 | Benjamin Peirce - Algebra - 1837 - 302 pages
...a proportion respectively a*— b2, 2(a + 6), a2 +2ab-\-b2 ; find the first. Ans. 2 (a — 6.) 65. When both the means of a proportion are the same quantity,...= B : C, B is a mean proportional between A and C. m 66. If the test is applied to the preceding proportion it gives B2 = AXC; whence B = \fA XC; that... | |
 | Benjamin Peirce - Algebra - 1837 - 300 pages
...proportion respectively tf — b2, 2 (a + 6), a2-f-2a6 + 62; find the first. Ans. 2 (a — b.) 65. When both the means of a proportion are the same quantity,...Mean Proportional. Continued Proportion. Thus, when A:B = B :C, B is a mean proportional between A and C. 66. If the test is applied to the preceding proportion... | |
 | Benjamin Peirce - Algebra - 1837 - 300 pages
...of a proportion respectively as _ b", 2 (a + b), a2 + 2 a 6 + 62 ; find the first. Ans. 2 (a — 6.) Mean Proportional. Continued Proportion.. Thus, when...= B : C, B is a mean proportional between A and C. 66. If the test is applied to the preceding proportion it gives B2 = AXC; whence B = \/AXC; that is,... | |
 | Benjamin Peirce - Algebra - 1843 - 308 pages
...find the first. Ans. 2 (a—b). Mean Proportional. Continued Proportion. Thus, when A : B = B : C, Ji is a. mean proportional between A and C. 91. If the...test is applied to the preceding proportion it gives B* = A x C; whence B = JA x C; that is, the mean proportional between two quantities is the square... | |
 | Benjamin Peirce - Algebra - 1851 - 294 pages
...a proportion respectively a 2 — b*, 2 (a + ft), a2 -j- 2 ab + 6" ; find the first. Ans. %(a—b). 90. When both the means of a proportion are the same...Mean Proportional. Continued Proportion. Thus, when A:B=B:C, B is a mean proportional between A and ('. 91. If the test is applied to the preceding proportion... | |
 | Benjamin Peirce - Algebra - 1855 - 296 pages
...terms of a proportion respectively aa_62,2(a-j_6)' a2-(_2a6 + t2; find the first. Ans. 2 (a— 6). 90. When both the means of a proportion are the same...test is applied to the preceding proportion it gives B* = AxC; whence _ _ B ^ v/ A xC; that is, the mean proportional between two quantities is the square... | |
 | Benjamin Peirce - Algebra - 1858 - 296 pages
...terms of a proportion respectively a2 — 62, 2(a + 6),a2 + 2a6 + 62; find the first. Ans. 2 (a—b). 90. When both the means of a proportion are the same...test is applied to the preceding proportion it gives B* = AxC; whence B = </ A x C; that is, the mean proportional between two quantities is the square... | |
 | Benjamin Peirce - Algebra - 1860 - 302 pages
...of a proportion respectively a* — b*, 2 (a + ft), a2 + 2a6 + 6 2 ; find the first. Ans. 2 (a—6). Mean Proportional. Continued Proportion. Thus, when...test is applied to the preceding proportion it gives B* = A*C; whence S ^ ^ A x C; that is, the mean proportional between two quantities is the square root... | |
 | Charles Davies - Algebra - 1860 - 412 pages
...same, either of these is said to be a mean proportional between the other two. Thus, in the proportion a : b : : b : c, b is a mean proportional between a and c, and c is said to be a third proportional to a and b. 185. Two quantities are reciprocally proportional... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...first ratio, and an antecedent in the second. Thus, if we have three magnitudes A, B, and C, such that A : B : : B : C, B is a mean proportional between A and C. 12. Two magnitudes are reciprocally, or inversely proportional when, in undergoing changes in value,... | |
| |
C; that is, the mean proportional between two quantities is the square root of their product. 
