 | John Hill - Arithmetic - 1765 - 428 pages
...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 this... | |
 | Alexander Ewing - Logarithms - 1799 - 512 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.... | |
 | Jeremiah Paul - Arithmetic - 1801 - 238 pages
...multiplier 2 ; and 729, 243, 81, 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, 9, 27,... | |
 | 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 Vyse - Arithmetic - 1806 - 342 pages
...the common Divisor or Ratio is 3. In any Series of Numbers in Geometrical Prpgression, the Prodjct of the two Extremes is equal to the Product of any two Means that are equally distant from the Extremes. * A. 3. 9. 27. 81. 243. 729. Here 3 X 729 = 27 X... | |
 | Arithmetic - 1811 - 230 pages
...geometrical piogreiSon or proportion ; ie increafing or decreaiing by an У equal ratio •, the produdl of the two extremes, is equal to the product of any two means equally diftant from the extremes, and is equal to the fquare of the middle term ; as, 2,4,8,16,32-,... | |
 | 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 - 620 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 - 456 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 is... | |
 | 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... | |
| |
In any continued geometrical progression, the product of the two extremes is equal to the product of any two means... 
