A Treatise on Conic Sections: And the Application of Algebra to GeometryPrinted at the University Press, for J. & J.J. Deighton, 1845 - 228 Seiten |
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Häufige Begriffe und Wortgruppen
a²b² abscissa asymptotes axis of x ay² b²x² becomes bisects centre chord circle co-ordinate axes coefficients coincide cone conic section conjugate diameters conjugate hyperbola constant cx² denote determine diagonals directrix double point draw ellipse equa equal find the equation find the locus fixed point focal distances foci focus given line given point Hence hyperbola infinite inscribed latus rectum line joining m² a² major axis meet the curve middle point negative normal nth order ordinate origin parabola parallel parallelogram pass perpendicular plane point Q points of contact points of intersection polar equation positive quadrilateral radius rectangular represents right angles second order shews sides Similarly sin² tangent third order touching transverse axis trapezium triangle values vertex
Beliebte Passagen
Seite 41 - Pappus, the locus of a point whose distance from a given point is in a given ratio to its distance from a fixed...
Seite 148 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Seite 101 - To find the locus of a point, the difference of whose distances from two fixed points is always equal to a given quantity 2 a.
Seite 50 - If the ordinate of P meets the axis in M, and the tangent and normal at P meet the axis in T and N respectively, then MT is the subtangent...
Seite 31 - From the preceding equations to the circle, which assume no other property of a circle than that it is the locus of a point which is always at the same distance from a given fixed point, all the theorems relative to the circle established in geometry, may readily be deduced.
Seite 67 - Find the locus of a point the sum of whose distances from two fixed intersecting lines is constant, ie, is equal to a given line.
Seite 203 - If SY, HZ be perpendiculars from the foci upon the tangent at any point P of an ellipse, then SZ and HY will intersect in the middle point of the normal at P : and the locus of their intersection will be an ellipse whose axes are <г(1 +eг) and a(1 — eг)^.