 | Charles Butler - 1814 - 528 σελίδες
...and one for z \ the four theorems for rinding the value of n, may be expressed four proportionals, the product of the two extremes is equal to the product of the two means ; and in three proportionals, the product of the extremes !• opal to the square of... | |
 | 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... | |
 | Charles Vyse - 1815 - 340 σελίδες
...common multiplier or ratio is 2. Also 729. 24.3. 81. 27. 9. 3. Here the common divisor or ratio is 3. In any series of numbers in geometrical progression, the product of the two extremes is jqual to the product of any two means that are equally distant from the extremes. As 3. Q. '21 81.... | |
 | 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 odd.... | |
 | 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 odd.... | |
 | 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... | |
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In any continued geometrical progression, the product of the two extremes is equal to the product of any two means that are equally distant from them, or equal to the square of the middle term when there is an uneven number of terms. 
