 | Robert Heath - 1760 - Liczba stron: 448
...Radius : Dif. Long, nearly. J Ltt. : Dif. Longitude. J Mid. Lat. : Dif. Longitude. SINCE the Produft of the two Extremes is equal to the Product of the two middle Terms, in any Proportion, therefore fubftituting in the 5th Proportion Difl. run X Sine Courfe... | |
 | John Hill - 1765 - Liczba stron: 428
...96 by 24 ; all being. terms equally diftant. THEOREM IV. In any geometrical progreffion whatfoever, the product of the two extremes is equal to the product of any other two immediate terms of like diftance from both. EXAMPLE. 5, 20, 80, 320, 1280, 5120. So in... | |
 | Alexander Ewing - 1799 - Liczba stron: 512
...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. When four quantities-are... | |
 | Jeremiah Paul - 1801 - Liczba stron: 238
...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,... | |
 | Charles Hutton - 1811 - Liczba stron: 406
...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. br = ar x i, z:... | |
 | Charles Hutton - 1812 - Liczba stron: 620
...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 - 1813 - Liczba stron: 456
...• — • • » 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... | |
 | John Gough - 1813 - Liczba stron: 358
...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 - 1814 - Liczba stron: 304
...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.... | |
 | Charles Butler - 1814 - Liczba stron: 528
...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;... | |
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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. 
