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 Libros Libros 71 a 80 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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Solid Geometry

George Albert Wentworth - 1902 - 218 páginas
...middle point M will move along MR towards S; finally, R, 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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Notes on Analytical Geometry: An Appendix

Alfred Clement Jones - 1903 - 171 páginas
...the y-coordinate of the middle points of parallel chords of a parabola is constant ; in other words, the locus of the middle points of a system of parallel chords of a parabola is a straight line parallel to the axis. This locus is called a diameter ; hence all...
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The Encyclopedia Americana, Volumen 12

...curve (2) r = - • I — cos в Diameter of the Parabola. — A diameter of any curve is defined to be the locus of the middle points of a system of parallel chords. Let (xt, J>i) and (.r-, y~) be the co-ordinates of P, and P:, the extremities of the chord Pi Pi (Fig....
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The Elements of Analytic Geometry

Percey Franklyn Smith, Arthur Sullivan Gale - 1904 - 424 páginas
...varies so that B1 — 4 AC approaches zero, how does the center of the locus behave ? 98. Diameters. The locus of the middle points of a system of parallel chords of a curve is called a diameter of the curve. Consider the ellipse and the system of parallel lines...
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Plane and Solid Geometry

George Albert Wentworth - 1904 - 473 páginas
...middle point M will move along MR towards S ; finally, E, 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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A Text-book of Euclid's Elements for the Use of Schools, Libro 1

Euclid, H. S. Hall, F. H. Stevens - 1904 - 456 páginas
...line joining the middle points of two parallel chords of a circle passes through the centre. 11. 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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The Elements of Analytic Geometry

Percey Franklyn Smith, Arthur Sullivan Gale - 1904 - 424 páginas
...varies so that B2 — 4 AC approaches zero, how does the center of the locus behave ? 98. Diameters. The locus of the middle points of a system of parallel chords of a curve is called a diameter of the curve. Consider the ellipse 62x2 4- a2?/2 = o2b2 and the system...
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Analytic Geometry, a First Course

William Henry Maltbie - 1906 - 142 páginas
...special case of the general equation developed in article 62, or it may be found directly by determining the locus of the middle points of a system of parallel chords. If the latter method is adopted, the student should remember that in any locus problem the thing sought...
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Algebraic Geometry

W.M. Baker - 1906
...and by (1) this straight line passes through (xv y^) P, which proves the proposition. 145. To find the locus of the middle points of a system of parallel chords. Let OO' be a chord of the system, making an angle 0 with the axis of #, 0 being constant. Let (\$!,...
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Mathematics for Engineering Students

Samuel Smith Keller, W. F. Knox - 1908 - 356 páginas
...chords. ART. 82. The equation to a diameter oj the ellipse. The diameter it will be remembered, is the locus of the middle points of a system of parallel chords. Analytical Geometry. Let RS be any one of a system of parallel chords of the ellipse ABA'B' (Fig. 44),...
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