Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 páginas |
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Página 46
... diameter through any point B , PV a semi - ordinate , Q any other point on the curve ; and if QB cut PV in R , then VR.VR ' = VP2 , R ' being the point in which the diameter through Q meets PV . 79. QSQ ' is a focal chord parallel to AP ...
... diameter through any point B , PV a semi - ordinate , Q any other point on the curve ; and if QB cut PV in R , then VR.VR ' = VP2 , R ' being the point in which the diameter through Q meets PV . 79. QSQ ' is a focal chord parallel to AP ...
Página 58
... semi - circle , is a right angle . A A S Also or CO + OY = HP + SP , from ... diameter parallel to the tangent at P or perpendicular to the normal PF ... diameter of the circle , since YZV is a right angle . [ Construction . = Hence CY CV ...
... semi - circle , is a right angle . A A S Also or CO + OY = HP + SP , from ... diameter parallel to the tangent at P or perpendicular to the normal PF ... diameter of the circle , since YZV is a right angle . [ Construction . = Hence CY CV ...
Página 61
... semi - latus rectum , since the semi - latus rectum is equal to PK . [ Prop . x . , p . 12 . and PROP . XIV . To prove that PF.PG = CB3 , PF.Pg = CA , F being the point in which the normal meets the diameter parallel to the tangent at P ...
... semi - latus rectum , since the semi - latus rectum is equal to PK . [ Prop . x . , p . 12 . and PROP . XIV . To prove that PF.PG = CB3 , PF.Pg = CA , F being the point in which the normal meets the diameter parallel to the tangent at P ...
Página 66
... diameter , and the tangent to the circle at the point where it meets the latus rectum passes through the foot of the directrix . 4. Hence prove that CS . SX - CB2 and deduce that CB is a mean proportional between CA and the semi - latus ...
... diameter , and the tangent to the circle at the point where it meets the latus rectum passes through the foot of the directrix . 4. Hence prove that CS . SX - CB2 and deduce that CB is a mean proportional between CA and the semi - latus ...
Página 67
... diameter in an ellipse . 11. If SY be perpendicular to the tangent at P , then SY : CB SP : 2 CA - SP . = 12. If the ... semi - latus rectum , A the vertex ; LA pro- duced meets the directrix in Q , and QS intersects the tangent at the ...
... diameter in an ellipse . 11. If SY be perpendicular to the tangent at P , then SY : CB SP : 2 CA - SP . = 12. If the ... semi - latus rectum , A the vertex ; LA pro- duced meets the directrix in Q , and QS intersects the tangent at the ...
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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 Alternando asymptotes auxiliary circle axis in G bisects the angle CA² Cambridge CB² CD² centre chord of contact chord of curvature chord PQ chords parallel cone Conic Sections conjugate diameters conjugate hyperbola 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 Lemma Let the tangent locus major axis meet the axis meet the directrix meet the minor meets the curve middle point minor axis opposite sides ordinate parabola parallel chords parallelogram pass pencil perpendicular plane point of intersection point Q points of contact polar produced projection Prop prove quadrilateral rectangular hyperbola right angles semi-diameter semi-latus rectum similar triangles Similarly straight line drawn touches vertex
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Página 226 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools.