Geometrical conic sections |
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Page 8
... touch a sphere when it touches the circle in which the plane through the line and the centre of the sphere cuts the sphere . It is evident that if a plane be drawn at right angles to the diameter of a sphere through its extremity ...
... touch a sphere when it touches the circle in which the plane through the line and the centre of the sphere cuts the sphere . It is evident that if a plane be drawn at right angles to the diameter of a sphere through its extremity ...
Page 9
... touch the sphere . 5. All the lines drawn from one point to touch a sphere are equal . Let TP ( fig . § 3 ) be any line drawn from the point T to touch the sphere ABCD whose centre is O in the point P. Join OP . Then TP touches a circle ...
... touch the sphere . 5. All the lines drawn from one point to touch a sphere are equal . Let TP ( fig . § 3 ) be any line drawn from the point T to touch the sphere ABCD whose centre is O in the point P. Join OP . Then TP touches a circle ...
Page 18
... touching it at the extremities of conjugate diameters = 4AC . BC . We have seen that the tangents at the extremities of any diameter are parallel , and if these be drawn at the extremities of two conjugate diameters they will form a ...
... touching it at the extremities of conjugate diameters = 4AC . BC . We have seen that the tangents at the extremities of any diameter are parallel , and if these be drawn at the extremities of two conjugate diameters they will form a ...
Page 25
... touch the cone in the circles KRL , K'R'L ' . Every point of each of these circles is equidistant from V , and therefore the distance RR ' from one circle to another along a generating line of the cone will be invariable . Also OS , O'H ...
... touch the cone in the circles KRL , K'R'L ' . Every point of each of these circles is equidistant from V , and therefore the distance RR ' from one circle to another along a generating line of the cone will be invariable . Also OS , O'H ...
Page 26
... touch the sphere centre in S and R , therefore PS PR , and PH , PR touch the sphere centre O in H and R ' , therefore PH- PR . Hence SP + HP - PR + PR = RR = KK ' = AA ' . Hence the sum of the distances of any point of the ellipse from ...
... touch the sphere centre in S and R , therefore PS PR , and PH , PR touch the sphere centre O in H and R ' , therefore PH- PR . Hence SP + HP - PR + PR = RR = KK ' = AA ' . Hence the sum of the distances of any point of the ellipse from ...
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Common terms and phrases
AC² Algebra ARITHMETIC asymptotes auxiliary circle axis major BC² BEGINNERS bisects the angle Cambridge CD² centre Chap Christ's College cloth Conic Sections conjugate diameters conjugate hyperbola CP² Crown 8vo cutting plane directrix draw drawn parallel ELEMENTARY TREATISE ellipse English equal angles equally inclined Examination Papers Extra fcap extremities fcap focal chord foci focus GEOMETRY given Grammar Greek Hence intersect John's College Latin latus rectum line joining manual Mathematical meet the curve method Metric System middle point MIXED MATHEMATICS parabola parallelogram perpendicular point of contact produced meet Professor projection proposition prove quadrilateral rectangle rectangular hyperbola render revised right angles Schools Second Edition semi-diameters shew sphere straight line subtend tangent touch transverse axis triangles Trigonometry University of Cambridge vertex
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