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From Here to Infinity : Tracing the Origin and Development of Projective Geometry / by Andrea Del Centina, Alessandro Gimigliano

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Sources and Studies in the History of Mathematics and Physical SciencesPublisher: Cham : Springer Nature Switzerland, 2025Publisher: Cham : Imprint: Springer, 2025Edition: 1st ed. 2025Description: 1 Online-Ressource(XLII, 788 p. 448 illus.)ISBN:
  • 9783031725852
Subject(s): Additional physical formats: 9783031725845 | 9783031725869 | 9783031725876 | Erscheint auch als: 9783031725845 Druck-Ausgabe | Erscheint auch als: 9783031725869 Druck-Ausgabe | Erscheint auch als: 9783031725876 Druck-AusgabeDDC classification:
  • 510.9 23
DOI: DOI: 10.1007/978-3-031-72585-2Online resources: Summary: - 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.Summary: 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.PPN: PPN: 1919516093Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
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