 | John Gough - Arithmetic - 1813 - 358 pages
...be equal to the product of the extremes. Proposition Proposition 3. In any geometrical progression the product of the two extremes, is equal to the product of any two terms equally distant from the two extremes. 3, 6, 12, 24, 48, 96, 3, 6, 12, 24, 48, 9/5, 102,... | |
 | 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;... | |
 | Charles Hutton - Mathematics - 1816 - 610 pages
...are similar to those in Arithmetical Proportion, using multiplication for addition, See. 1. When 1. When four quantities are in geometrical proportion, the product of the two extremes is equal to tue product of the 'wo means. As in these, 3, 6, 4, 8, where 3X8=6 X 4 = 24 ; and in these, a, or,... | |
 | 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... | |
 | Arithmetic - 1818 - 264 pages
...numbers geometrically proportional. And it is a principle in Mathematicks, that, if three numbers be in geometrical proportion, the product of the two extremes, is equal to the square of tl\p mean. (See Euclid's Eliments, 20th prop. 7th book.) And on the contrary, if the rec«... | |
 | 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
...extremes, from being placed at the extremities, and the terms lying between them are called mean terms. When four quantities are in geometrical proportion,...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... | |
 | Charles Hutton - Mathematics - 1825 - 608 pages
...Geometrical Prooortion is contained in the following theorems1. When 1 . When four quantities are in proportion, the product of the two extremes is equal to the product of the two means. As in these, 3, 6,4, 8, where 3X8=6X4=24 ; and in these, a, ar, b, br, where a)(.br=ar')<.b—abr.... | |
 | 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... | |
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If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means. 
