Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 páginas |
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Página 8
... touches the curve , we obtain , as above , SL : TNSA : AX . Hence , if T be But the hypotenuse ST is greater than SL . taken anywhere on TR or TR produced , the ratio ST : TN will be greater than SA : AX , except when L coincides with P ...
... touches the curve , we obtain , as above , SL : TNSA : AX . Hence , if T be But the hypotenuse ST is greater than SL . taken anywhere on TR or TR produced , the ratio ST : TN will be greater than SA : AX , except when L coincides with P ...
Página 9
... touches the conic . [ Prop . III . , Cor . Similarly , if TM be the other tangent from T to the circle , and SM meet the conic in Q , then TQ will be the tangent at Q. PROP . VI . The tangents at P , Q intersect in T. To prove that TP ...
... touches the conic . [ Prop . III . , Cor . Similarly , if TM be the other tangent from T to the circle , and SM meet the conic in Q , then TQ will be the tangent at Q. PROP . VI . The tangents at P , Q intersect in T. To prove that TP ...
Página 12
... touches the circle ( Euc . III . , 16 , Cor . ) . Therefore Also M X S L SPG = SMP . L PSG = SPM , since SG , MP are parallel . [ Euc . III . , 32 . [ Euc . I. , 29 . Hence the triangles SPG , SMP are similar , and SG : SP SP : PM ...
... touches the circle ( Euc . III . , 16 , Cor . ) . Therefore Also M X S L SPG = SMP . L PSG = SPM , since SG , MP are parallel . [ Euc . III . , 32 . [ Euc . I. , 29 . Hence the triangles SPG , SMP are similar , and SG : SP SP : PM ...
Página 21
... touches . Prove that the chord of the circle drawn through the focus and either point of contact is of constant length . 20. If the circle pass through the focus determine the focal radii to the points of contact . 21. If SE be the semi ...
... touches . Prove that the chord of the circle drawn through the focus and either point of contact is of constant length . 20. If the circle pass through the focus determine the focal radii to the points of contact . 21. If SE be the semi ...
Página 23
... touches the locus of Y. 36. The normal at Y to the locus of Y bisects SP . 37. If a diameter of a conic meet the curve in two points , the tangents at those points are parallel . 38. Given a conic ; determine the position of its axis ...
... touches the locus of Y. 36. The normal at Y to the locus of Y bisects SP . 37. If a diameter of a conic meet the curve in two points , the tangents at those points are parallel . 38. Given a conic ; determine the position of its axis ...
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 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
Pasajes populares
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.