Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 páginas |
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Página 179
... Pencil is the anharmonic ratio of the range in which its rays are intersected by any transversal . Pencils and ... pencil . Then the anharmonic ratio of the pencil P is denoted by P { ABCD } . 2. The transversal may cut the rays of the ...
... Pencil is the anharmonic ratio of the range in which its rays are intersected by any transversal . Pencils and ... pencil . Then the anharmonic ratio of the pencil P is denoted by P { ABCD } . 2. The transversal may cut the rays of the ...
Página 182
... pencil may be harmonic . ( i ) Let OB , OD ( fig . , p . 178 ) be the internal and external bisectors of the angle AOC . Then will the pencil O be harmonic . For , if ABCD be any transversal , then Therefore AB : BC = AO : CO [ Euc . VI ...
... pencil may be harmonic . ( i ) Let OB , OD ( fig . , p . 178 ) be the internal and external bisectors of the angle AOC . Then will the pencil O be harmonic . For , if ABCD be any transversal , then Therefore AB : BC = AO : CO [ Euc . VI ...
Página 183
... pencil P. { CRBQ } = { BRCQ } , or the pencils 0 , P are harmonic . So too is the pencil Q. [ § 7 . ANHARMONIC PROPERTIES OF CONICS . 10. The range in which four tangents to a conic are inter- sected by any fifth tangent is equal to the ...
... pencil P. { CRBQ } = { BRCQ } , or the pencils 0 , P are harmonic . So too is the pencil Q. [ § 7 . ANHARMONIC PROPERTIES OF CONICS . 10. The range in which four tangents to a conic are inter- sected by any fifth tangent is equal to the ...
Página 184
... pencil P meet the directrix in the A B C D P a b C S. points a , b , c , d . Then the angle aSb is constant , since it is equal to half the angle ASB . [ Prop . VII . , p . 10 . Similarly it may be shown that each of the angles b.Sc ...
... pencil P meet the directrix in the A B C D P a b C S. points a , b , c , d . Then the angle aSb is constant , since it is equal to half the angle ASB . [ Prop . VII . , p . 10 . Similarly it may be shown that each of the angles b.Sc ...
Página 190
... pencil is harmonic , Art . 9 , the range O ' , M , O , M ' is harmonic . Similarly the range O ' , N , O , N ' is harmonic ; which proves the proposition . EXAMPLES . 1. If a pencil cut two transversals , neither of which is parallel to ...
... pencil is harmonic , Art . 9 , the range O ' , M , O , M ' is harmonic . Similarly the range O ' , N , O , N ' is harmonic ; which proves the proposition . EXAMPLES . 1. If a pencil cut two transversals , neither of which is parallel to ...
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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
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.