An Analytical System of Conic Sections: Designed for the Use of Students |
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Common terms and phrases
a² a² a² b² a² sin² a² y² a²² a²b² abscissa axes of co-ordinates axis AX b2 a² b² cos² b²² b²x² b²x²² b²xx bisect centre circle Conic Section conjugate diameters curve cuts the axis denote directrix distance draw equal equation required fall the perpendicular find the equation find the intersection find the locus focus given in position given point given straight line Hence hyperbola joining the points latus rectum let fall locus major axis meeting the ellipse middle points oblique ordinate origin pairs of tangents parabola parallel to AX point Q points of contact points of intersection polar equation proved rectangle contained rectangular right angles semi-minor axis sin y ß² substitution subtangent supplemental chords supposed theory of equations values vertex x²²
Popular passages
Page 144 - AB describe a segment of a circle containing an angle equal to the given angle, (in.
Page 191 - Fig. 83,84. conjugate diameters is equal to the sum of the squares of the axes ; but in an hyperbola the difference of the squares of any two conjugate diameters is equal to the difference of the squares of the axes.
Page 41 - When it is affirmed (for instance) that " if two straight lines in a circle intersect each other, the rectangle contained by the segments of the one is equal to the rectangle contained by the segments of the other...
Page iv - A conic section is the locus of a point whose distances from a fixed point and a fixed line are in a constant ratio. 4. Show that every conic is represented by an equation of the second degree in x and y. Hint. Take Y Y' to coincide with the fixed line, and draw XX
Page 176 - In any equation in its simplest form the coefficient of the second term is equal to the sum of the roots with their signs changed ; the coefficient of the third term is equal to the sum of the products of every two...
Page 204 - L'l is an asymptote to the other portions. Hence the asymptotes may be considered as the limits of the tangents (Art. 198). 206. If any chord of a hyperbola be produced to meet the asymptotes, the parts of it intercepted between the curve and the asymptotes will be equal. Let Qq (fig.
Page 50 - To draw a tangent to a circle from a given point without it. Let (a...
Page 14 - To find the equation to a straight line which passes through a given point.
Page 81 - Hence if from the several points of any straight line pairs of tangents be drawn to an ellipse, the straight lines which join the corresponding points of contact will all pass through the same point.
Page ix - HYMERS'S Theory of Equations, Art. 174. 64. We will exemplify the articles of this chapter by applying them to prove some properties of a triangle. The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point.