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
A²y abscissa Analytical Geometry asymptotes axis of X bisects the angle CA² chord circle circumference co-ordinate axes cone conjugate diameters conjugate hyperbola Cosine Cotang curve cuts the axis degree denote directrix distance draw 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 radius vector rectangle referred represent right angles right-angled triangle SCHOLIUM secant line semi-major axis side Sine 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 2 - 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...
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 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 71 - The difference of any two sides of a triangle is less than the third side.
Page 50 - THEOREM. The latus rectum is equal to four times the distance from the focus to the vertex. Let AVB be a parabola, of which F is the focus, and V the principal vertex; then the „ latus rectum AFB will be equal to four times FV. Let CD be the directrix, and let AC be drawn perpendicular to it; then, according D to Def.
Page 2 - O's, points or dots are introduced instead of the O's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. N.
Page 63 - PROPOSITION XXI.— THEOREM. If a cone be cut by a plane parallel to one of its elements, the section will be a parabola. Let M VN be a section of a cone by a plane passing through its axis, and in this section draw AH parallel to the element VM.
Page 47 - Fff, we have Ft=tB. PROPOSITION IV.— THEOREM. The distance from the focus of a parabola to the point of contact of any tangent line to the curve, is equal to the distance from the focus to the intersection of the tangent with the axis. Through the point P of the parabola of which F is the focus and BH the directrix, draw the tangent line PT, meeting the axis produced at the point TO.
Page 22 - ... two sides, as the difference of the sides is to the difference of the segments of the base.
Page 192 - ... (74.) By removing the' origin of the axes of coordinates from the centre, O, to the vertex, A, of the transverse axis, by a transformation similar to that employed in the ellipse, the equation becomes B2 AV — BV + 2AB2 x = 0, or y> = -^ (^ — 2 Ax) (7), the equation A.