An Elementary Treatise on Solid Geometry |
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... Cylinder . The Ellipsoid . The Hyper- boloids . The Paraboloids . Asymptotic Surfaces CHAPTER IV . Transformation of Co - ordinates CHAPTER V. On Generating lines and sections of Quadrics CHAPTER VI . Diametral Planes . Conjugate ...
... Cylinder . The Ellipsoid . The Hyper- boloids . The Paraboloids . Asymptotic Surfaces CHAPTER IV . Transformation of Co - ordinates CHAPTER V. On Generating lines and sections of Quadrics CHAPTER VI . Diametral Planes . Conjugate ...
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... Cylinders 112 CHAPTER IX . On Curves in Space . The Tangent . Normal and Osculating Planes . Line of Greatest Slope . Curvature of Curves CHAPTER X. On Envelopes , with one and two parameters . Reciprocal Polars CHAPTER XI . On ...
... Cylinders 112 CHAPTER IX . On Curves in Space . The Tangent . Normal and Osculating Planes . Line of Greatest Slope . Curvature of Curves CHAPTER X. On Envelopes , with one and two parameters . Reciprocal Polars CHAPTER XI . On ...
Page 40
... Cylinder . A cylinder is a surface generated by a straight line which always passes through a fixed curve and remains parallel to itself . Let the plane of the curve be taken as the plane of xy , and let its equation be Ax2 + Cy2 + Ex ...
... Cylinder . A cylinder is a surface generated by a straight line which always passes through a fixed curve and remains parallel to itself . Let the plane of the curve be taken as the plane of xy , and let its equation be Ax2 + Cy2 + Ex ...
Page 60
... cylinder admit of being generated by the motion of a straight line . This is also the case with the hyperboloid of one sheet and with the hyperbolic paraboloid , but not with any other surfaces whose equations are of the second degree ...
... cylinder admit of being generated by the motion of a straight line . This is also the case with the hyperboloid of one sheet and with the hyperbolic paraboloid , but not with any other surfaces whose equations are of the second degree ...
Page 63
... cylinder , with which this is the case . Let us first take the equation Ax2 + By2 + Cz2 = 1 ..... . ( 1 ) , which includes the ellipsoid and the two hyperboloids ; and if possible let the line whose equations are OC - 7 α y - B_z - Y ...
... cylinder , with which this is the case . Let us first take the equation Ax2 + By2 + Cz2 = 1 ..... . ( 1 ) , which includes the ellipsoid and the two hyperboloids ; and if possible let the line whose equations are OC - 7 α y - B_z - Y ...
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Common terms and phrases
2nd Edition a² b2 Ax² axes axis b2 c² bisects By² centre chords circular section co-ordinate planes cone conics constant cos² Crown 8vo curve cylinder Cz² d²x d²z dF dF dF differential equation direction-cosines distance dt dt dt dx dy dz dz dx dz dz ellipse ellipsoid equa F. A. Paley Fcap Find the equation fixed straight lines formulæ geodesic given point Hence hyperbolas hyperboloid last article latus rectum Let the equation lines of curvature meet obtained origin osculating plane parabola paraboloid perpendicular plane of xy planes parallel Post 8vo quadric radii radius of curvature respectively right angles right conoid satisfied second degree Shew sin² sphere surface surface of revolution tangent plane umbilicus values vanish vertex whence x₁ x² y² y₁ y²+z²
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