Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 σελίδες |
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Σελίδα 3
... determined . For , let S be the focus , MM ' the directrix . Draw SX meeting the directrix at right angles in X , and in SX take a point A such that the ratio of SA to AX may be equal to the eccentricity . Then A is the vertex of the ...
... determined . For , let S be the focus , MM ' the directrix . Draw SX meeting the directrix at right angles in X , and in SX take a point A such that the ratio of SA to AX may be equal to the eccentricity . Then A is the vertex of the ...
Σελίδα 4
... 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 possible . Similarly , the cases of the ellipse and hyperbola may be discussed . 5. Again , let ...
... 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 possible . Similarly , the cases of the ellipse and hyperbola may be discussed . 5. Again , let ...
Σελίδα 20
... determine the points of contact . 11. The tangents at P , Q intersect in R. Prove that if PR be parallel to SQ , then SP = PR . 12. Tangents at the extremities of a focal chord meet the tangents parallel to the chord in the points R , R ...
... determine the points of contact . 11. The tangents at P , Q intersect in R. Prove that if PR be parallel to SQ , then SP = PR . 12. Tangents at the extremities of a focal chord meet the tangents parallel to the chord in the points R , R ...
Σελίδα 21
... determine the focal radii to the points of contact . 21. If SE be the semi - latus rectum , QSQ any focal chord , and PG the normal to which it is perpendicular , then PG " SQ.SQ = QO.SE , = O being the middle point of the chord . For ...
... determine the focal radii to the points of contact . 21. If SE be the semi - latus rectum , QSQ any focal chord , and PG the normal to which it is perpendicular , then PG " SQ.SQ = QO.SE , = O being the middle point of the chord . For ...
Σελίδα 23
... determine the position of its axis . 39. Every diameter of a conic bisects the curve . 40. Parallel diameters of similar and similarly situated conics bisect the same systems of parallel chords . CHAPTER III . THE PARABOLA . Def . A ...
... determine the position of its axis . 39. Every diameter of a conic bisects the curve . 40. Parallel diameters of similar and similarly situated conics bisect the same systems of parallel chords . CHAPTER III . THE PARABOLA . Def . A ...
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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.