 | Alexander Ewing - Logarithms - 1799 - 514 pages
...antecedents-, and the feconct and fourth terms, 32 and 24, are confequents. In four proportional numbers, the product of the two extremes is- equal to the product of -the two means ; End. B. 6 prop. 16. ; thus^ if -1€ s• 3* • 1 12 ! 24, then 16X24=32X 12 = 384.... | |
 | Arithmetic - 1801 - 242 pages
...27, 9,3, 1, decrease by the common divisor 3. In any series of numbers, in Geometrical Progression, the product of the two extremes, is equal to the product of any two means, equally distant therefrom ; or of the product of the middle term by itself: Thus, 1, 3,... | |
 | Tiberius Cavallo - Physics - 1803 - 546 pages
...multiplied by AS. Then D is the centre of percuflion. And fmce, when four quantities are proportional, the product of the two extremes is equal to the product of the two means; therefore if the weight of A multiplied by AS, be again multiplied by AD, the product... | |
 | Charles Hutton - Mathematics - 1811 - 406 pages
...multiplication for addition, &c, , - 1. When 1. Wh.en four quantities are in geometrical 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=6 X 4 = 24; and in these, a, ar, b, br, where ax.... | |
 | Charles Hutton - Mathematics - 1812 - 622 pages
...contained in the following theorems. THEOREM 1. When four quantities are in geometrical proportion, 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 2 X 6 = 3 x 4 = 12. And hence, if the product of... | |
 | John Bonnycastle - Algebra - 1813 - 460 pages
...• — • • » 2 ' 6 ' ' 3 • 9' a • b • ' с • d 9. 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... | |
 | 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,... | |
 | Jeremiah Day - Algebra - 1814 - 304 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... | |
 | 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... | |
 | 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 terms... | |
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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. 
