Collineations and conic sections : an introduction to projective geometry in its history /: an introduction to projective geometry in its history. (2020)
- Record Type:
- Book
- Title:
- Collineations and conic sections : an introduction to projective geometry in its history /: an introduction to projective geometry in its history. (2020)
- Main Title:
- Collineations and conic sections : an introduction to projective geometry in its history
- Further Information:
- Note: Christopher Baltus.
- Other Names:
- Baltus, Christopher
- Contents:
- Intro -- Preface -- Contents -- 1 Introduction: The Projective Plane and Central Collineations -- 1.1 The Projective Plane -- 1.2 Homogeneous Coordinates and the Real Projective Plane -- 1.3 Central Collineation: Definition and Elementary Properties -- 1.4 Excursion: Finite Affine and Projective Planes of Minimum Size -- 1.5 Looking Ahead -- 1.6 Notes and Exercises -- 1.7 Some Hints and Solutions to Exercises -- References -- 2 Central Collineations: Properties -- 2.1 Specifying a Central Collineation -- 2.2 Central Collineations and Desargues' Theorem 2.3 Composition of Central Collineations -- 2.4 Group Properties -- 2.5 Excursion: Two Commutative Groups of Central Collineations -- 2.6 Notes and Exercises -- 2.7 Some Hints and Solutions -- References -- 3 The Geometry of Euclid's Elements -- 3.1 Ancient Greek Mathematics Before Euclid -- 3.2 The Geometry of Euclid's Elements: A. Preliminaries in Book 1 -- 3.3 The Geometry of Euclid's Elements: B. Straightedge/Compass Constructions in Book 1 -- 3.4 The Geometry of Euclid's Elements: C. Angles and Parallels 3.5 The Geometry of Euclid's Elements: D. Triangle Similarity and Circles in Books 6 and 3 -- 3.6 Exercises -- References -- 4 Conics in Greek Geometry: Apollonius, Harmonic Division, and Later Greek Geometry -- 4.1 Conic Sections in Ancient Greece -- 4.2 The Conics of Apollonius -- 4.3 Harmonic Division of a Segment -- 4.4 Conics and the Harmonic Relation -- 4.5 Late Antiquity and Steps Toward Projective Geometry -- 4.6Intro -- Preface -- Contents -- 1 Introduction: The Projective Plane and Central Collineations -- 1.1 The Projective Plane -- 1.2 Homogeneous Coordinates and the Real Projective Plane -- 1.3 Central Collineation: Definition and Elementary Properties -- 1.4 Excursion: Finite Affine and Projective Planes of Minimum Size -- 1.5 Looking Ahead -- 1.6 Notes and Exercises -- 1.7 Some Hints and Solutions to Exercises -- References -- 2 Central Collineations: Properties -- 2.1 Specifying a Central Collineation -- 2.2 Central Collineations and Desargues' Theorem 2.3 Composition of Central Collineations -- 2.4 Group Properties -- 2.5 Excursion: Two Commutative Groups of Central Collineations -- 2.6 Notes and Exercises -- 2.7 Some Hints and Solutions -- References -- 3 The Geometry of Euclid's Elements -- 3.1 Ancient Greek Mathematics Before Euclid -- 3.2 The Geometry of Euclid's Elements: A. Preliminaries in Book 1 -- 3.3 The Geometry of Euclid's Elements: B. Straightedge/Compass Constructions in Book 1 -- 3.4 The Geometry of Euclid's Elements: C. Angles and Parallels 3.5 The Geometry of Euclid's Elements: D. Triangle Similarity and Circles in Books 6 and 3 -- 3.6 Exercises -- References -- 4 Conics in Greek Geometry: Apollonius, Harmonic Division, and Later Greek Geometry -- 4.1 Conic Sections in Ancient Greece -- 4.2 The Conics of Apollonius -- 4.3 Harmonic Division of a Segment -- 4.4 Conics and the Harmonic Relation -- 4.5 Late Antiquity and Steps Toward Projective Geometry -- 4.6 Notes and Exercises -- 4.7 Some Solutions -- References -- 5 Conic Sections in Early Modern Europe. First Part: Philippe de la Hire on Circles -- 5.1 Philippe de la Hire 5.2 On Circles: La Hire's First 17 Lemmas of 1673 -- 5.3 Notes and Exercises -- References -- 6 Conic Sections in Early Modern Europe. Second Part: Philippe de la Hire on Conics -- 6.1 Plani-Coniques -- 6.2 Conic Properties Developed by La Hire, 1673 -- 6.3 Notes and Exercises -- 6.4 Some Hints and Solutions -- References -- 7 Central Collineations: Complete Quadrilateral, Involution, and Hexagon Theorems -- 7.1 The Complete Quadrilateral -- 7.2 Involution -- 7.3 Collineations that Map a Circle to a Circle -- 7.4 Theorems of Pascal and Brianchon -- 7.5 Notes and Exercises 7.6 Some Hints and Solutions -- References -- 8 Nineteenth Century -- 8.1 Monge and Carnot: Steps Toward Projective Geometry -- 8.2 Jean-Victor Poncelet -- 8.3 Dilations and the Inverse Homologue -- 8.4 The Ideal Common Secant and Homology, 1813 -- 8.5 More Material in Poncelet's Cahiers of 1813-1814 -- 8.6 Poncelet's Traité of 1822 -- 8.7 Poncelet in 1822: Inverse Homologues, the Common Secant as Axis and Vanishing Line -- 8.8 Notes and Exercises -- References -- 9 Foci -- 9.1 Foci Before Poncelet -- 9.2 Foci in Poncelet and Chasles -- References … (more)
- Publisher Details:
- Cham : Springer
- Publication Date:
- 2020
- Extent:
- 1 online resource (189 pages)
- Subjects:
- 516/.5
Geometry, Projective -- History
Mathematics -- History
Electronic books - Languages:
- English
- ISBNs:
- 9783030462871
3030462870 - Related ISBNs:
- 9783030462864
3030462862 - Notes:
- Note: Includes bibliographical references and index.
Note: Description based on print version record. - Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.550298
- Ingest File:
- 03_167.xml