Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 páginas |
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Página vii
... asymptotes is bisected at the point of contact . I have in general made it an object to prove analogous properties by similar methods , the tendency of this arrange- ment being to diminish the labour of the student . Com- pare Props ...
... asymptotes is bisected at the point of contact . I have in general made it an object to prove analogous properties by similar methods , the tendency of this arrange- ment being to diminish the labour of the student . Com- pare Props ...
Página xi
... Asymptotes • 118 119 The tangent and normal meet the asymptotes and axes respec- tively in four points which lie on a circle 119 • The tangent , terminated by the asymptotes , is bisected at the point of contact 120 • PF.CDCA.CB ...
... Asymptotes • 118 119 The tangent and normal meet the asymptotes and axes respec- tively in four points which lie on a circle 119 • The tangent , terminated by the asymptotes , is bisected at the point of contact 120 • PF.CDCA.CB ...
Página 118
... asymptotes . Conjugate Diameters and Supplemental Chords may be de- fined as on p . 75 . Let PP ' ( fig . , Prop . VIII . ) be any diameter of a hyperbola , terminated by the curve . Then the conjugate diameter will not meet the curve ...
... asymptotes . Conjugate Diameters and Supplemental Chords may be de- fined as on p . 75 . Let PP ' ( fig . , Prop . VIII . ) be any diameter of a hyperbola , terminated by the curve . Then the conjugate diameter will not meet the curve ...
Página 119
... asymptotes in Q , then Since componendo But , since CB to CA. Therefore Hence or QN - PN CB2 . = [ fig . , p . 123 . PN2 : CB2 = CN2 - CA : CA3 , [ Prop . XVI . , p . 109 . PN2 + CB2 : CB ” = CN2 : CA2 . is a point on an asymptote , QN ...
... asymptotes in Q , then Since componendo But , since CB to CA. Therefore Hence or QN - PN CB2 . = [ fig . , p . 123 . PN2 : CB2 = CN2 - CA : CA3 , [ Prop . XVI . , p . 109 . PN2 + CB2 : CB ” = CN2 : CA2 . is a point on an asymptote , QN ...
Página 120
... asymptotes is bisected at the point of contact . Let the tangent and normal at P meet the asymptotes and axes respectively in the points L , M ; G , g . Then a circle goes round Lg CMG . [ Prop . II . But Gg passes through the centre of ...
... asymptotes is bisected at the point of contact . Let the tangent and normal at P meet the asymptotes and axes respectively in the points L , M ; G , g . Then a circle goes round Lg CMG . [ Prop . II . But Gg passes through the centre of ...
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.