Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 páginas |
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Página 48
... vertices P , R upon the opposite side . 96. Apply properties of the parabola to prove that- ( i ) In any triangle , the feet of the three perpendiculars from any point of the circumscribing circle to the sides of the triangle , lie on ...
... vertices P , R upon the opposite side . 96. Apply properties of the parabola to prove that- ( i ) In any triangle , the feet of the three perpendiculars from any point of the circumscribing circle to the sides of the triangle , lie on ...
Página 50
... Vertices . Let BCB ' be the central chord perpendicular to AA ' . Then AA ' is the Major and BB ' the Minor Axis . AA ' is sometimes called the Transverse and BB ' the Conjugate axis . Also , when THE axis is spoken of , AA ' is always ...
... Vertices . Let BCB ' be the central chord perpendicular to AA ' . Then AA ' is the Major and BB ' the Minor Axis . AA ' is sometimes called the Transverse and BB ' the Conjugate axis . Also , when THE axis is spoken of , AA ' is always ...
Página 52
... vertices ; S , H the foci ; C the centre . From any point P on the curve draw PM perpendicular to the directrix MX , and let MS meet the minor axis in g . Draw PGg cutting the major axis in G. Then SG : SP = SA : AX , as 52 THE ELLIPSE .
... vertices ; S , H the foci ; C the centre . From any point P on the curve draw PM perpendicular to the directrix MX , and let MS meet the minor axis in g . Draw PGg cutting the major axis in G. Then SG : SP = SA : AX , as 52 THE ELLIPSE .
Página 90
... vertices . 5. The sum of the squares of normals at the extremities of conjugate diameters is constant . 6. The tangent and normal at P and a perpendicular from that point meet the minor axis in t , g , n . Prove that Pn.gt = CD2 . 7 ...
... vertices . 5. The sum of the squares of normals at the extremities of conjugate diameters is constant . 6. The tangent and normal at P and a perpendicular from that point meet the minor axis in t , g , n . Prove that Pn.gt = CD2 . 7 ...
Página 91
... vertices perpen- dicular to the tangent at any point P , the locus of the point of intersection of PS , QA will be a circle . 1 13. If the tangent and normal at P meet the axis in T , G , and TQ touch the circle on AA ' in Q , then TQ ...
... vertices perpen- dicular to the tangent at any point P , the locus of the point of intersection of PS , QA will be a circle . 1 13. If the tangent and normal at P meet the axis in T , G , and TQ touch the circle on AA ' in Q , then TQ ...
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
ABCD abscissa asymptotes auxiliary circle axis in G bisects the angle CA² Cambridge CB² CD² centre chord of contact chord of curvature chords parallel cone conic Conic Sections conjugate diameters conjugate hyperbola conjugate points constant ratio corresponding CP² Crown 8vo Draw drawn parallel ellipse equally inclined fixed point fixed straight line focal chord foci focus harmonic Hence inscribed latus rectum Let the tangent locus major axis meet the asymptotes meet the axis meet the curve meet the directrix meet the minor middle point minor axis opposite sides ordinate parabola parallelogram pass pencil perpendicular plane PM perpendicular point of intersection point Q points of contact polar projection Prop prove quadrilateral rectangular hyperbola right angles semi-latus rectum similar triangles Similarly straight line drawn subtends touches vertex
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