| Algebra - 1813
...rale, Whence the numbers are 3, "¡, 11, and 15. 8. Itisrequired to find three numbers in geometrir cal **progression^, such that their sum shall be 14, and the sum of their squares 84.** Let x, y, and z be the three numbers, Then xz=y*, by the nature of proportion, ,, the Hence x + z=... | |
| John Bonnycastle - Algebra - 1818 - 260 pages
...consequently x=— 6+ </ (36 + 45) = — 6+9=3, by the rule, Whence the numbers are 3, 7, 11, and 15. 8. **It is required to find three numbers in geometrical...sum shall be 14, and the sum of their squares 84.** Let x, y, and z be the three numbers, Then xx=y3 , by the nature of proportion, y the question, . Hence... | |
| Jeremiah Day - Algebra - 1820 - 332 pages
...geometrical progression, may be solved, as in other parts of algebra, by the reduction of equations. Prob. 1. **Find three numbers in geometrical progression, such...sum shall be 14, and the sum of their squares 84.** Let the three numbers be x, y, and z. By the conditions, x:y::y:z, or xz=y3 And x+y+z=l4 And *a+y2+z*=84... | |
| John Bonnycastle, James Ryan - Algebra - 1825 - 312 pages
...consequently i= 6 + ^(36-4-45)= — 6+9=3, by the rule. Whence the numbers are 3, 7, 11, and 15. 8. **It is required to find three numbers in geometrical progression, such that their sum shall be 14,** anil the sum of their squares 84. Let x, y. and z he the three numbers, Then xz—y3, by the nature... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...-аг" 3|0_3(Э'°— а") »(Д9049— 1024) *- r— I ~ 1— г ~~ _2 "~ 3le " ~ 59049 " 59049 3. **Find three numbers in geometrical progression, such, that their sum shall be** equal to 7, and the gum of their squares to 21. Let the numbers be «»y, and z; then by question And... | |
| Jeremiah Day - Algebra - 1827 - 332 pages
...geometrical progression, may be solved, as in other parts of algebra, by the reduction of equations. Prob.l. **Find three numbers in geometrical progression, such...sum shall be 14, and the sum of their squares 84*** Let the three numbers be x, y and z. By the conditions x : y. '.y : z, or xz=y3 i And x+y+z = l4> And... | |
| Alexander Ingram - 1830
...third, and so on. In what time will he overtake the first ? oix _ i -^ — * = (*+7)9. Ans. 18 days. 7- **To find three numbers in geometrical progression, such, that their sum shall be** , . and the sum of their squares 21. Liet x, y, 2, be the numbers. xz=y*, x+y + z = J, aa+y* + z* =21.... | |
| Jeremiah Day - 1832
...geometrical progression, may be solved, as in other parts of algebra, by the reduction of equations. Prob. 1. **Find three numbers in geometrical progression, such that their sum shall be 14, and the sum of** thensquares 84. Let the three numbers be x, y, and z. By the conditions, x :y : :y : z, or xz=yl And... | |
| John Bonnycastle, Samuel Maynard - 1836
...numbers are 3, 7, 11, and 15. 8. It is required to find three numbers iu geometrical progression, Mich **that their sum shall be 14, and the sum of their squares 84.** Let x, y, and z, be the three numbers, then xz—y1, by the nature of the progression. y the hence... | |
| John Radford Young - 1839
...— 4, or — 10 : hence the three numbers are 5, 9, and 19 ; or rather 19, 9, and 5. QUESTION II. **It is required to find three numbers in geometrical...sum shall be 14, and the sum of their squares 84.** Let -, x, and xy, be the three numbers ; У then, by the question, - + x + xy = 14, У .-. from the... | |
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