Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 σελίδες |
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Σελίδα ix
... Diameters Central Conics • SPPH constant CHAPTER III . 6 6 7 9 12 12 14 15 18 19 THE PARABOLA Diameters 25 The tangent at P makes equal angles with SP , PM The subnormal is constant = PN2 4AS . AN QV2 = 4SP.PV 222288 25 26 27 30 ...
... Diameters Central Conics • SPPH constant CHAPTER III . 6 6 7 9 12 12 14 15 18 19 THE PARABOLA Diameters 25 The tangent at P makes equal angles with SP , PM The subnormal is constant = PN2 4AS . AN QV2 = 4SP.PV 222288 25 26 27 30 ...
Σελίδα 12
... diameter passes through S , since PSR is a right angle ; and also through M , where PM is the perpendicular from P on the directrix . But PG , being at right angles to PR , touches the circle ( Euc . III . , 16 , Cor . ) . Therefore ...
... diameter passes through S , since PSR is a right angle ; and also through M , where PM is the perpendicular from P on the directrix . But PG , being at right angles to PR , touches the circle ( Euc . III . , 16 , Cor . ) . Therefore ...
Σελίδα 14
... diameter describe a circle , and let it cut SR in M. This circle passes through Y , since SYQ is a right angle . T M Ꭱ First , let R lie in PQ produced . Take any point T in PS produced . Then SR bisects the angle QST . Therefore L RST ...
... diameter describe a circle , and let it cut SR in M. This circle passes through Y , since SYQ is a right angle . T M Ꭱ First , let R lie in PQ produced . Take any point T in PS produced . Then SR bisects the angle QST . Therefore L RST ...
Σελίδα 15
... DIAMETER . Let O be the middle point of a chord PQ , which meets R Y R X the directrix in R. angles in Y , and let directrix . A S Draw SY , meeting the chord at right V be the point in which SY meets the Then Therefore SP : PR = SQ ...
... DIAMETER . Let O be the middle point of a chord PQ , which meets R Y R X the directrix in R. angles in Y , and let directrix . A S Draw SY , meeting the chord at right V be the point in which SY meets the Then Therefore SP : PR = SQ ...
Σελίδα 16
... diameter VO meets the curve is parallel to the chords which that diameter bisects . COR . 2. The following is a construction for the diameter bisecting a given chord . Join the middle point of the chord to the point in which the focal ...
... diameter VO meets the curve is parallel to the chords which that diameter bisects . COR . 2. The following is a construction for the diameter bisecting a given chord . Join the middle point of the chord to the point in which the focal ...
Άλλες εκδόσεις - Προβολή όλων
Geometrical Conics: Including Anharmonic Ratio and Projection, with numerous ... Charles Taylor Περιορισμένη προεπισκόπηση - 2022 |
Geometrical Conics: Including Anharmonic Ratio and Projection, with numerous ... Charles Taylor Περιορισμένη προεπισκόπηση - 2022 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 226 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools.