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Libros Libros 41 a 50 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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Elements of analytic geometry

Simon Newcomb - 1885 - 356 páginas
...term, the plane passes through the origin, that is, the centre of the quadric. Hence: THEOREM. VI. The locus of the middle points of a system of parallel chords of a quadric is a plane through the centre. Def. A plane through the centre of a quadric is called...
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Examinations Papers

1886
...the circle Hence or otherwise find the condition that this circle may touch the axis of x. 8. Prove that the locus of the middle points of a system of parallel chords of a parabola is a straight line, and shew that the tangent at the point where this straight line meets...
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An Elementary Treatise on Solid Geometry

William Steadman Aldis - 1886 - 276 páginas
...is therefore the area required. 81. It can be shewn by an investigation similar to that in Art. 71, that the locus of the middle points of a system of parallel chorda of the surface By" + Cz* = x, whose direction-cosines are I, m, n, is 2Bmy + 2Cnz = I. Also...
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Elements of Analytic Geometry

George Albert Wentworth - 1886 - 300 páginas
...chord whose length is constant. THE CIRCLE. SUPPLEMENTARY PROPOSITIONS. 68. A Diameter of a curve is the locus of the middle points of a system of parallel chords. The chords which any diameter bisects are called the Chords of that diameter. 69. To find the equation...
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Elements of Analytic Geometry

George Albert Wentworth - 1886 - 221 páginas
...that the locus is a straight line passing through the centre, and perpendicular to the chords (§ 48). The locus of the middle points of a system of parallel chords is called a Diameter of the circle ; and the chords which it bisects are called the Ordinates of the diameter....
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An Elementary Treatise on Conic Sections and Algebraic Geometry ...

George Hale Puckle - 1887 - 379 páginas
...-Ihxy -y* + 2gx + 2fy+c = 0 cuts the rectangular co-ordinate axes, is equal to the circle 49. Find the locus of the middle points of a system of parallel chords, drawn between an hyperbola and the conjugate hyperbola. 60. If, in two concentric hyperbolas, whose...
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Syllabus of Elementary Geometrical Conics

Association for the Improvement of Geometrical Teaching (Great Britain) - 1887 - 32 páginas
...; and the tangent at either end of the straight line is parallel to the chords. Def. of diameter as the locus of the middle points of a system of parallel chords. NOTE. — The word diameter is frequently used to denote the length of the portion of this straight...
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Elements of Plane Analytic Geometry, Volumen 25

John Daniel Runkle - 1888 - 344 páginas
...SP'S'. FIG. 60. IX. All the results in Arts. 147, 148, 149, 150, are true for the hyperbola. • X. The locus of the middle points of a system of parallel chords, having a direction parameter m (Art. 151). (a) XI. For a pair of conjugate diameters mm' = —^ (Art....
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A Text-book of Geometry

George Albert Wentworth - 1888 - 437 páginas
...COR. 2. The perpendicular erected at the middle of a chord bisects the arc of the chord. 235. COR. 3. The locus of the middle points of a system of parallel chords is the diameter perpendicular to them,. PROPOSITION VII. THEOREM. 236. In the same circle, or equal circles,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1892 - 518 páginas
...line joining the middle points of two parallel chords of 1i 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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