| Mathematics - 1801 - 446 pages
...to the square of the mean ; it 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... | |
| John Gough - Arithmetic - 1813 - 358 pages
...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 and Ox 48=288, &c.... | |
| William Enfield (M.A.) - Amusements - 1821 - 302 pages
...whatever of the series be assumed, as 2, 4, 8, 16, 32, 64, the product of the extremes, 2 and 64, will be equal to the product of any two terms equally distant from them, as 4 and 32, or 8 -and 16. If the number of terms be odd, it is evident that there will be only one... | |
| Zadock Thompson - Arithmetic - 1826 - 176 pages
...less 1, and the same will hold, whatever be the series. When a geometrical series 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... | |
| Frederick Emerson - Arithmetic - 1834 - 300 pages
...the product of the means. Furthermore, in any series of continual proportionals, the product of the extremes is equal to the product of any two terms equally distant from them; and equal to the second power of the middle term, when there is an uneven number of terms. For instance,... | |
| Silas Totten - Algebra - 1836 - 360 pages
...demonstrated without the aid of Algebra. (73.) 1st. In every geometrical progression, the product of the two extremes is equal to the product of any two terms equally distant from them, or equal to the square of the middle term, when there is an odd number of terms. For example, in the progression... | |
| Frederick Emerson - Arithmetic - 1839 - 300 pages
...the product of the means. Furthermore, in any series of continual proportionals, the product of the extremes is equal to the product of any two terms equally distant from them; and equal to the second power of the middle term, when there is an uneven number of terms. For instance,... | |
| James Thomson - 1844 - 328 pages
...term into the last but two, we get the same still ; and so on. Hence, therefore, the product of the extremes is equal to the product of any two terms equally distant from them. If the number of terms be odd, the middle term of the series will be r^n~l>tv the multiplication by... | |
| Alexander Ingram - 1844 - 262 pages
...two terms equally distant from them. For axy = arx- = ar' x —,, &c. Cor. 1. The square of any term is equal to the product of any two terms equally distant from it. Cor. 2. If there be four terms, the product of the means, divided by either extreme, gives the... | |
| James Thomson - Algebra - 1845 - 328 pages
...term into the last but two, we get the same still ; and so on. Hence, therefore, the product of the extremes is equal to the product of any two terms equally distant . rom them. If the number of terms be odd, the middle term of the series will be r^i"~1l^, the multiplication... | |
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