 | John Hill - 1765 - 428 σελίδες
...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 - 1799 - 512 σελίδες
...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.... | |
 | 1801 - 446 σελίδες
...follows, that in any geometrical series, when it consists of an even number of terms, the product of the extremes is equal to the product of any two means, equally distant from the extremes ; and, when the number of terms is odd, the product of the extremes is equal to the... | |
 | Tiberius Cavallo - 1803 - 546 σελίδες
...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 - 1806 - 342 σελίδες
...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 81 = 9... | |
 | 1811 - 230 σελίδες
...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-, 2x32=4x... | |
 | Charles Hutton - 1811 - 406 σελίδες
...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 - 1812 - 620 σελίδες
...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 Gough - 1813 - 358 σελίδες
...product of the means will 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, As 3X06=233... | |
 | John Bonnycastle - 1813 - 456 σελίδες
...• — • • » 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 odd.... | |
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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. 
