 | Colin MacLaurin - Calculus - 1801 - 428 pages
...1 ^ cc? to ca l ; consequently CtP + CL 1 is equal to CA 1 + ccr, or CA 1 + CU l ; that is, the sum of the squares of any two conjugate diameters is equal to the sum of the squaresof the ax is AB and DE. 617. Any rectangle ghlk (Jig. 273) in the plane of the circle... | |
 | Isaac Dalby - Mathematics - 1813 - 538 pages
...opposite sides are bisected at the points of contact H, K, V, P, as in the ellipse (art. 281). 291. The difference of the squares of any two conjugate...diameters, is equal to the difference of the squares of the two axes: OF THE HYPERBOLIC ASYMPTOTES. k 2Q2. If I le the centre of the hyperbola, CG the transverse... | |
 | Robert Simson - Conic sections - 1817 - 298 pages
...together with the rectangle EFD, that is, to the (5. 2. Elem.) square of CD. COR. 3. Hence the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the axis. Let CD, CL be (he semiaxes, and CA, CB conjugate semidiameters; let... | |
 | Abram Robertson - 1818 - 196 pages
...any two Fig. 83,84. conjugate diameters is equal to the sum of the squares of the axes ; but in an hyperbola the difference of the squares of any two...diameters is equal to the difference of the squares of the axes. BOOK D PxPE=(5- ii.) C E2=CD 2 ; but in the hyperbola For the rest remaining, as in the last... | |
 | Rev. John Allen - Astronomy - 1822 - 508 pages
...if the angles contained by the 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. Part 1. Let CB and CM be semiaxes of an ellipse, AB and MN being the axes, and CP and CO two... | |
 | Rev. John Allen - Astronomy - 1822 - 516 pages
...within the acute angles, is greater than its conjugate. Cor. In ellipses, the sum, and in hyperbolas, the difference of the squares, of any two conjugate diameters, is equal to the sum or difference, as the case may be, of the squares of any other conjugate diameters, being each,... | |
 | John Radford Young - Conic sections - 1830 - 390 pages
...—B' 2 = A 2 —B 2 (4), •0) ..(2) ..(3). 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, the parallelogram... | |
 | Edinburgh encyclopaedia - 1830 - 828 pages
...is equal to the square of CA, the semidiameter. Fer CE 1 - r .CG'=CEĢ+AE.En=CA l . COR. 3. The sum of the squares of any two conjugate diameters, is equal to the sum of the squares of ihe axes. Let Aa, B6 be the axes, and Pp, Qtf any two conju1 , therefore PROP.... | |
 | Henry Parr Hamilton - Mathematics - 1834 - 272 pages
...contained by the Segments of the other 232 SECT. II. On the Properties of Conjugate Diameters, p. 164. The Difference of the Squares of any two Conjugate...Diameters is equal to the Difference of the Squares of the Axes 234 The Area of all Parallelograms, whose Sides are parallel to any two Conjugale Diameters, is... | |
 | Ireland commissioners of nat. educ - 1834 - 370 pages
...transverse and conjugate diameters. For AC 2 + CD 2 = (N0 2 + R* 2 + C* 2 + CN 2 —) Cor. 6. Hence the sum of the squares of any two conjugate diameters is equal to the sum of the squares of any other two conjugates. PROPOSITION XI. ^4 Parallelogram described about any... | |
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the hyperbola, the difference of the squares of any two conjugate diameters is equal to the difference of the squares of the principal diameters 
