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Elements Of Analytic Geometry. by George Albert Wentworth

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1Elements Of Analytic Geometry

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2Elements Of Analytic Geometry

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3Elements Of Analytic Geometry

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

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4Elements Of Analytic Geometry

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

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5Elements Of Analytic Geometry

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6Linear Algebra With Elements Of Analytic Geometry

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About the book This study aid follows the course on linear algebra with elementary analytic geometry and is intended for technical school students specializing in applied mathe­matics. The text deals with the elements of analytic geometry, the theory of matrices and determinants, systems of linear equations, vectors, and Euclidean spaces. The material is presented in an informal manner. Many interesting examples will help the reader to grasp the material easily. The book was translated from the Russian by Tamara Baranovskaya and was published by Mir in 1990.  CONTENTS Preface 8 Part One. ANALYTIC GEOMETRY 10 Chapter 1. VECTORS IN THE PLANE AND IN SPACE. CARTESI­ AN COORDINATE SYSTEM 10 1.1. Vectors 10 1.2. Vector Basis in the Plane and in Space 20 1.3. Cartesian Coordinate System on a Straight Line, in the Plane, and in Space 28 Exercises to Chapter 1 35 Chapter 2. RECTANGULAR CARTESIAN COORDINATES. SIM­PLE PROBLEMS IN ANALYTIC GEOMETRY 37 2.1. Projection of a Vector on an Axis 37 2.2. Rectangular Cartesian Coordinate System 40 2.3. Scalar Product of Vectors 47 2.4. Polar Coordinates 54 Exercises to Chapter 2 55 Chapter 3. DETERMINANTS 57 3.1. Second-Order Determinants. Cramer’s Rule 57 3.2. Third-Order Determinants 60 3.3. n-th-Order Determinants 62 3.4. Transposition of a Determinant 67 3.5. Expansion of a Determinant by Rows and Columns 69 3.6. Properties of nth-Order Determinants 71 3.7. Minors. Evaluation of nth-Order Determinants 77 3.8. Cramer’s Rule for an n x n System 82 3.9. A Homogeneous n x n System 86 3.10. A Condition for a Determinant to Be Zero 91 Exercises to Chapter 3 95 Chapter 4. THE EQUATION OF A LINE IN THE PLANE. A STRAIGHT LINE IN THE PLANE 100 4.1. The Equation of a Line 100 4.2. Parametric Equations of a Line 105 4.3. A Straight Line in the Plane and Its Equation 107 4.4. Relative Position of Two Straight Lines in the Plane 122 4.5. Parametric Equations of a Straight Line 124 4.6. Distance Between a Point and a Straight Line 125 4.7. Half-Planes Defined by a Straight Line 127 Exercises to Chapter 4 128 Chapter 5. CONIC SECTIONS 131 5.1. The Ellipse 131 5.2. The Hyperbola 140 5.3. The Parabola 148 Exercises to Chapter 5 153 Chapter 6. THE PLANE IN SPACE 156 6.1. The Equation of a Surface in Space. The Equation of a Plane 156 6.2. Special Forms of the Equation of a Plane 163 6.3. Distance Between a Point and a Plane. Angle Between Two Planes 168 6.4. Half-Spaces 169 Exercises to Chapter 6 171 Chapter 7. A STRAIGHT LINE IN SPACE 174 7.1. Equations of a Line in Space. Equations ofa Straight Line 174 7.2. General Equations of a Straight Line 178 7.3. Relative Position of Two Straight Lines 183 7.4. Relative Position of a Straight Line anda Plane 186 Exercises to Chapter 7 189 Chapter 8. QUADRIC SURFACES 192 8.1. The Ellipsoid 192 8.2. The Hyperboloid 195 8.3. The Paraboloid 198 Part Two. LINEAR ALGEBRA 202 Chapter 9. SYSTEMS OF LINEAR EQUATIONS 203 9.1. Elementary Transformations of a System of Linear Equations 203 9.2. Gaussian Elimination 205 Exercises to Chapter 9 216 Chapter 10. VECTOR SPACES 218 10.1. Arithmetic Vectors and Operations with Them 218 10.2. Linear Dependence of Vectors 222 10.3. Properties of Linear Dependence 227 10.4. Bases in Space R^n 230 10.5. Abstract Vector Spaces 233 Exercises to Chapter 10  239 Chapter 11. MATRICES 241 11.1. Rank of a Matrix 242 11.2. Practical Method for Finding the Rank of a Matrix 245 11.3. Theorem on the Rank of a Matrix 247 11.4. Rank of a Matrix and Systems of Linear Equations 249 11.5. Operations with Matrices 250 11.6. Properties of Matrix Multiplication 253 11.7. Inverse of a Matrix 255 11.8. Systems of Linear Equations in Matrix Form 259 Exercises to Chapter 11 263 Chapter 12. EUCLIDEAN VECTOR SPACES 266 12.1. Scalar Product. Euclidean Vector Spaces 266 12.2. Simple Metric Concepts in Euclidean Vector Spaces 269 12.3. Orthogonal System of Vectors. Orthogonal Basis 271 12.4. Orthonormal Basis 274 Exercises to Chapter 12 275 Chapter 13. AFFINE SPACES. CONVEX SETS AND POLY­HEDRONS 277 13.1. The Affine Space A^n 277 13.2. Simple Geometric Figures in A^n 279 13.3. Convex Sets of Points in A^n. Convex Polyhedrons 282 Exercises to Chapter 13 286 Index 288

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7Elements Of Analytic Geometry

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vi, 221, 26 p. 19 cm

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8Elements Of Analytic Geometry

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14

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9Elements Of Calculus And Analytic Geometry

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Includes bibliographical references and index

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10Elements Of Analytic Geometry

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11Elements Of Analytic Geometry

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12(1) Elements Of Plane And Spherical Trigonometry (2) Homogeneous Coordinates For Use In Colleges And Schools (3) A Geometry For Schools (4) Analytic Geometry

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13The Elements Of Analytic Geometry

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14Elements Of Analytic Geometry And Of The Differential And Integral Calculus

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15Elements Of Calculus And Analytic Geometry

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16Elements Of Calculus And Analytic Geometry

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17The Elements Of Analytic Geometry

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18Elements Of Analytic Geometry

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19The Elements Of Plane And Solid Analytic Geometry

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20The Elements Of Analytic Geometry

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21Elements Of Analytic Geometry

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xvi, 365 p. 23 cm

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22The Elements Of Analytic Geometry

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xii, 424 p. 21 cm

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23Elements Of Analytic Geometry

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vii, 280 p. 20 cm

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24The Elements Of Plane Analytic Geometry. A Text-book Including Numerous Examples And Applications, And Especially Designed For Beginners

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iv p., 1 l., 191 p. 19 cm

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25The Elements Of Analytic Geometry

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26The Elements Of Plane And Solid Analytic Geometry

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x, 248 p. 21 cm

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27The Elements Of Plane And Solid Analytic Geometry

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28Elements Of Analytic Geometry

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29The Elements Of Analytic Geometry

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viii, 302 p., 1 l. 22 cm

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30Elements Of Analytic Geometry

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viii, 302 p., 1 l. 22 cm

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31Elements Of Analytic Geometry

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viii, 302 p., 1 l. 22 cm

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32Elements Of Analytic Geometry

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33Elements Of Analytic Geometry

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34Elements Of Analytic Geometry

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35Elements Of Analytic Geometry

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36Elements Of Analytic Geometry And Of The Differential And Integral Calculus

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37The Elements Of Plane Analytic Geometry: A Text-book Including Numerous Examples And ...

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38Elements Of Analytic Geometry

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39Elements Of Plane Analytic Geometry

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40Elements Of Calculus And Analytic Geometry : Solution Manual

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41Elements Of Analytic Geometry

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42Elements Of Calculus With Analytic Geometry

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Includes index

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43The Elements Of Plane Analytic Geometry. A Text-book Including Numerous Examples And Applications, And Especially Designed For Beginners

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45Elements Of Analytic Geometry

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46The Elements Of Plane Analytic Geometry: A Text-book Including Numerous Examples And ...

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47The Elements Of Analytic Geometry

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xii, 424 p. 21 cm

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48Elements Of Analytic Geometry

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xii, 424 p. 21 cm

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49Elements Of Analytic Geometry

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xii, 218 p. 21 cm

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50Elements Of Analytic Geometry,

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"Course of reading in geometry" appended

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Source: The Open Library

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1Elements of analytic geometry

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“Elements of analytic geometry” Metadata:

  • Title: Elements of analytic geometry
  • Author:
  • Language: English
  • Number of Pages: Median: 221
  • Publisher: ➤  Ginn & Company - Ginn & Co. - Ginn - Ginn & company
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  • Publish Location: ➤  New York [etc.] - New York - Boston

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  • First Year Published: 1886
  • Is Full Text Available: Yes
  • Is The Book Public: Yes
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    2Elements of analytic geometry

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    • Language: English
    • Number of Pages: Median: 221
    • Publisher: Ginn & company
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    • Publish Location: Boston

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    • First Year Published: 1886
    • Is Full Text Available: Yes
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      3Elements of Analytic Geometry

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      • Language: English
      • Number of Pages: Median: 184
      • Publisher: Ginn & Company - Ginn & Co.
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      • First Year Published: 1888
      • Is Full Text Available: Yes
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        1Fairy Tales from Gold Lands Volume One

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        California, both old and new, is the scene of these fairy stories. They are unique tales written with with a pleasant tinge of romance about them to fix yourr attention, and a touch of pathos that goes to the heart, to make them good and happy. - Summary by phil chenevert and the author

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        • Number of Sections: 10
        • Total Time: 04:02:24

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        2Fairy Tales from Gold Lands Volume Two

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        High as the clouds are the mountains bold<br> That tower in the glorious Land of Gold,<br> And cañons dusky with twilight deep<br> Where a thousand mystic shadows peep.<br> There are vineyards graceful with trailing vine<br> Rich in the wealth of the rosy wine,<br> There are orange groves and lime trees green<br> That glint in the sunlight’s glowing sheen,<br> There are deserts yellow with priceless sand,<br> All these you will find in the Golden Land. - Summary by May Wentworth

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        • Total Time: 03:32:53

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        3Grey Mask

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        Charles Moray is jilted on the eve of his wedding. He then leaves the country for a few years. Upon returning, he finds strangers are using his house. As he watches from a childhood hideaway he sees a man having a discussion with several people one of whom he recognises. - Summary by Sandra Cullum

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        • Language: English
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        • Format: Audio
        • Number of Sections: 45
        • Total Time: 08:29:43

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        • File Name: greymask_2507_librivox
        • File Format: zip
        • Total Time: 08:29:43
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        4Astonishing Adventure of Jane Smith

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        Later - Summary by Sandra Cullum

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        • Title: ➤  Astonishing Adventure of Jane Smith
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        • Language: English
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        • Format: Audio
        • Number of Sections: 29

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        • Number of Sections: 29 sections

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