 | Isaac Dalby - 1806 - 526 páginas
...points of contact H, K, V, P, as iu the ellipse (art. 278). 288. The difference of the squares of any two conjugate diameters, is equal to the difference of the squares of the two axes : That is, HV — PK" = CC' — ZBJ. In the ellipse their are equal, '«)•/. '2790 OF THE... | |
 | Abram Robertson - 1818 - 196 páginas
...equal to the sum of the squares of the axes ; but in an hyperbola the difference of the squares of any two conjugate diameters is equal to the difference of the squares of the axes. For the rest remaining, as in the last two articles, let AB, DE be the axes, and then the angles at... | |
 | Rev. John Allen - 1822 - 516 páginas
...asymtotes be not right, any two conjugate diameters are unequal ; and the difference of the squares of any two conjugate diameters, is equal to the difference of the squares of the axes. Q Part 1. Let CB and CM he semiaxes of an ellipse, AB and MN being the axes, and CP and CO two other... | |
 | Henry Parr Hamilton - 1826 - 354 páginas
...constant." It may in like manner be proved, that " in the hyperbola, the difference of the squares of any two conjugate diameters is equal to the difference of the squares of the principal diameters :" and that "the area of -all inscribed parallelograms, of which the sides are... | |
 | John Radford Young - 1830 - 390 páginas
...adding (1) and (2) A'2 — B'2= A2— B2 (4), that is, the difference of the squares of any system of conjugate diameters is equal to the difference of the squares of the principal diameters. From equation (3) there results 4A'B'sin. [A'B'J = 4AB. Hence, as in the ellipse,... | |
 | John Radford Young - 1830 - 360 páginas
...adding (1) and (2) A'2 — B'S = A2 — B2 (4), that is, the difference of the squares of any system of conjugate diameters is equal to the difference of the squares of the principal diameters. From equation (3) there results 4A'B'sin. [A'B'J = 4AB. Hence, as in the ellipse,... | |
 | Henry Parr Hamilton - 1834 - 240 páginas
...\- — * 1 I ** = «" : U v ~ " ' or a262a,'2 = a'y'2; x 234. The difference of the squares of any two conjugate diameters is equal to the difference of the squares of the semiaxes. Let CP, CD be any two semi-conjugate diameters, then denoting them by a' and 6' respectively,... | |
 | Henry Parr Hamilton - 1834 - 272 páginas
...in (2), and dividing the result by 62, we have or a , -y; 234. The difference of the squares of any two conjugate diameters is equal to the difference of the squares of the semiaxes. Let CP, CD be any two semi-conjugate diameters, then denoting them by a' and b' respectively,... | |
 | John Radford Young - 1835 - 298 páginas
...adding (1) and (2), A'2— B'2 — A2— B' (4), that. is the difference of the squares of any system of conjugate diameters is equal to the difference of the squares of the principal diameters. From equation (3) there results 4A' B' sin. [A' B'] = 4AB. Hence, as in the ellipse,... | |
 | William Wallace - 1837 - 248 páginas
...shown that CE* = CG* + CR*, therefore CE* — CG* = CR*. COR. 3. The difference of the squares of any two conjugate diameters is equal to the difference of the squares of the axes. Let Rr, Ss be the axes, and Pp, Qq any two conjugate diameters; draw PE, QG perpendicular to Rr, and... | |
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That the difference of the squares of any two conjugate diameters is equal to the difference of the squares of the axes. Hence, there can be no equal conjugate diameters unless A=B, and then every diameter will be equal to its conjugate : that is, A'=B'. 
