Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 σελίδες |
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Σελίδα vi
... notes that have formed the basis of several proofs in the Chapter now under consideration . The above propositions are also useful in establishing theorems not usually proved by elementary geometrical processes ( see Ex . 25 , p . 22 ) ...
... notes that have formed the basis of several proofs in the Chapter now under consideration . The above propositions are also useful in establishing theorems not usually proved by elementary geometrical processes ( see Ex . 25 , p . 22 ) ...
Σελίδα 1
... Note . Let S be the focus , MX the directrix , P and P ' any two points on a given conic . Draw SX , PM , P'M ' perpendi- cular to the directrix , and through P , P ' draw any two parallel straight lines meeting the direc- trix in R , R ...
... Note . Let S be the focus , MX the directrix , P and P ' any two points on a given conic . Draw SX , PM , P'M ' perpendi- cular to the directrix , and through P , P ' draw any two parallel straight lines meeting the direc- trix in R , R ...
Σελίδα 5
... Note . It follows that a straight line , which meets a conic , will , in general , meet it in two points . Conversely , it may be shown that no straight line can meet a conic in more points than two . From this property conics are ...
... Note . It follows that a straight line , which meets a conic , will , in general , meet it in two points . Conversely , it may be shown that no straight line can meet a conic in more points than two . From this property conics are ...
Σελίδα 6
... Note . Hence SR bisects the angle QSO ( Euc . vI . , A ) , or QSR is half the sum of the angles QSR , OSR . Let the point Q move up to P. Then the chord PQ in its limiting position , when Q coincides with M R X A S Р P , is the tangent ...
... Note . Hence SR bisects the angle QSO ( Euc . vI . , A ) , or QSR is half the sum of the angles QSR , OSR . Let the point Q move up to P. Then the chord PQ in its limiting position , when Q coincides with M R X A S Р P , is the tangent ...
Σελίδα 8
... Note . If PSR be a right angle , then , without assuming that PR touches the curve , we obtain , as above , SL : TN SA : AX . Hence , if T be But the hypotenuse ST is greater than SL . taken anywhere on TR or TR produced , the ratio ST ...
... Note . If PSR be a right angle , then , without assuming that PR touches the curve , we obtain , as above , SL : TN SA : AX . Hence , if T be But the hypotenuse ST is greater than SL . taken anywhere on TR or TR produced , the ratio ST ...
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 asymptotes auxiliary circle axis in G bisects the angle CA² Cambridge CB² CD² centre chord of contact chord of curvature chords parallel cone conic Conic Sections conjugate diameters conjugate hyperbola conjugate points 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 Let the tangent locus major axis meet the asymptotes meet the axis meet the curve meet the directrix meet the minor middle point minor axis opposite sides ordinate parabola parallelogram pass pencil perpendicular plane PM perpendicular point of intersection point Q points of contact polar projection Prop prove quadrilateral rectangular hyperbola right angles semi-latus rectum similar triangles Similarly straight line drawn subtends 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.