An Elementary Treatise on Conic Sections and Algebraic Geometry ...Macmillan and Company, 1887 - 379 pàgines |
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An Elementary Treatise on Conic Sections and Algebraic Geometry: With ... George Hale Puckle Visualització completa - 1870 |
An Elementary Treatise on Conic Sections and Algebraic Geometry: With ... George Hale Puckle Visualització completa - 1870 |
An Elementary Treatise on Conic Sections and Algebraic Geometry: With ... George Hale Puckle Visualització completa - 1870 |
Frases i termes més freqüents
2Hxy asymptotes Ax² axes being rectangular axis axis of x By² centre chord of contact circle x² coefficients coincident condition conic section conjugate diameters conjugate hyperbola constant cos² directrix distance ellipse equa equal equation Art equation becomes find the equation find the locus focus four points given point Hence the equation hyperbola imaginary inclined infinitely distant intercepts latus rectum Let the equation meet the curve middle point negative obtain ordinates pair parabola perpendicular point x'y points of contact points of intersection polar equation pole positive quantity radius ratio represents two straight right angles roots second degree shew shewn Similarly sin² straight line drawn straight line joining straight line passing tangent tion touch triangle of reference values vertex written
Passatges populars
Pàgina 139 - Prove algebraically that the angles in the same segment of a circle are equal, and that the angle in a semicircle is a right angle.
Pàgina 51 - If < = 0, or the problem be to find the equation to a straight line which passes through a given point, and is parallel to a given straight line, the equation is COR.
Pàgina 308 - ... same equation. 322. Sections of the Cone. The surface described by an indefinite straight line, which is carried round the perimeter of a given circle, always passing through a given point, is called a cone. The circle is called the base of the cone, the fixed point the vertex, and the line joining the vertex and the centre of the base is called the axis. A cone is said to be right if the axis is perpendicular to the plane of the base, and oblique if the axis is inclined at any other angle to...
Pàgina 88 - ... the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.
Pàgina 233 - Find the locus of the intersection of tangents to an ellipse, which are parallel to conjugate diameters. 28. Find the equation to the locus of the middle points of all chords of a given length, in an ellipse. 29. If two concentric equilateral hyperbolas be described, the axes of the one being the asymptotes of the other, they will intersect at right angles.
Pàgina 252 - To find the polar equation to the parabola, the focus being the pole. Here we have to find the polar equation to the locus of Art. 273, the given point being the focus, and the given line the directrix. Exactly as in Art. 209, if we make e = 1, we obtain as the equation - = 1 — cos 6, P 274 (ii).
Pàgina 299 - A convex or concave line is such that it cannot be cut by a straight line in more than two points ; the concavity of the intercepted portion is turned towards the straight line, and the convexity from it.
Pàgina 233 - The radius of a circle, which touches an hyperbola and its asymptotes, is equal to that part of the latus rectum produced, which is intercepted between the curve and the asymptote.
Pàgina 45 - Qx = 2y, (5) |+yj=2, (6) 2*+ 3 = 0. 2. Find the equation to the straight line which passes through the points (2, 5) and (0, — 7).
Pàgina 53 - To find the area of a triangle in terms of the coordinates of the angular points, the axes being rectangular. Let the three points be (xy), (x'y'), (x'y").