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 Libros Libros 1 a 10 de 120 sobre To prove that the locus of the middle points of a system of parallel chords of a...
To prove that the locus of the middle points of a system of parallel chords of a parabola is a straight line parallel to the axis of the parabola.
A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... - Página 13
de Bartholomew Price - 1862
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## The Mathematical Miscellany, Volúmenes 1-2

1836
...Rules for finding the logarithms of numbers. (5G). QUESTION VI. By . Def. A diameter of a curve is the locus of the middle points of a system of parallel chords. Find the equations of the diameters of the curves represented by the general equation of the second...
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## A Treatise on Conic Sections and the Application of Algebra to Geometry

John Hymers - 1837 - 130 páginas
...is С and radius equal to ^/a* + b3. The Ellipse referred to its conjugate Diameters. 138. To find the locus of the middle points of a system of parallel chords. Let the chords be parallel to a line CD (fig. 45) through fhe center, whose equation is y = mx; then...
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## Two Geometrical Memoirs on the General Properties of Cones of the Second ...

Michel Chasles, Charles Graves - 1837 - 112 páginas
...consequently HP=2a + r, we have . 2а + r The Hyperbola referred to its Conjugate Diameters. 187- To find the locus of the middle points of a system of parallel chords. Let the chords be parallel to a line CW through the center (fig. 57), whose equation is y — mx ;...
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## The Cambridge University Magazine, Volumen 1,Número 1

1840
...Sln T~ ' . c AB C . a+b and sin - . cos — — — = sin — . sin -•;;--• m im £i £i 8. Find the locus of the middle points of a system of parallel chords of the curve whose equation is ax* + bxy + cy* + dx -f ey +f = 0. Hence shew that the curve has generally...
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## The Educational Magazine

.... sin ~~£ 2 2 2 ' c A — BC , o + 4 and sin T..COS.•• = sm — . sm — — ' 9 31 22 8. Find the locus of the middle points of a system of parallel chords of the curve whose equation is aa* + hxy + cy* + dx + ey +/= 0. Heuce show that the curve has generally...
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## THE SOLUTIONS OF GEOMETRICAL PROBLEMS

...tangents to the latter. Find the locus of the intersections of the latter pairs of tangents. 15. Find the locus of the middle points of a system of parallel chords drawn between an hyperbola and the conjugate hyperbola. 16. If a pair of conjugate diameters of an...
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## A Treatise on Analytical Geometry of Tree Dimensions: Containing the Theory ...

John Hymers - 1848 - 324 páginas
...proposed equation must be capable of being resolved into two rational factors of the first degree. 136. The locus of the middle points of a system of parallel chords of any proposed surface is called its diametral surface. This surface will have several sheets, if...
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## PROBLEMS IN ILLUSTRATION OF THE PRINCIPLES OF PLANE COORDINATE GEOMETRY.

WILLIAM WALTON, M.A., - 1851
...QR.QR' = Zl'\ Similarly gr.gr' = 26'2. De la Hire : Sectwnes Conicm, lib. IV. prop. 34. 2. To find the locus of the middle points of a system of parallel chords drawn between an hyperbola and the conjugate hyperbola. Let two conjugate diameters be taken as axes...
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## Iron: An Illustrated Weekly Journal for Iron and Steel ..., Volumen 66

Sholto Percy - 1857
...intelligible to the great bulk of students; and that mode of investigation which is made to depend on the locus of the middle points of a system of parallel chords is more unexceptionable, as jhe peculiar difficulties of the doctrine of limits are therein almost entirely...
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## The Oxford, Cambridge, and Dublin Messenger of Mathematics, Volumen 1

1862
...tangent lines parallel to a is = 0. XXVII. To study the nature of the surface more closely, let us find the locus of the middle points of a system of parallel chords. Let them be parallel to a, then, if ts be the vector of the middle point of one of them, ts + xa. and...
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