From Here to Infinity

• Verfasst von: Del Centina, Andrea [VerfasserIn]
• Verfasst von: Gimigliano, Alessandro [VerfasserIn]
• Titel: From Here to Infinity
• Titelzusatz: Tracing the Origin and Development of Projective Geometry
• Verf.angabe: by Andrea Del Centina, Alessandro Gimigliano
• Ausgabe: 1st ed. 2025.
• Verlagsort: Cham
• Verlagsort: Cham
• Verlag: Springer Nature Switzerland
• Verlag: Imprint: Springer
• E-Jahr: 2025
• Jahr: 2025.
• Jahr: 2025.
• Umfang: 1 Online-Ressource(XLII, 788 p. 448 illus.)
• Gesamttitel/Reihe: Sources and Studies in the History of Mathematics and Physical Sciences
• ISBN: 978-3-031-72585-2
• DOI: doi:10.1007/978-3-031-72585-2
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• K10plus-PPN: 1919516093
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

- 1. The Greek Legacy -- 2. Perspective in the Renaissance -- 3. New ways of looking at conics -- 4. Desargues, the dawn of projective geometry -- 5. Pascal’s geometrical achievements -- 6. An interlude a century and a half long -- 7. Towards a new geometry -- 8. Poncelet, the projective properties of figures -- 9. The algebraic way to projective geometry -- 10. The synthetic route: the contributions of Steiner and Chasles -- 11. Von Staudt’s pure synthetism -- 12. Projective geometry 1870-1930 and beyond.

Abstract

This monograph traces the development of projective geometry from its Greek origins to the early 20th century. It covers Renaissance perspective studies and insights from the late sixteenth to seventeenth centuries, examining the contributions of Desargues and Pascal. Most of the book is devoted to the evolution of the subject in the 19th century, from Carnot to von Staudt. In particular, the book offers an unusually thorough appreciation of Brianchon's work, a detailed study of Poncelet's innovations, and a remarkable account of the contributions of Möbius and Plücker. It also addresses the difficult question of the historical relationship between synthetic and analytic points of view in geometry, analyzing the work of prominent synthetic geometers Steiner, Chasles, and von Staudt in detail. The book concludes around 1930, after the synthetic point of view was axiomatized and the analytic point of view became intertwined with algebraic geometry. Balancing historical analysis with technical precision and providing deep insights into the evolution of the mathematics, this richly illustrated book serves as a central reference on the history of projective geometry.