A Treatise on Analytic Geometry: Especially as Applied to the Properties of Conics; Including the Modern Methods of Abridged Notation |
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Common terms and phrases
a²b² abscissa algebraic Analytic Geometry Ax+By+C=0 axis of x bisectors bisects Cartesian chord of contact circle co-efficients co-ordinates condition conic constant construction convenient Corollary corresponding curve denotes determine diagram distance draw drawn ellipse equa equal equation Art equation of Art expression find the locus fixed point focal radii Form the equation formulæ Geom geometric meaning given equation given line given point Hence hyperbola imaginary initial line inscribed intercepts intersection latus rectum length loci middle points negative obtain ordinate origin parabola perpendicular plane point of contact point x'y polar equation pole positive radical axis radius ratio rectangle rectangular axes Remark represent required equation right line passing satisfy second degree sides square subtangent suppose symbols tangent Theorem tion transformation transverse axis triangle Trig values variables vertex vertices
Popular passages
Page 254 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 476 - A conic section is by definition the locus of a point whose distance from a fixed point is in a constant ratio to its distance from a fixed straight line.
Page 238 - ... proved that, if a point and a straight line be such that the straight line joining the centre of a circle to the point is at right angles to the line, and the rectangle contained by the distances of the point and the line from the centre is equal to the square on the radius of the circle, the point is the pole of the line, and the line the polar of the point with respect to the circle. In the diagram O is the centre of the circle : H is a point in OP such that the rectangle OP, OH is equal to...
Page 192 - To find the locus of the centre of a circle which passes through a given point and touches a given straight line.
Page 221 - The straight lines joining the vertices of a triangle to the middle points of the opposite sides meet in a point* which is for each line the point of trisection further from the vertex.
Page 250 - The perpendiculars erected at the middle points of the sides of a triangle meet in a point equidistant from the three vertices.
Page 249 - The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point.
Page 169 - The two fixed points, F' and F, are called the foci of the curve ; and the variable distances with a constant difference, F'P and FP, are termed its focal radii. The portion A' A of the right line drawn through the foci, is called the transverse axis.
Page 319 - The perpendicular from the vertex to the base of an isosceles triangle bisects the base. 2. The perpendicular from the vertex to the base of an isosceles triangle bisects the vertical angle.
Page 222 - What is the locus of a point, the sum of the squares of the perpendiculars from which on the sides of a triangle is constant?