 | Charles Butler - Mathematics - 1814 - 528 pages
...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 the mean. logarithmically;... | |
 | George G. Carey - Arithmetic - 1818 - 602 pages
...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 a geometrical... | |
 | John Bonnycastle - Algebra - 1818 - 284 pages
...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... | |
 | William Jillard Hort - 1822 - 308 pages
...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 of the extremes... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...and reason of the practice in the Rule of Three. THEOREM 2. 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... | |
 | John Bonnycastle - Algebra - 1825 - 336 pages
...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... | |
 | Ferdinand Rudolph Hassler - Arithmetic - 1826 - 224 pages
...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 - Algebra - 1827 - 352 pages
...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 Arithmetic.... | |
 | Ira Wanzer - Arithmetic - 1831 - 408 pages
...reason of the practice in the Rule of Three. THEOREM 2. — 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 second power of the middle term when... | |
 | Charles Davies - Arithmetic - 1833 - 284 pages
...th« divisor by the quotient is equal to the dividend, it follows, That in any geometrical proportion the product of the two extremes is equal to the product of the two means. Thus in the first example, 1 : 6 :: 2 : 12 we have, 1 X 12=frx2=12 and in the second, 4 : 12 : : 8... | |
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AC and by clearing the equation of fractions we have BO=AD; that is, Of four proportional quantities, the product of the two extremes is equal to the product of the two means. 
