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| Introduction | |
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| Getting Started | |
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| Introduction | |
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| Historical Background | |
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| What's on the CD-ROM | |
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| Mathematica | |
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| Starting Descarta2D | |
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| Outline of the Book | |
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| Descarta2D Tour | |
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| Points | |
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| Equations | |
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| Lines | |
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| Line Segments | |
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| Circles | |
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| Arcs | |
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| Triangles | |
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| Parabolas | |
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| Ellipses | |
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| Hyperbolas | |
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| Transformations | |
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| Area and Arc Length | |
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| Tangent Curves | |
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| Symbolic Proofs | |
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| Next Steps | |
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| Elementary Geometry | |
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| Coordinates and Points | |
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| Numbers | |
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| Rectangular Coordinates | |
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| Line Segments and Distance | |
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| Midpoint between Two Points | |
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| Point of Division of Two Points | |
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| Collinear Points | |
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| Explorations | |
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| Equations and Graphs | |
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| Variables and Functions | |
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| Polynomials | |
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| Equations | |
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| Solving Equations | |
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| Graphs | |
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| Parametric Equations | |
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| Explorations | |
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| Lines and Line Segments | |
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| General Equation | |
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| Parallel and Perpendicular Lines | |
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| Angle between Lines | |
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| Two-Point Form | |
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| Point-Slope Form | |
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| Slope-Intercept Form | |
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| Intercept Form | |
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| Normal Form | |
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| Intersection Point of Two Lines | |
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| Point Projected Onto a Line | |
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| Line Perpendicular to Line Segment | |
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| Angle Bisector Lines | |
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| Concurrent Lines | |
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| Pencils of Lines | |
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| Parametric Equations | |
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| Explorations | |
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| Circles | |
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| Definitions and Standard Equation | |
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| General Equation of a Circle | |
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| Circle from Diameter | |
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| Circle Through Three Points | |
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| Intersection of a Line and a Circle | |
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| Intersection of Two Circles | |
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| Distance from a Point to a Circle | |
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| Coaxial Circles | |
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| Radical Axis | |
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| Parametric Equations | |
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| Explorations | |
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| Arcs | |
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| Definitions | |
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| Bulge Factor Arc | |
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| Three-Point Arc | |
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| Parametric Equations | |
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| Points and Angles at Parameters | |
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| Arcs from Ray Points | |
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| Explorations | |
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| Triangles | |
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| Definitions | |
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| Centroid of a Triangle | |
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| Circumscribed Circle | |
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| Inscribed Circle | |
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| Solving Triangles | |
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| Cevian Lengths | |
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| Explorations | |
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| Conics | |
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| Parabolas | |
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| Definitions | |
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| General Equation of a Parabola | |
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| Standard Forms of a Parabola | |
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| Reduction to Standard Form | |
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| Parabola from Focus and Directrix | |
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| Parametric Equations | |
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| Explorations | |
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| Ellipses | |
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| Definitions | |
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| General Equation of an Ellipse | |
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| Standard Forms of an Ellipse | |
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| Reduction to Standard Form | |
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| Ellipse from Vertices and Eccentricity | |
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| Ellipse from Foci and Eccentricity | |
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| Ellipse from Focus and Directrix | |
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| Parametric Equations | |
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| Explorations | |
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| Hyperbolas | |
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| Definitions | |
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| General Equation of a Hyperbola | |
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| Standard Forms of a Hyperbola | |
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| Reduction to Standard Form | |
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| Hyperbola from Vertices and Eccentricity | |
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| Hyperbola from Foci and Eccentricity | |
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| Hyperbola from Focus and Directrix | |
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| Parametric Equations | |
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| Explorations | |
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| General Conics | |
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| Conic from Quadratic Equation | |
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| Classification of Conics | |
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| Center Point of a Conic | |
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| Conic from Point, Line and Eccentricity | |
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| Common Vertex Equation | |
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| Conic Intersections | |
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| Explorations | |
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| Conic Arcs | |
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| Definition of a Conic Arc | |
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| Equation of a Conic Arc | |
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| Projective Discriminant | |
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| Conic Characteristics | |
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| Parametric Equations | |
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| Explorations | |
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| Medial Curves | |
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| Point-Point | |
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| Point-Line | |
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| Point-Circle | |
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| Line-Line | |
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| Line-Circle | |
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| Circle-Circle | |
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| Explorations | |
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| Geometric Functions | |
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| Transformations | |
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| Translations | |
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| Rotations | |
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| Scaling | |
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| Reflections | |
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| Explorations | |
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| Arc Length | |
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| Lines and Line Segments | |
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| Perimeter of a Triangle | |
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| Polygons Approximating Curves | |
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| Circles and Arcs | |
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| Ellipses and Hyperbolas | |
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| Parabolas | |
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| Chord Parameters | |
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| Summary of Arc Length Functions | |
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| Explorations | |
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| Area | |
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| Areas of Geometric Figures | |
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| Curved Areas | |
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| Circular Areas | |
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| Elliptic Areas | |
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| Hyperbolic Areas | |
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| Parabolic Areas | |
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| Conic Arc Area | |
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| Summary of Area Functions | |
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| Explorations | |
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| Tangent Curves | |
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| Tangent Lines | |
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| Lines Tangent to a Circle | |
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| Lines Tangent to Conics | |
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| Lines Tangent to Standard Conics | |
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| Explorations | |
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| Tangent Circles | |
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| Tangent Object, Center Point | |
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| Tangent Object, Center on Object, Radius | |
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| Two Tangent Objects, Center on Object | |
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| Two Tangent Objects, Radius | |
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| Three Tangent Objects | |
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| Explorations | |
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| Tangent Conics | |
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| Constraint Equations | |
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| Systems of Quadratics | |
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| Validity Conditions | |
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| Five Points | |
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| Four Points, One Tangent Line | |
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| Three Points, Two Tangent Lines | |
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| Conics by Reciprocal Polars | |
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| Explorations | |
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| Biarcs | |
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| Biarc Carrier Circles | |
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| Knot Point | |
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| Knot Circles | |
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| Biarc Programming Examples | |
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| Explorations | |
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| Reference | |
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| Technical Notes | |
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| Computation Levels | |
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| Names | |
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| Descarta2D Objects | |
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| Descarta2D Packages | |
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| Descarta2D Functions | |
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| Descarta2D Documentation | |
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| Command Browser | |
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| Error Messages | |
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| Packages | |
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| D2DArc2D | |
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| D2DArcLength2D | |
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| D2DArea2D | |
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| D2DCircle2D | |
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| D2DConic2D | |
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| D2DConicArc2D | |
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| D2DEllipse2D | |
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| D2DEquations2D | |
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| D2DExpressions2D | |
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| D2DGeometry2D | |
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| D2DHyperbola2D | |
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| D2DIntersect2D | |
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| D2DLine2D | |
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| D2DLoci2D | |
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| D2DMaster2D | |
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| D2DMedial2D | |
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| D2DNumbers2D | |
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| D2DParabola2D | |
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| D2DPencil2D | |
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| D2DPoint2D | |
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| D2DQuadratic2D | |
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| D2DSegment2D | |
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| D2DSketch2D | |
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| D2DSolve2D | |
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| D2DTangentCircles2D | |
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| D2DTangentConics2D | |
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| D2DTangentLines2D | |
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| D2DTangentPoints2D | |
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| D2DTransform2D | |
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| D2DTriangle2D | |
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| Explorations | |
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| Epilogue | |
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| Installation Instructions | |
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| Bibliography | |
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| Index | |