. When four quantities are in geometrical proportion, the product of the two extremes is equal to the product of the two means. The whole theory of geometrical proportion rests upon this property. Since the product... | |
| Charles Hutton - 1822 - 616 σελίδες
...Proportion, is contained in the following theorems. THEOREM 1. When four quantities are in proportion, the product of the two extremes is equal to the product of the two mean?. Thus, in the four 2, 4, 3, 6, it is 2 X fi = 3 X 4 = 12. And hence, if the product of... | |
| John Bonnycastle - 1825 - 336 σελίδες
...product of the two extremes is equal to that of the two means. 6. In any continued geometrical series, the product of the two extremes is equal to the product of any two means that are equally distant from them ; or to the square of the mean, when the number of terms is... | |
| Ferdinand Rudolph Hassler - 1826 - 224 σελίδες
...3+5 x 3-t-5a X.'H-6» X 3+5« x 3+5" X 3+5« x 3 &c. The law of continued geometric proportion, that the product of the two extremes is equal to the product of the mean term into itself, evidently holds good here, and we have, for instance, by the product of... | |
| Jeremiah Day - 1827 - 352 σελίδες
...section, so far as to admit the principle that " when four quantities are in geometrical proportion, the product of the two extremes is equal to the product of the two means :" a principle which is at the foundation of the Rule of Three in arithmetic. See Webber's... | |
| Ira Wanzer - 1831 - 408 σελίδες
...THEOREM 1. — When four quantities are in geometrical proportion, (either continued or discontinued,') the product of the two extremes is equal to the product of the two means. Thus, in the four 2, 4, 3, 6, it is 2x6=4x3=12. And hence, if the product of the two... | |
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