 | George Salmon - 1855 - 376 sider
...Again, we have or =(«2-a;'2) + hence • b'" = a2 - e From these values we have a'2 + 6'2 = a2 or, The sum of the squares of any pair of conjugate diameters of an ellipse is constant (see Ex. 3, Art. 162). 178. In the hyperbola we must change the signs of b'1 and 6'2, and we get a'"... | |
 | George Salmon - 1855 - 376 sider
...Again, we have hence b'2 = a? - e*x'*. From these values we have a"' + b"i = a? + fr ; • or, Tfie sum of the squares of any pair of conjugate diameters of an ellipse is constant (see Ex. 3, Art. 162). 178. In the hyperbola we must change the signs of b* and b'-, and we get •;.'•£.... | |
 | Charles Davies, William Guy Peck - 1855 - 628 sider
...conjugate, is always constant for the same curve. The third equation of the first group shows that the sum of the squares of any pair of conjugate diameters of the ellipse is constant ; and the third equation of the second group shows that the difference of the... | |
 | George Salmon - 1879 - 448 sider
...= b' + e'x". (2) Again, we have --+? hence 5'" = a* — eV. From these values we have or, T^e SMOT of the squares of any pair of conjugate diameters of an ellipse is constant (see Ex. 3, Art. 159). 174. In the hyperbola we must change the signs of b* and b'", and we get an-b^... | |
 | George Salmon - 1879 - 446 sider
...°- x'* = V + eV. a (2) Again, we have or =ahence Z>'2 = a2 From these values we have or, 7%e swm o/" the squares of any pair of conjugate diameters of an ellipse is constant (see Ex. 3, Art. 159). 174. In the hyperbola we must change the signs of i" and I"*, and we get a"'-b^... | |
 | Edward Albert Bowser - 1880 - 334 sider
...«2 _ ya + ^a-'i (Art. 71); hence, b' 2 — aa — ex 2. (2) , Сов. — Adding (1) and (a), we get that is, the sum of the squares of any pair of conjugate diameters is equal to the sum of the squares of the axes. [See Salmon's Conic Sections, p. 163.] 85. To find... | |
 | De Volson Wood - 1890 - 372 sider
...them we deduce the following results : Adding the first and second gives or 4a'3 + 4&'3 = 4a2 + 4&s; (5) that is : The sum of the squares of any pair of...ellipse is constant, and equals the sum of the squares <>f the ax?x. When the axes and one of the conjugate diameters is given, the other conjugate diameter... | |
 | Eldred John Brooksmith - 1901 - 368 sider
...equation 9. Find what curve is represented by the equation and give a figure of the curve. 10. Prove that the sum of the squares of any pair of conjugate diameters of an ellipse is constant. Being given in magnitude and position two conjugate diameters of an ellipse, find, by geometrical construction,... | |
 | 1901 - 488 sider
...an intercept of constant length : prove that the locus of its centre is a parabola. 10. Prove that the sum of the squares of any pair of conjugate diameters of an ellipse is constant. HISTORY (FIRST PAPER) : Civil History of Great Britain and Ireland from 1588 to 1815.— 100 Marks.... | |
 | George Salmon - 1904 - 426 sider
...(2) Again, we have or .(a-)4 hence ft" = a" - «V. From these values we have or, 2ft« SMTW 0/"«A« squares of any pair of conjugate diameters of an ellipse is constant (see Ex. 3, Art. 159). 174. In the hyperbola we must change the signs of V and 6", and we get d"-y»... | |
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From these values we have or, 7%e swm o/" the squares of any pair of conjugate diameters of an ellipse is constant (see Ex. 3, Art. 159). 174. In the hyperbola we must change the signs of i... 
