Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 páginas |
Otras ediciones - Ver todo
Geometrical Conics: Including Anharmonic Ratio and Projection, with numerous ... Charles Taylor Vista previa restringida - 2022 |
Geometrical Conics: Including Anharmonic Ratio and Projection, with numerous ... Charles Taylor Vista previa restringida - 2022 |
Términos y frases comunes
abscissa Alternando asymptotes auxiliary circle axis in G bisects the angle CA² CB² CD² centre chord of contact chord PQ chords parallel circle described conjugate diameters conjugate hyperbola constant angle constant ratio CP² Draw drawn parallel ellipse equal angles equally inclined fixed point fixed straight line focal chord focal perpendicular foci focus Hence inscribed latus rectum Lemma Let the tangent locus major axis meet the axis meet the curve meet the directrix meet the minor middle point minor axis opposite sides ordinate parabola parallel chords parallelogram passes plane point of intersection point Q points of contact polar produced projection Prop prove Q intersect quadrilateral rectangular hyperbola right angles right-angled triangles semi-latus rectum semi-minor axis similar triangles Similarly straight line drawn tangent and normal touches vertex
Pasajes populares
Página 82 - 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...
Página 24 - For example, the locus of a point which moves in such a way that its distance from a fixed point is always equal to its distance from a fixed straight line, is a parabola.
Página 47 - A parabola touches one side of a triangle in its middle point, and the other two sides produced ; prove that the perpendiculars, drawn from the angular points of the triangle upon any tangent to the parabola, are in harmonical progression.
Página 47 - Д0 be the area of the triangle formed by joining the points of contact...
Página 170 - Given a right cone and a point within it, there are but two sections which have this point for focus ; and the planes of these sections make equal angles with the straight line joining the given point and the vertex of the cone. 123. If the curve formed by the intersection...
Página 1 - It may also lie defined as the curve traced out by a point which moves in such a way that its distance from a fixed point, called the ' focus,' is always equal to its perpendicular distance from a fixed straight line, called the 'directrix.
Página 117 - A'; P being any point on the curve, A'P meets the latus rectum in K. Prove that DK and SP intersect on a certain fixed circle.
Página 96 - To prove this, the abstract terms are forthwith abandoned, and the proposition is re-stated in a concrete form. " Let ABC be an isosceles triangle, of which the side AB is equal to the side AC ; then the angle ABC shall be equal to the angle AC B.
Página 44 - If A PC be a sector of a circle of which the radius CA is fixed, and a circle be described touching the radii CA, CP and the arc AP, shew that the locus of the centre of this circle is a parabola and describe it. 14. Given a segment of a circle, describe the parabola which is the locus of the centres of the circles inscribed in it. 15. If from a point P of a circle PC be drawn to the centre, and R be the middle...