 | William Webster - 1767 - 262 σελίδες
...in any rank of numbers in Geometrical Progreffien, confifting of four, or any even number of terms, the product of the two extremes will be equal to the product of the two middle numbers, or of any two means equally diftant from the faid extremes. 2, 4, 8, 1 6, 32,... | |
 | John Thomas Hope - 1790 - 430 σελίδες
...= 45 x IJ each being 675, Hence if ever fo many numbers are in geometrical prpgrefTion, the produft of the two extremes will be equal to the product of any two means, that are didanc from the extremes, As in thefe 3, 9, 27, St, 243, 729, Here 3 x 729 = 9 x 24.1 =27... | |
 | 1801 - 446 σελίδες
...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 square of the mean... | |
 | Thomas Keith - 1822 - 354 σελίδες
...extremes, and the common multiplier or divisor the ruth. Note 1. If three numbers be in geometrical progression, the product of the two extremes will be equal to the square of the mean. Thus, if 3. 9. 27. be in geometrical progression. Then will 3x21=9x9. 2. If four... | |
 | Peter Nicholson - 1823 - 210 σελίδες
...contains the like part of the fourth. THEOREM 39. 113. If four quantities, a, b, c, d, are proportionals, the product of the two extremes will be equal to the product of the two means. Let the first, a, contain the wth part of the second b, m times ; then, by the definition,... | |
 | Zadock Thompson - 1826 - 176 σελίδες
...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 is equal to the square of the middle... | |
 | 1829 - 196 σελίδες
...is actually true ; for 6 X 10 = 60, and 4 x 15 = 60. Hence, If four numbers be proportional, 1 TO* The product of the TWO EXTREMES will be EQUAL to the product of the TWO MEANS. Consequently, the product of the means divided by EITHER extreme will give the OTHER... | |
 | Charles Hutton - 1831 - 660 σελίδες
...fractions or ratios are equal. Therefore, THBORBH i. If four quantities be in geometrical proportion, the product of the two extremes will be equal to the product of the two means. And hence, if the product of the two means be divided by one of the extremes, the quotient... | |
 | Thomas Conkling (W.) - 1831 - 302 σελίδες
...is called an ascending, and the last, a descending series. In any series of numbers in geometrical progression, the product of the two extremes, will be equal to the proiy two means equally distant from the extremes. As mber by which the series increase, or decrease,... | |
 | William Ruger - 1832 - 282 σελίδες
...the series is diminished, is called the ratio. When any number of terms is continued in Geometrical Progression, the product of the two extremes will...any two .means equally distant from the extremes, or when the terms are odd, equal to the square of the middle term; thus, 2, 4, 8, 16, 32; 2x32=64,... | |
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When any number of terms is continued in Geometrical Progression, the product of the two extremes will be equal to the product of any two means equally distant from the extremes... 
