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, Part 1 |
Other editions - View all
Common terms and phrases
a² b2 abscissa asymptotes Ax² axes of co-ordinates axis of x 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 referred right angles right line second degree shew sin² subtangent suppose tangents drawn transfer the origin triangle turning the axes values vertex zero
Popular passages
Page 20 - 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.
Page 56 - 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.
Page 49 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 132 - 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
Page 79 - 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...
Page 52 - 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...
Page 55 - 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.
Page 153 - 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.
Page 38 - ... y * cos a - x * sin a 4. Clipping: Clipping is done by separating a specific section from a picture with the help of a rectangular window. 5.6.6 Display File This file contains the code that is stored in the refresh memory; it operates the display screen. To obtain a...
Page 93 - ... k) to the given circle. This line (or chord of contact) is known as the polar of the point...