Conic Sections and Analytical Geometry: Theoretically and Practically Illustrated |
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Conic Sections and Analytical Geometry: Theoretically and Practically ... Horatio N. Robinson No preview available - 2017 |
Common terms and phrases
abscissa Analytical Geometry asymptotes axis of X bisects the angle CA² chord circle circumference co-ordinate axes cone conic sections conjugate diameters conjugate hyperbola cos.v Cosine Cotang curve cuts the axis denote directrix distance ellipse equa equal equation becomes equation sought find the equation foci Geom Geometry give given line given point Hence the theorem hyperbola line passing line whose equation lines drawn major axis meets the axis minor axis minus N.sine nate negative numerically ordinate parabola parallel parallelogram parameter perpendicular plane xy point of contact polar equation positive Prop PROPOSITION put in eq radius vector rectangle referred represent right angles right-angled triangle SCHOLIUM secant line semi-major axis side straight line substituted in eq subtract Take any point Tang tangent line term tion trapezoid trigonometry variable vertex vertices Whence y=ax+b zero point
Popular passages
Page 200 - 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 274 - In any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle. That is (Fig. 6), a...
Page 11 - ... sides of the vertical triangular section ; as A and B. Hence the ellipse and the opposite hyperbolas, have each two vertices ; but the parabola only one ; unless we consider the other as at an infinite distance. 10. The Axis, or Transverse Diameter, of a conic section, is the line or distance AB between the vertices. Hence the axis of a parabola is infinite in length, Ab being only a part of it. Ellipse.
Page 65 - A radius is any straight line drawn from the center to the circumference, as DA. A diameter is a straight line passing through the center, and terminating in the circumference, as AE. 164. An arc is a part of the circumference. A.
Page 2 - TO 10,000. NB In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced instead of the O's through the...
Page 158 - To find the equation of the ellipse referred to its center and conjugate diameters. The equation of the ellipse referred to its major and minor axes, is into oblique, the origin being the same, are (Prop. 9, Chap. 1,) x=-x' cos. m+y' cos. n. y=x
Page 63 - If a cone be cut by a plane parallel to one of its sides, the section will be a parabola.
Page 276 - Now the areas of these two sectors must be to each other as the area of the ellipse is to the area of the circle.
Page 259 - Y, and b the distance from the origin to the point in which the plane cuts the axis of Z.
Page 22 - If a perpendicular be let fall from any angle of a triangle to its opposite side or base, 'this base is to the sum of the other two sides, as the difference of the sides is to the difference of the segments of the base.