Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 σελίδες |
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Σελίδα 4
... construction , will not intersect . For such positions of N no points on the curve can be determined . Let the curve be a parabola and let N lie to the right of A. Then SP , or NX , is greater than SN , and the con- struction is ...
... construction , will not intersect . For such positions of N no points on the curve can be determined . Let the curve be a parabola and let N lie to the right of A. Then SP , or NX , is greater than SN , and the con- struction is ...
Σελίδα 16
... construction for the diameter bisecting a given chord . Join the middle point of the chord to the point in which the focal perpendicular upon the chord meets the directrix . Note . If the tangent at o be parallel to PQ , and meet SY in ...
... construction for the diameter bisecting a given chord . Join the middle point of the chord to the point in which the focal perpendicular upon the chord meets the directrix . Note . If the tangent at o be parallel to PQ , and meet SY in ...
Σελίδα 19
... construction used in the Lemma . = MN : AX . EXAMPLES . 1. Any point , whose distance from the focus of a given conic bears to its perpendicular distance from the directrix a ratio greater than the eccentricity , lies on the convex side ...
... construction used in the Lemma . = MN : AX . EXAMPLES . 1. Any point , whose distance from the focus of a given conic bears to its perpendicular distance from the directrix a ratio greater than the eccentricity , lies on the convex side ...
Σελίδα 26
... construction ; therefore SP is equal to PR , and consequently greater than the perpendicular distance of R from the directrix . Hence it may be shown that all points on the straight line PR , except P , lie on the convex side of the ...
... construction ; therefore SP is equal to PR , and consequently greater than the perpendicular distance of R from the directrix . Hence it may be shown that all points on the straight line PR , except P , lie on the convex side of the ...
Σελίδα 29
... construction . Therefore PV = PT . COR . Since VT = 2PT , therefore QV = 2RP . PROP . VIII . To determine the length of any focal chord PSQ . Draw PM , QN perpendicular to the directrix , and SR , perpendicular to PQ , to meet the ...
... construction . Therefore PV = PT . COR . Since VT = 2PT , therefore QV = 2RP . PROP . VIII . To determine the length of any focal chord PSQ . Draw PM , QN perpendicular to the directrix , and SR , perpendicular to PQ , to meet the ...
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.