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Libros Libros 51 a 60 de 130 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: The dynamics of material systems. 1862 - Página 13
1862
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A Text-book of Geometry

George Albert Wentworth - 1892 - 437 páginas
...the line RM is the locus of the middle points of all chords drawn parallel to the tangent at S. 830. The locus of the middle points of a system of parallel chords in a parabola is called a diameter. The parallel chords are called the ordinatcs of the diameter. 831....
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AN ELEMENTARY TREATISE ON THE GEOMETRY OF CONICS.

ASUTOSH MUHKOPADHYAY - 1893
...at V. is a fixed straight line bisecting all chords parallel to QQ\ Bel A diameter of any curve is the locus of the middle points of a system of parallel chords drawn in the curve. It has just been proved that the diameters of a parabola are straight lines. It...
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A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic ...

John Casey - 1893 - 564 páginas
...semidiameters differ by -. 6. Apply the method of the eccentric angle to the proof of the proposition that the locus of the middle points of a system of parallel chorda is a right line. 6. Find the equation of the hyperbola, referred to a pair of conjugate diameters...
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Railroad Curves and Earthwork

Calvin Frank Allen - 1894 - 194 páginas
...seldom that parabolic curves would be laid out by. instrument. 130. Properties of the Parabola. (a)* 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 (ie a diameter). (6) The locus...
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The Elements of Geometry

Webster Wells - 1894 - 378 páginas
...parallel chords be drawn in a circle, their middle points lie in the same straight line. 60. What is the locus of the middle points of a system of parallel chords in a circle ? 61. What is the locus of the middle po^^pf a system of chords of given length in a circle...
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Calendar, for the Year ...

1896
...that its polar is the same for every circle of the system. How many such points are there ? 6. Shew 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. Find also the locus of the middle...
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Syllabus of Geometry

George Albert Wentworth - 1896 - 50 páginas
...Cor. 2. The perpendicular erected at the middle of a chord bisects the arcs of the chord. 235. Cor. 3. The locus of the middle points of a system of parallel chords is the diameter perpendicular to them. 236. In the same circle, or equal circles, equal chords are equally...
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THE ELEMENTS OF COORDINATE GEOMETRY

S.L. LONEY - 1896
...point is, by Art. 205, a y = mx H -- , tt and is therefore parallel to each of the given chords. Hence the locus of the middle points of a system of parallel chords of a parabola is a straight line which is parallel to the axis and meets the curve at a point the tangent...
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Plane and Solid Analytic Geometry

Frederick Harold Bailey - 1897 - 371 páginas
...circle is the definition of the diameter for all the conies. Hence the diameter of the parabola is the locus of the middle points of a system of parallel chords. / II Fio. 84. Let y3 = 4px (1) be the parabola, and let m be the common slope of the parallel chords....
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The Essentials of Geometry (plane)

Webster Wells - 1898 - 242 páginas
...chords be drawn in a circle, their middle points lie in the same straight line. (§ 162.) 57. What is the locus of the middle points of a system of parallel chords in a circle ? 58. What is the locus of the middle points of a system of chords of given length in a...
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