Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ExamplesMacmillan, 1863 - 222 páginas |
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Página vii
... III . , and for central Conics in Chapter V. In the last Chapter , the method of Conical Projection has been explained and illustrated with the help of figures . The treatment of the subject is elementary and geome- trical PREFACE . vii.
... III . , and for central Conics in Chapter V. In the last Chapter , the method of Conical Projection has been explained and illustrated with the help of figures . The treatment of the subject is elementary and geome- trical PREFACE . vii.
Página xii
... Figure , dele S. See p . 171 . 66 46 102 , After line 12 , insert Therefore the supplements HPG , PNH are equal . 127 , line 4 from bottom , for part , read point . GEOMETRICAL CONICS . DEFINITIONS . A CONIC is the curve xii CONTENTS .
... Figure , dele S. See p . 171 . 66 46 102 , After line 12 , insert Therefore the supplements HPG , PNH are equal . 127 , line 4 from bottom , for part , read point . GEOMETRICAL CONICS . DEFINITIONS . A CONIC is the curve xii CONTENTS .
Página 5
... figure . When the eccentricity is greater than unity , the straight line RS falls within the angle MSX , and P , Q ... figures in the chapters upon the hyperbola . If the eccentricity be equal to unity , the angles MSR , MSX will be ...
... figure . When the eccentricity is greater than unity , the straight line RS falls within the angle MSX , and P , Q ... figures in the chapters upon the hyperbola . If the eccentricity be equal to unity , the angles MSR , MSX will be ...
Página 63
... figures TH , TS are rectangles and their opposite sides are equal . Hence TY.TZ = SY ' . HZ ' = CB ' . [ Prop . x . Let TO be drawn touching the auxiliary circle in 0 . Then since Y , Z are points on the circle ( Prop . IX ...
... figures TH , TS are rectangles and their opposite sides are equal . Hence TY.TZ = SY ' . HZ ' = CB ' . [ Prop . x . Let TO be drawn touching the auxiliary circle in 0 . Then since Y , Z are points on the circle ( Prop . IX ...
Página 78
... CA.CB. = It is evident from the figure that the area of the cir- cumscribing parallelogram is equal to 4PF.CD , that is to 4CA.CB or AA ' . BB ' . PROP . VI . Tangents drawn to an ellipse from 78 THE ELLIPSE CONTINUED .
... CA.CB. = It is evident from the figure that the area of the cir- cumscribing parallelogram is equal to 4PF.CD , that is to 4CA.CB or AA ' . BB ' . PROP . VI . Tangents drawn to an ellipse from 78 THE ELLIPSE CONTINUED .
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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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