An Analytical System of Conic Sections: Designed for the Use of Students

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Printed at the University Press, for J. W. Parker, 1843 - 276
 

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Strona 40 - Straight line and circle. A straight line cannot cut a circle in more than two points. In fact, an unlimited straight line may (i) cut a circle in two points, eg AB or CD in fig.
Strona 142 - AB describe a segment of a circle containing an angle equal to the given angle, (in.
Strona 189 - 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.
Strona 59 - 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
Strona 39 - 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...
Strona 174 - 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...
Strona 79 - 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.

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