Analytical solid geometry
By: S. Pirzada, T.A. Chishti
Publisher: Universities Press (India); Distributed by Orient Longman
Published: 2007
Place of publication: Hyderabad
Language: eng
Number of pages: 326
ISBN-13: 9788173715808
Table of contents: title: Preface
pagenum: v; label: Chapter 1
title: Coordinates
pagenum: 1; label: 1.1
title: Introduction
pagenum: 1; label: 1.2
title: The Direction of Rotation
pagenum: 2; label: 1.3
title: Cylindrical Coordinates
pagenum: 3; label: 1.4
title: Spherical Coordinates (Polar Coordinates)
pagenum: 4; label: 1.5
title: The Distance Formula
pagenum: 6; label: 1.6
title: Section Formula
pagenum: 7; label: 1.7
title: Centroid of a Triangle
pagenum: 8; label: 1.8
title: Centroid of a Tetrahedron
pagenum: 9; title: Problem Set 1.1
pagenum: 10; label: 1.9
title: Projections
pagenum: 11; label: 1.10
title: Direction Cosines
pagenum: 12; label: 1.11
title: Direction Ratios
pagenum: 14; label: 1.12
title: Angle between Two Lines
pagenum: 15; title: Problem Set 1.2
pagenum: 19; label: Chapter 2
title: The Plane
pagenum: 22; label: 2.1
title: Introduction
pagenum: 22; label: 2.2
title: Equation of a Plane
pagenum: 24; label: 2.3
title: The Intercept Form
pagenum: 25; label: 2.4
title: Plane through Three Given Points
pagenum: 26; label: 2.5
title: Angle between Two Planes
pagenum: 28; title: Problem Set 2.1
pagenum: 31; label: 2.6
title: Points on Either Side of a Plane
pagenum: 33; label: 2.7
title: Planes Bisecting the Angles between Two Given Planes
pagenum: 35; label: 2.8
title: Equation of Pair of Planes
pagenum: 36; label: 2.9
title: Projection of a Closed Plane Figure
pagenum: 37; label: 2.10
title: Area of a Planar Object
pagenum: 39; label: 2.11
title: Volume of a Tetrahedron
pagenum: 39; title: Problem Set 2.2
pagenum: 45; label: Chapter 3
title: The Straight Line
pagenum: 47; label: 3.1
title: Introduction: Symmetrical Form of Equations of a Line
pagenum: 47; label: 3.2
title: Angle Between a Line and a Plane
pagenum: 49; label: 3.3
title: Symmetrical Form of Equations of a Line
pagenum: 50; label: 3.4
title: Constants in the Equations of a Line
pagenum: 51; label: 3.5
title: The Plane and the Straight Line
pagenum: 52; label: 3.6
title: The Straight Line and the Point
pagenum: 52; title: Problem Set 3.1
pagenum: 56; label: 3.7
title: Coplanar Lines
pagenum: 58; label: 3.8
title: The Shortest Distance between Two Lines
pagenum: 60; label: 3.9
title: The Simplest Form of the Equations of Two Lines
pagenum: 63; title: Problem Set 3.2
pagenum: 67; label: 3.10
title: Lines Intersecting Two Given Lines
pagenum: 69; label: 3.11
title: Lines Intersecting Three Given Lines
pagenum: 69; label: 3.12
title: Intersection of Three Planes
pagenum: 70; title: Problem Set 3.3
pagenum: 72; label: Chapter 4
title: Change of Axes
pagenum: 75; label: 4.1
title: Introduction: Changing the Origin of Coordinates
pagenum: 75; label: 4.2
title: Change of Axes
pagenum: 76; label: 4.3
title: Relations between Direction Cosines
pagenum: 77; label: 4.4
title: Invariants
pagenum: 79; label: 4.5
title: Transformation of Direction Cosines
pagenum: 80; title: Problem Set 4.1
pagenum: 82; label: Chapter 5
title: The Sphere
pagenum: 85; label: 5.1
title: Introduction: Equation of a Sphere
pagenum: 85; label: 5.2
title: General Form of the Equation of a Sphere
pagenum: 85; label: 5.3
title: Conditions Satisfied by a Sphere
pagenum: 86; label: 5.4
title: Diameter Form
pagenum: 87; label: 5.5
title: Plane Section of a Sphere
pagenum: 87; label: 5.6
title: Intersection of Two Spheres
pagenum: 88; label: 5.7
title: Equations of a Circle
pagenum: 88; label: 5.8
title: Sphere through a given Circle
pagenum: 88; title: Problem Set 5.1
pagenum: 92; label: 5.9
title: Intersection of a Sphere and a Line
pagenum: 94; label: 5.10
title: The Power of a Point with Respect to a Sphere
pagenum: 95; label: 5.11
title: Tangent Plane
pagenum: 95; label: 5.12
title: Plane of Contact
pagenum: 96; label: 5.13
title: Polar Plane
pagenum: 97; label: 5.14
title: Pole of a Given Plane
pagenum: 98; label: 5.15
title: Polar Lines
pagenum: 99; title: Problem Set 5.2
pagenum: 102; label: 5.16
title: Angle of Intersection of Two Spheres
pagenum: 104; label: 5.17
title: Orthogonality of Two Spheres
pagenum: 105; label: 5.18
title: Distance of a Point from a Sphere
pagenum: 105; label: 5.19
title: Power of a Point and the Radical Plane
pagenum: 106; label: 5.20
title: Radical Line
pagenum: 106; label: 5.21
title: Radical Centre
pagenum: 106; label: 5.22
title: Equations of Two Spheres in the Simplest Form
pagenum: 107; label: 5.23
title: Coaxal Spheres
pagenum: 107; label: 5.24
title: Limiting Points of a Coaxal System
pagenum: 108; title: Problem Set 5.3
pagenum: 110; label: Chapter 6
title: The Cone
pagenum: 112; label: 6.1
title: Introduction: Equation of a Cone
pagenum: 112; label: 6.2
title: The Enveloping Cone
pagenum: 114; label: 6.3
title: Equation of a Cone from a General Second Degree Equation
pagenum: 115; label: 6.4
title: The Right Circular Cone
pagenum: 117; title: Problem Set 6.1
pagenum: 122; label: 6.5
title: The Tangent Plane
pagenum: 125; label: 6.6
title: The Reciprocal Cone
pagenum: 127; label: 6.7
title: Section of a Cone by a Plane
pagenum: 128; label: 6.8
title: Intersection of Two Cones with a Common Vertex
pagenum: 132; label: 6.9
title: Elliptic Cones
pagenum: 132; title: Problem Set 6.2
pagenum: 136; label: Chapter 7
title: The Cylinder
pagenum: 139; label: 7.1
title: Introduction: Equation of a Cylinder
pagenum: 139; label: 7.2
title: Equation of a Right Circular Cylinder
pagenum: 140; label: 7.3
title: The Enveloping Cylinder
pagenum: 141; label: 7.4
title: The Tangent Plane of a Cylinder
pagenum: 142; title: Problem Set 7.1
pagenum: 144; label: Chapter 8
title: The Central Conicoids
pagenum: 146; label: 8.1
title: Introduction: Types of Conicoids
pagenum: 146; label: 8.2
title: The Central Conicoids
pagenum: 150; label: 8.3
title: Intersection of a Line and a Conicoid
pagenum: 151; label: 8.4
title: Tangents and Tangent Planes
pagenum: 151; title: Problem Set 8.1
pagenum: 153; label: 8.5
title: Normals to a Surface
pagenum: 156; label: 8.6
title: Poles and Polar Planes
pagenum: 160; label: 8.7
title: Enveloping Cone
pagenum: 163; label: 8.8
title: Enveloping Cylinder
pagenum: 163; label: 8.9
title: Section with a Given Centre
pagenum: 164; label: 8.10
title: Locus of Mid-Points of a System of Parallel Chords
pagenum: 165; title: Problem Set 8.2
pagenum: 165; label: 8.11
title: The Cone
pagenum: 169; label: 8.12
title: The Paraboloids
pagenum: 170; label: 8.13
title: Features Related to Paraboloids
pagenum: 172; label: 8.14
title: Conjugate Diameters and Conjugate Planes
pagenum: 175; label: 8.15
title: Practical Applications of Central Conicoids
pagenum: 179; title: Problem Set 8.3
pagenum: 180; label: Chapter 9
title: Plane Sections of a Conicoid
pagenum: 184; label: 9.1
title: Introduction: Axes of Plane Sections of a Conicoid
pagenum: 184; label: 9.2
title: Axes of a Central Plane Section
pagenum: 185; label: 9.3
title: Axes of Any Section of a Central Conicoid
pagenum: 187; label: 9.4
title: Axes of a Given Section of a Paraboloid
pagenum: 191; title: Problem Set 9.1
pagenum: 194; label: 9.5
title: Circular Sections
pagenum: 196; label: 9.6
title: Umbilics
pagenum: 200; title: Problem Set 9.2
pagenum: 201; label: Chapter 10
title: Generating Lines
pagenum: 206; label: 10.1
title: Introduction: Ruled Surfaces
pagenum: 206; label: 10.2
title: Section of a Ruled Surface by the Tangent Plane at a Point
pagenum: 208; label: 10.3
title: Condition for a Line to be on a Conicoid
pagenum: 209; label: 10.4
title: Conditions for a Line to be the Generator of a Conicoid
pagenum: 210; label: 10.5
title: Real Ruled Surfaces
pagenum: 210; label: 10.6
title: The Hyperboloid of One Sheet
pagenum: 211; label: 10.7
title: The Hyperbolic Paraboloid
pagenum: 217; title: Problem Set 10.1
pagenum: 222; label: 10.8
title: Conicoids through Three Given Lines
pagenum: 224; label: 10.9
title: Straight Lines which Meet Four Given Lines on the Conicoid
pagenum: 227; label: 10.10
title: Hyperboloid whose Two Generators are Coordinate Axes
pagenum: 227; label: 10.11
title: Properties of a Generating Line
pagenum: 228; label: 10.12
title: The Central Point and the Parameter of Distribution
pagenum: 229; title: Problem Set 10.2
pagenum: 231; label: Chapter 11
title: General Equations of the Second Degree
pagenum: 234; label: 11.1
title: Introduction
pagenum: 234; label: 11.2
title: Points of Intersection of a General Conicoid and a Line
pagenum: 234; label: 11.3
title: The Tangent Plane
pagenum: 235; label: 11.4
title: The Polar Plane
pagenum: 236; label: 11.5
title: The Enveloping Cone
pagenum: 237; label: 11.6
title: The Enveloping Cylinder
pagenum: 238; label: 11.7
title: Locus of Special Chords
pagenum: 238; label: 11.8
title: The Diametral Plane
pagenum: 239; label: 11.9
title: The Principal Planes
pagenum: 239; label: 11.10
title: The Principal Directions
pagenum: 246; label: 11.11
title: Symmetries of the Discriminating Cubic
pagenum: 247; label: 11.12
title: Transformation of f (x, y, z)
pagenum: 248; title: Problem Set 11.1
pagenum: 250; label: 11.13
title: Centre of a Conicoid
pagenum: 252; label: 11.14
title: Central Planes
pagenum: 254; label: 11.15
title: Reduction of the General Equation
pagenum: 255; label: 11.16
title: Reduction of a General Equation of Second Degree
pagenum: 261; label: 11.17
title: Conicoids of Revolution
pagenum: 264; label: 11.18
title: Invariants
pagenum: 265; title: Problem Set 11.2
pagenum: 267; label: Chapter 12
title: Confocal Conicoids
pagenum: 271; label: 12.1
title: Introduction
pagenum: 271; label: 12.2
title: The Three Confocals Through a Point
pagenum: 272; label: 12.3
title: Elliptic Coordinates
pagenum: 273; label: 12.4
title: Some Properties of Confocal Conicoids
pagenum: 274; label: 12.5
title: Parameters of Confocals through a Point on a Conicoid
pagenum: 276; label: 12.6
title: Locus of the Poles of a Plane with Respect to Confocals
pagenum: 277; label: 12.7
title: Normals of the Three Confocals through a Point
pagenum: 277; label: 12.8
title: Self-Polar Tetrahedron
pagenum: 279; label: 12.9
title: Axes of the Enveloping Cone
pagenum: 279; label: 12.10
title: Equation of the Enveloping Cone
pagenum: 279; label: 12.11
title: Equation of a Conicoid
pagenum: 280; title: Problem Set 12.1
pagenum: 280; label: 12.12
title: Corresponding Points on Coaxial Conicoids
pagenum: 283; label: 12.13
title: Foci of Conicoids
pagenum: 284; label: 12.14
title: Planes through the Intersection of Two Planes
pagenum: 285; label: 12.15
title: Foci of an Ellipsoid
pagenum: 285; label: 12.16
title: Foci of Paraboloids
pagenum: 288; label: 12.17
title: Concyclic Conicoids
pagenum: 290; title: Problem Set 12.2
pagenum: 291; label: Chapter 13
title: Systems of Conicoids
pagenum: 293; label: 13.1
title: Introduction: Intersection of Two Conicoids
pagenum: 293; label: 13.2
title: Cones through the Intersection of Two Conicoids
pagenum: 294; label: 13.3
title: The Cubic Curve Common to Two Conicoids
pagenum: 295; label: 13.4
title: Conicoids with Common Generators
pagenum: 296; label: 13.5
title: Conicoids with Double Contact
pagenum: 297; label: 13.6
title: Conicoids with Two Common Plane Sections
pagenum: 298; label: 13.7
title: Locus of Centres of all Conicoids which pass through Seven Given Points
pagenum: 300; label: 13.8
title: Tangential Equations
pagenum: 300; label: 13.9
title: Tangential Equation of a Conicoid
pagenum: 301; label: 13.10
title: Director Sphere
pagenum: 302; title: Problem Set 13.1
pagenum: 302; label: Chapter 14
title: General Surfaces
pagenum: 306; label: 14.1
title: Introduction: Degree of a Surface
pagenum: 306; label: 14.2
title: Tangents and Tangent Planes
pagenum: 307; label: 14.3
title: Inflectional Tangents
pagenum: 308; label: 14.4
title: Indicatrix
pagenum: 309; label: 14.5
title: Parametric Representation
pagenum: 310; label: 14.6
title: Conoids
pagenum: 311; label: 14.7
title: Wave Surface
pagenum: 312; label: 14.8
title: Surfaces Generated by Translations and Rotation
pagenum: 314; label: 14.9
title: Envelopes
pagenum: 315; label: 14.10
title: Edge of Regression
pagenum: 316; label: 14.11
title: Contact Between the Envelope and the Surfaces
pagenum: 316; label: 14.12
title: Envelopes of Surfaces with Two Arbitrary Parameters
pagenum: 316; label: 14.13
title: Families of Surfaces
pagenum: 317; title: Problem Set 14.1
pagenum: 320; title: Bibliography
pagenum: 323; title: Index
pagenum: 325