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Problems in illustration of the principles of plane coordinate geometry

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fullscreen: Problems in illustration of the principles of plane coordinate geometry

Monograph

Persistent identifier:: 856561894

Author:: Kolbe, Thomas H.

Title:: International Conference on 3D Geoinformation

Sub title:: ISPRS conference, Berlin, Germany, November 3 - 4, 2010

Scope:: VIII, 200 Seiten

Year of publication:: 2010

Place of publication:: Lemmer

Publisher of the original:: GITC

Identifier (digital):: 856561894

Illustration:: Illustrationen, Diagramme

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Monograph

Collection:: Earth sciences

Chapter

Title:: PART 3 Oral Presentations (Full Paper)

Document type:: Monograph

Structure type:: Chapter

Chapter

Title:: 3D CADASTRE IN THE PROVINCE OF QUEBEC: A FIRST EXPERIMENT FOR THE CONSTRUCTION OF A VOLUMETRIC REPRESENTATION. Jacynthe Pouliot, Tania Roy, Guillaume Fouquet-Asselin, Joanie Desgroseilliers

Document type:: Monograph

Structure type:: Chapter

Contents

Table of contents

Problems in illustration of the principles of plane coordinate geometry
Cover
ColorChart
Title page
PREFACE.
CONTENTS.
ERRATA.
STRAIGHT LINE.
SECTION I. Elementary Problems. Rectangular Axes.
SECTION II. Elementary Problems. Oblique Axes.
SECTION III. Polar Equation.
SECTION IV. Rectilinear Loci.
SECTION V. Transversals. Explicit Parameters.
SECTION VI. Transversals. Implicit Parameters.
SECTION VII. Rectilinear Areas.
CIRCLE.
SECTION I. Referred to two Perpendicular Diameters. Tangents.
SECTION II. Referred to two Perpendicular Diameters. Chords.
SECTION III. Referred to two Perpendicular Diameters. Points.
SECTION IV. Referred to any Rectangular Axes.
SECTION V. Referred to two Tangents as Axes of Coordinates.
SECTION VI. Referred to any Oblique Axes.
SECTION VII. Polar Coordinates.
SECTION VIII. Polar Equations to Tangents and Chords.
SECTION IX. Poles and Polars.
SECTION X. Radical Axes, Centres of Similitude, Ac.
SECTION XI. Inscribed and Circumscribed Polygons.
SECTION XII. Circular Loci.
PARABOLA.
SECTION I. Referred to the Axis and its Tangent. Ordinates.
SECTION II. Referred to the Axis and its Tangent. Tangents.
SECTION III. Referred to the Axis and its Tangent. Magical Equation to the Tangent.
SECTION IV. Referred to the Axis and its Tangent. Normals.
SECTION V. Referred to the Axis and its Tangent. Chords.
SECTION VI. Referred to the Axis and its Tangent. Focal Properties.
SECTION VII. Referred to a Tangent and its diameter as Axes.
SECTION VIII. Referred to two Tangents as Axes.
SECTION IX. Referred to any Rectangular Axes whatever. Reduction.
SECTION X. Polar Equation. Focus the Pole.
SECTION XI. Polar Equation. Vertex the Pole.
SECTION XII. Polar Equation. Pole a point in the Axis.
SECTION XIII. Polar Equation. Pole anywhere.
SECTION XIV. Linear Equation.
SECTION XV. Polar Equation to the Tangent.
SECTION XVI. Poles and Polars.
SECTION XVII. Intersection of Parabolas.
SECTION XVIII. Parabolic Loci.
SECTION XIX. Parabolic Envelops.
SECTION XX. Miscellaneous Problems.
ELLIPSE.
SECTION I. Referred to its Axes. Ordinates.
SECTION II. Referred to its Axes. Tangents.
SECTION III. Referred to its Axes. Magical Equation to the Tangent.
SECTION IV. Referred to its Axes. Normals.
SECTION V. Referred to its Axes. Chords.
SECTION VI. Referred to its Axes. Focal Properties.
SECTION VII. Referred to its Axes. Conjugate Diameters.
SECTION VIII. Referred to Axes parallel to the Axes of the Curve.
SECTION IX. Polar Equation. Centre the Pole.
SECTION X. Polar Equation. Focus the Pole.
SECTION XI. Polar Equation. End of the Axis Major the Pole.
SECTION XII. Polar Equation. End of the Axis Minor the Pole.
SECTION XIII. Polar Equation. Point in the Axis the Pole.
SECTION XIV. Polar Equation. Pole anywhere.
SECTION XV. Referred to Conjugate Diameters.
SECTION XVI. Deferred to any two Diameters.
SECTION XVII. Referred to any Rectangular Axes whatever. Reduction.
SECTION XVIII. Linear Equation.
SECTION XIX. Intersections of Ellipses.
SECTION XX. Polar Equation to the Tangent.
SECTION XXI. Polar Equation to a Chord.
SECTION XXII. Polar Equation to the Normal.
SECTION XXIII. Poles and Polars.
SECTION XXIV. Inscribed and Circumscribed Polygons.
SECTION XXV. Elliptic Loci.
SECTION XXVI. Elliptic Envelops.
SECTION XXVII. Miscellaneous Problems.
HYPERBOLA.
SECTION I. Referred to its Axes. Ordinates.
SECTION II. Referred to its Axes. Tangents.
SECTION III. Referred to its Axes. Magical Equation to the Tangent.
SECTION IV. Referred to its Axes. Focal Properties.
SECTION V. Referred to its Axes. Conjugate Diameters. Conjugate Hyperbola.
SECTION VI. Referred to its Axes. Asymptotes.
SECTION VII. Referred to its Transverse Axis and the Tangent at its Vertex.
SECTION VIII. Referred to Conjugate Diameters. Asymptotes.
SECTION IX. Referred to Conjugate Diameters. Conjugate Hyperbola.
SECTION X. Referred to any two Diameters. Conjugate Hyperbola.
SECTION XI. Referred to its Asymptotes.
SECTION XII. Referred to any Rectangular Axes.
SECTION XIII. Referred to any Rectangular Axes. Reduction.
SECTION XIV. Polar Equation. Centre the Pole.
SECTION XV. Polar Equation. Focus the Pole.
SECTION XVI. Polar Equation. Point in the Axis the Pole.
SECTION XVII. Polar Equation. Pole Anywhere.
SECTION XVIII. Poles and Polars.
SECTION XIX. Hyperbolic Loci.
SECTION XX. Miscellaneous Problems.
LINES OF THE SECOND ORDER.
SECTION I. Referred to a Principal Diameter and its Tangent. Normals.
SECTION II. Referred to a Principal Diameter and its Tangent. Chords.
SECTION III. Referred to a Principal Diameter and its Tangent. Focal Properties.
SECTION IV. Referred to any two Oblique Diameters.
SECTION V. Referred to two Tangents as Axes.
SECTION VI. Referred to a Tangent and Normal.
SECTION VII. Referred to any Axes whatever. Centres.
SECTION VIII. Referred to any Axes whatever. Tangents.
SECTION IX. Referred to any Axes whatever. Chords.
SECTION X. Referred to any Axes whatever. Directrix.
SECTION XI. Referred to any Axes whatever. Conjoint Lines and Circles.
SECTION XII. Passing through given Points.
SECTION XIII. Passing through given Points and touching given straight lines.
SECTION XIV. Determination of their Equations from given Conditions.
SECTION XV. Poles and Polars.
SECTION XVI. Polar Equations.
SECTION XVII. Linear Equation.
SECTION XVIII. Polar Equation to the Tangent.
SECTION XIX. Polar Equation to the Chord of a Conic Section.
SECTION XX. Inscribed Polygons.
SECTION XXI. Circumscribed Polygons.
SECTION XXII. Problems relating to several Curves.
SECTION XXIII. Intersections of Conic Sections. Common Chords.
SECTION XXIV. Double Contact.
SECTION XXV. Conical Loci.
SECTION XXVI. Envelopes.
SECTION XXVII. Similar Curves.
SECTION XXVIII. Miscellaneous Problems.
APPENDIX.
Cover

Full text

MISCELLANEOUS PROBLEMS. 
169 
parallel straight lines so as to make OK always equal to OX, 
0 being a fixed point in the locus of K. 
Let 0 be the origin of rectangular coordinates, the locus 
of K being the axis of x. Let B be the intersection of the 
axis of y with the locus of X. Let OB = b. Then the required 
locus will be a parabola defined by the equation 
x l — b.{b — 2 y). 
6. A straight line cuts off from a parabola a segment equal 
to a given area: to find the equation to the curve to which this 
line in any position is a tangent. 
Let c l represent the given area; then, the equation to the 
parabola being y 2 = frnx, 
that to the required envelop will be 
Section XX. 
Miscellaneous Problems. 
1. The equation to a parabola, referred to rectangular axes, 
y* + 4ay cot a = 4ax, 
to find its equation when referred to oblique axes inclined to 
each other at an angle a, the axis of x remaining the same. 
The required equation is 
2. P is any point in a parabola of which the vertex is A, 
and focus S] T is the point where the directrix intersects the 
axis; TP is joined and produced to cut the latus-rectum in iV; 
SPQ is drawn to meet NQ, which is parallel to ST, in Q: to 
find the locus of Q.

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kolbe, thomas h. International Conference on 3D Geoinformation. GITC, 2010.

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