 | John D. Williams - 1840 - 634 pages
...usually called the extremes, and the common multiplier or divisor the ratio. 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 3X27=9X9. 2. If four... | |
 | William Ruger - 1841 - 268 pages
...divisor, 2, by which 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 be equal to the product of any two means equally distant from the extremes, or when the terms are odd, equal to the square of the middle term... | |
 | John Darby (teacher of mathematics.) - 1843 - 236 pages
...taken ; Then 2 X 128 = 16 x 16If the series 81, 27, 9, 3, 1, |, ¿, ^ be taken ; Then 81 x ^ = 3x1; Or, the product of the two extremes will be equal to the product of any two moans, equidistant from the extremes. Then 2 x 128 =r 4 x 64 ; Or 81 x тУ = 9 X тThe equidistant... | |
 | mrs. Henry Ayres - 1843 - 470 pages
...product of the two extremes, as above 16 X 16 = 256. If 4 quantities be in Geometrical Proportion, the product of the two extremes will be equal to the product of the two means ; therefore, if the product of the two means be divided by one of the extremes, the quotient... | |
 | mrs. Henry Ayres - 1846 - 400 pages
...product of the two extremes ; as above, 16 x 16=256. If four quantities be in Geometrical Proportion, the product of the two extremes will be equal to the product of the two means ; therefore, if the product of the two means be divided by one of the extremes, the quotient... | |
 | William Vogdes - 1847 - 324 pages
...that of the two extremes. Thus, if 3 : 6 : : 12 : 24,3x24=6x12. If any number of terms be 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; where, as in 2,4, 8, 16,32, 64, 2x64 = 4x32=8x 16, each product... | |
 | Charles Davies - 1850 - 218 pages
...would dimmish, and their product would not be changed. THEOREM I. If four quantities are in proportion, the product of the two extremes will be equal to the product of the two means. If we have the proportion A : B : : C : D we have, by Def. 2, £_!> A~ C and by clearing... | |
 | Oliver Byrne - 1851 - 310 pages
...contained in the following theorems : THEOREM 1. — If four quantities be in geometrical proportion, the product of the two extremes will be 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... | |
 | Francis Walkingame - 1855 - 186 pages
...by the multiplier 2, and 16, 8, 4, 2, decreases by the divisor 2. NOTE. When any number of terms is in geometrical progression, the product of the two...extremes will be equal to the product of any two means, equally distant from the extremes : as 2, 4, 8, 16, 32, 64, where 64 x 2 are = 4 x 32, = 8 x 16 = 128.... | |
 | Charles Davies - 1855 - 340 pages
...diminish, and their product would not be changed- < THEOREM IIf four quantities are in proportion, the product of the two extremes will be equal to the product of the two meansIf we have the proportion A : B :: C : D we have, by Def- 2, £_!) A~C and by clearing... | |
| |
When any number of terms is continued in Geometrical Progression, the product of the two extremes will be equal to... 
