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Libros Libros 31 a 40 de 129 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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Conic Sections Treated Geometrically

Samuel Holker Haslam, Joseph Edwards - 1881 - 137 páginas
...point perpendicular to the axis, prove that PN: 2AS-TN : PN 87. By means of the last example prove that the locus of the middle points of a system of parallel straight lines is a straight line parallel to the axis. 88. A chord PP' of a parabola is normal to...
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Conic Sections Treated Geometrically

Samuel Holker Haslam, Joseph Edwards - 1881 - 137 páginas
...point perpendicular to the axis, prove that PN : 2AS::TN : PN 87. By means of the last example prove that the locus of the middle points of a system of parallel straight lines is a straight line parallel to the axis. 88. A chord PP' of a parabola is normal to...
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Essentials of Geometry

Alfred Hix Welsh - 1883 - 267 páginas
...is the point of intersection of the perpendiculars to two chords at their middle points? 3. What is the locus of the middle points of a system of parallel chords? I THEOREM III. In the same circle or in equal circles, equal chords are equally distant from the centre....
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An Elementary Treatise on Conic Sections

Charles Smith - 1883 - 352 páginas
...The equation of the polar of 0 is gx +fy + c = 0 ; .•O c From (i) and (ii) we see that 182. To find the locus of the middle points of a system of parallel chords of a conic. Let (x, y) and (x", y") be two points on the conic. The equation a (xx) (x - x") + h {(x...
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Cambridge university examination papers

Cambridge univ, exam. papers - 1884
...P1, where PP is a double ordinate to either axis, pass through the ends of the other axis. xi. Prove that the locus of the middle points of a system of parallel chorda of a hyperbola is a straight line. From a point У on a common diameter AB of two concentric...
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An Elementary Treatise on Solid Geometry: By Charles Smith

Charles Smith - 1884 - 300 páginas
...through the point of intersection of the . dF dF dF . planes -5- = -r- = -5-=0. dx dy dz 59. To find the locus of the middle points of a system of parallel chords of a conicoid. As in the preceding Article, (a, /3, 7) will be the middle point of the chord whose...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - 1885 - 312 páginas
...related, that any one being proved directly, the other two follow by the Eule of Identity. Cor. 2. — The locus of the middle points of a system of parallel chords of a circle is the diameter of the circle perpendicular to them all. Cor. 3. — If a line intersect...
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A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic ...

John Casey - 1885 - 331 páginas
...standing on a circular base be cut by any plane not parallel to the base, the section is an ellipse. 121. The locus of the middle points of a system of parallel chords of an ellipse is a right line. Let PP' be a chord of the ellipse, and let the eccentric angles of P,...
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The first six books of the Elements of Euclid, and propositions i ..., Libro 11

Euclides, John Casey - 1885
...related, that any one being proved directly, the other two follow by the Rule of Identity. Cor. 2. — The locus of the middle points of a system of parallel chords of a circle is the diameter of the circle perpendicular to them all. Cor. 3. — If a line intersect...
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An Easy Introduction to the Higher Treatises on the Conic Sections

John Hunter - 1885 - 87 páginas
...to a circle is always perpendicular to the radius passing through the point of contact. 31. To find the locus of the middle points of a system of parallel chords. Let PP' be one of the chords ; sef, y' the coordinates of P ; and x", y" those of P'. The equation...
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