A Treatise on Plane Co-ordinate Geometry: Or, The Application of the Method of Co-ordinates to the Solution of Problems in Plane Geometry. Pt. 1, Μέρος 1Deighton's, 1844 - 180 σελίδες |
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a² b2 abscissa Ax² axes of co-ordinates axis of x b2 a² b² cos² becomes x² bisected centre chord co-ordinate axes conic section conjugate diameters conjugate hyperbola cos² Cy² determine the locus directrix ellipse equal equation becomes equation required find the equation find the locus formulæ given equation given line given point gives hyperbola joining the points latus rectum Let hk let the equation line joining locus represented locus required middle point negative ordinate parabola point hk point of intersection point xy points of contact polar co-ordinates polar equation positive direction prime radius PROP proposition quantity right angles right line second degree shew sin² subtangent suppose tangents drawn transfer the origin triangle turning the axes values vertex zero
Δημοφιλή αποσπάσματα
Σελίδα 22 - In this equation n is the tangent of the angle which the line makes with the axis of abscissae, and B is the intercept on this axis from the origin.
Σελίδα 58 - Given the base and the sum of the sides of a triangle to find the locus of the centre of the circle touching the base, and the prolongation of the other two sides.
Σελίδα 134 - QQ', RR' be two chords of a conic, and P their point of intersection, the ratio PQ . PQ' : PR . PR' is not altered by moving each chord parallel to itself, and so shifting the position of P in any manner. The reader will observe that this conclusion might have been deduced from the equations of Arts. 114, 176, 251. COR. 1. Let CV, CS be semi-diameters parallel to QQ', RR respectively ; then PQ.PQ
Σελίδα 51 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Σελίδα 81 - C., the axis is inclined to the plane of the base at an angle other than a right angle. A truncated C. is the lower part of a C. cut by a plane parallel...
Σελίδα 54 - Polar of any point in respect to a conic section, is the locus of the intersection of the two tangents drawn at the extremities of any chord passing through the point. It will be shown in Article 152, that this locus ia a straight line. Thus, if P be any point in a conic section, FIG. 125. MM...
Σελίδα 57 - The angle between a tangent to a circle and a chord through the point of contact is equal to the angle in the alternate segment. *The notion of a locus.
Σελίδα 155 - SOLUTIONS of the GEOMETRICAL PROBLEMS proposed at St. John's College, Cambridge, from 1830 to 1846, consisting chiefly of Examples in Plane Coordinate Geometry. With an Appendix, containing several general Properties of Curves of the Second Order, and the Determination of the Magnitude and Position of the Axes of the Conic Section, represented by the General Equation of the Second Degree.
Σελίδα 95 - ... k) to the given circle. This line (or chord of contact) is known as the polar of the point...