Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 páginas |
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... parallel semi - diameters 84 They are also as the lengths of the parallel focal chords Poles and Polars Area of the ellipse 3588 85 87 89 CHAPTER VI . THE HYPERBOLA 100 ~ SP HP constant 100 The tangent at P bisects the angle SPH . 103 ...
... parallel semi - diameters 84 They are also as the lengths of the parallel focal chords Poles and Polars Area of the ellipse 3588 85 87 89 CHAPTER VI . THE HYPERBOLA 100 ~ SP HP constant 100 The tangent at P bisects the angle SPH . 103 ...
Página 1
... parallel straight lines meeting the direc- trix in R , R ' . Then by similar triangles PMR , P'M'R ' , M R R P ' Χ S ... parallel to any fixed straight line which meets the directrix . The B ordinary definition results from supposing ...
... parallel straight lines meeting the direc- trix in R , R ' . Then by similar triangles PMR , P'M'R ' , M R R P ' Χ S ... parallel to any fixed straight line which meets the directrix . The B ordinary definition results from supposing ...
Página 3
... parallel to the directrix . Let PM , P'M ' be the perpendiculars from P , P ' on the directrix . Then PM is equal to NX . Therefore SP : PM – SA : AX , or P is a point on the curve . Similarly = SP ' : P'M ' = SA : AX , or P ' is a ...
... parallel to the directrix . Let PM , P'M ' be the perpendiculars from P , P ' on the directrix . Then PM is equal to NX . Therefore SP : PM – SA : AX , or P is a point on the curve . Similarly = SP ' : P'M ' = SA : AX , or P ' is a ...
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... parallel to the axis of a parabola , meets the curve in one point only . Hence the parabola consists of one infinite branch . 6. Let MP be any straight line which meets the directrix in M and the curve in P. Make the angle MSR equal to ...
... parallel to the axis of a parabola , meets the curve in one point only . Hence the parabola consists of one infinite branch . 6. Let MP be any straight line which meets the directrix in M and the curve in P. Make the angle MSR equal to ...
Página 12
... parallel . [ Euc . III . , 32 . [ Euc . I. , 29 . Hence the triangles SPG , SMP are similar , and SG : SP SP : PM = = SA : AX . PROP . X. If GK be the perpendicular upon SP from the foot of the normal at P , then PK will be equal to ...
... parallel . [ Euc . III . , 32 . [ Euc . I. , 29 . Hence the triangles SPG , SMP are similar , and SG : SP SP : PM = = SA : AX . PROP . X. If GK be the perpendicular upon SP from the foot of the normal at P , then PK will be equal 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
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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.