 | Sir Asutosh Mookerjee - Conic sections - 1893 - 197 pages
...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... | |
 | George Albert Wentworth - Geometry - 1894 - 456 pages
...extremities of a chord, and is therefore in the perpendicular erected 'at the middle of the chord. § 122 234. COR. 2. The perpendicular erected at the middle of a chord bisects the arcs of the chord. ARCS AND CHORDS. PROPOSITION VII. THEOREM. 236. In the same circle, or equal circles, equal chords... | |
 | Calvin Frank Allen - Railroads - 1894 - 232 pages
...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... | |
 | Webster Wells - Geometry - 1894 - 394 pages
...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... | |
 | George Albert Wentworth - Geometry - 1895 - 458 pages
...extremities of a chord, and is therefore in the perpendicular erected at the middle of the chord. § 122 234. COR. 2. The perpendicular erected at the middle of a chord biftet-ls the arcs of the chord. 235. COR. 3. The locus of the middle points of a system of parallel... | |
 | 1896 - 154 pages
...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... | |
 | Sidney Luxton Loney - Coordinates - 1896 - 447 pages
...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... | |
 | Frederick Harold Bailey - Geometry, Analytic - 1897 - 392 pages
...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.... | |
 | George Albert Wentworth - Geometry - 1898 - 266 pages
...extremities of a chord, and is therefore in the perpendicular erected at the middle of the chord. § 122 234. COR. 2. The perpendicular erected at the middle...parallel chords is the diameter perpendicular to them. PROPOSITION VII. THEOREM. 236. In the same circle, or equal circles, equal chords are equally distant... | |
 | John Henry Tanner, Joseph Allen - Geometry, Analytic - 1898 - 458 pages
...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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The locus of the middle points of a system of parallel chords is the diameter perpendicular to them. 
