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Libros Libros 61 a 70 de 131 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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An Elementary Course in Analytic Geometry

John Henry Tanner, Joseph Allen - 1898 - 418 páginas
...auxiliary circle. 152. Diameters. As already shown in Articles 129 and 139, the definition of a diameter as the locus of the middle points of a system of parallel chords leads directly to its equation. Let TO be the slope of the given system of parallel chords of the ellipse...
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Calendar

University of Sydney - 1898
...equation in Cartesian co-ordinates. Shew that it is perpendicular to the line joining the centres. 3. Find the locus of the middle points of a system of parallel chords of a parabola. Obtain also the equation to the locus of the middle points of all chords of a parabola...
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Plane Geometry

William James Milne - 1899 - 242 páginas
...383. Find the locus of the center of a circle tangent to each of two intersecting lines. Ex. 384. Find the locus of the middle points of a system of parallel chords drawn in a circle. Ex. 385. Find the locus of the middle points of equal chords of a given circle....
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Solid Geometry, Volúmenes 6-9

George Albert Wentworth - 1899 - 218 páginas
...middle point M will move along MR towards S ; finally, -E, M, P, and Q will all coincide at S. 888. DBF. 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 ordinates of the diameter. 889....
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Key to Milne's Plane and Solid Geometry

William James Milne - 1899 - 313 páginas
...bisectors of the two pairs of vertical A formed by the lines constitute the required locus. Ex. 384. Find the locus of the middle points of a system of parallel chords drawn in a circle. Solution. Since, Ex. 187, a diameter that bisects one of the chords is perpendicular...
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Plane and Solid Geometry

George Albert Wentworth - 1899 - 473 páginas
...middle point M will move along MR towards S; finally, R, M, P, and Q will all coincide at S. 888. DEF. 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 ordinates of the diameter. 889....
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The Elements of Plane Geometry

Charles Austin Hobbs - 1899 - 240 páginas
...locus of the centre of a circle whose circumference passes through two given points. Ex. 251. Find the locus of the middle points of a system of parallel chords drawn in a circle. Ex. 252. Through a given point within a given circle to draw a chord which shall...
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Plane and Solid Analytic Geometry: An Elementary Textbook

Charles Hamilton Ashton - 1902 - 266 páginas
...point of contact from the centre. CHAPTER XI DIAMETERS 79. The diameter of a conic may be defined as the locus of the middle points of a system of parallel chords. The method of finding this locus has already been illustrated for the circle on page 94. We shall repeat...
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A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV.

Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 páginas
...line joining the middle points of two parallel chords of a circle passes through the centre. I1. Find the locus of the middle points of a system of parallel chords drawn in a circle. 12. If two circles cut one another, any two parallel straight lines drawn through...
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Vector Analysis: A Text-book for the Use of Students of Mathematics and ...

Josiah Willard Gibbs, Edwin Bidwell Wilson - 1901 - 436 páginas
...:j~- fy & r.0.r = -,+ |s+^ = l (9) a3 b3 c2 or N • 0-1 • N = a2 uz + bz v* + c2 w* = 1. (10) 138.] The locus of the middle points of a system of parallel chords in an ellipsoid is a plane. This plane is called the diametral plane conjugate with the system of chords....
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