Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 páginas |
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Página vi
... focus ; the latter being perhaps one of the most obvious deductions from the fundamental properties of tangents . Another proof has been given ( p . 171 ) , which depends upon the definition only . Prop . II . , Chapter IV . , viz ...
... focus ; the latter being perhaps one of the most obvious deductions from the fundamental properties of tangents . Another proof has been given ( p . 171 ) , which depends upon the definition only . Prop . II . , Chapter IV . , viz ...
Página ix
... focus SL : TN SA : AX = Tangents subtend equal angles at the focus SG : SP SA : AX = PK latus rectum == Lemma 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 ...
... focus SL : TN SA : AX = Tangents subtend equal angles at the focus SG : SP SA : AX = PK latus rectum == Lemma 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 ...
Página 1
... Focus , bears always the same ratio to its perpendicular distance from a fixed straight line , called the Directrix . M Note . Let S be the focus , MX the directrix , P and P ' any two points on a given conic . Draw SX , PM , P'M ...
... Focus , bears always the same ratio to its perpendicular distance from a fixed straight line , called the Directrix . M Note . Let S be the focus , MX the directrix , P and P ' any two points on a given conic . Draw SX , PM , P'M ...
Página 2
... focus , of any point on the curve , bears to its perpen- dicular distance from the directrix . A conic is called a Parabola , Ellipse , or Hyperbola , accord- ing as its eccentricity is equal to , less or greater than unity . The Axis ...
... focus , of any point on the curve , bears to its perpen- dicular distance from the directrix . A conic is called a Parabola , Ellipse , or Hyperbola , accord- ing as its eccentricity is equal to , less or greater than unity . The Axis ...
Página 3
... focus , directrix , and eccentricity of a conic are given , any number of points on the curve may be 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 ...
... focus , directrix , and eccentricity of a conic are given , any number of points on the curve may be 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 ...
Otras ediciones - Ver todo
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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