Solid geometry and conic sections |
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Términos y frases comunes
ABCD AC² altitude AP BP asymptotes axis BC² bisect bisector called central conic centre circumference collinear cone conic section conjugate cylinder diameter dihedral directrix draw drawn edges ellipse faces Find the locus fixed point focal chord focus four right angles frustum given plane given point given straight line gonal harmonic pencil height Hence hyperbola join lateral surface latus rectum Let ABC Let the plane line of intersection locus of points opposite ordinate parabola parallel planes parallel to CD parallelepiped parallelogram pass perpendicular plane MN polar polygon polyhedra polyhedron prism Proof prove pyramid radius right circular right prism segments similar triangles Similarly slant side solid sphere tangent tetrahedron THEOREM transversal trihedral angle vertex vertices volume
Pasajes populares
Página 63 - Prove that the lines joining the vertices of a triangle to the points of contact of the inscribed circle are concurrent.
Página v - SOLID GEOMETRY AND CONIC SECTIONS. With Appendices on Transversals and Harmonic Division. For the Use of Schools. By JM WILSON, MA New Edition.
Página vii - Eleventh Book are usually all the Solid Geometry that a boy reads till he meets with the subject again in the course of his analytical studies. And this is a matter of regret, because this part of Geometry is specially valuable and attractive. In it the attention of the student is strongly called to the subject matter of the reasoning ; the geometrical imagination is exercised ; the methods employed in it are more ingenious than those in Plane Geometry, and have greater difficulties to meet ; and...
Página 90 - ... to a chord contained between the two tangents drawn through the ends of the chord is bisected by the diameter of the chord at the point of contact. For the point S is also the middle point of the tangent TV.
Página 35 - The volume of the frustum of any pyramid is equal to the sum of the volumes of three pyramids whose common altitude is the altitude of the frustum, and whose bases are the lower base, the upper base, and the mean proportional between the bases of the frustum.
Página 11 - The projection of a point on a plane is the foot of the perpendicular let fall from the point to the plane.
Página 84 - PZP' is a right angle. For PZ and PZ bisect the adjacent angles MZF, XZF. Hence tangents at the extremities of a focal chord intersect at right angles in the directrix.
Página 134 - The locus of the foot of the perpendicular from the centre on any chord that subtends a right angle at the centre is a circle.
Página 3 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Página 133 - If from the extremities of the axes of an ellipse any four parallel straight lines be drawn, the points at which they cut the curve will be the extremities of conjugate diameters.