From Here to Infinity: Tracing the Origin and Development of Projective Geometry
暫譯: 從此到無限：追溯射影幾何的起源與發展

del Centina, Andrea, Gimigliano, Alessandro

From Here to Infinity: Tracing the Origin and Development of Projective Geometry
  • 出版商: Springer
  • 出版日期: 2026-03-04
  • 售價: $10,100
  • 貴賓價: 9.5 折 $9,595
  • 語言: 英文
  • 頁數: 788
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031725875
  • ISBN-13: 9783031725876
  • 相關分類: 離散數學 Discrete-mathematics

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商品描述

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.

商品描述(中文翻譯)

這本專著追溯了射影幾何的發展，從其希臘起源到20世紀初。它涵蓋了文藝復興時期的透視研究以及十六世紀末到十七世紀的見解，並探討了德薩爾格（Desargues）和帕斯卡（Pascal）的貢獻。

本書大部分內容專注於19世紀該學科的演變，從卡諾（Carnot）到馮·斯陶特（von Staudt）。特別是，本書對布里昂雄（Brianchon）的工作提供了異常深入的評價，詳細研究了龐塞萊（Poncelet）的創新，並對莫比烏斯（Möbius）和普呂克（Plücker）的貢獻進行了卓越的描述。它還探討了合成與解析幾何觀點之間的歷史關係這一困難問題，詳細分析了著名的合成幾何學家斯坦納（Steiner）、查斯勒（Chasles）和馮·斯陶特的工作。本書結束於1930年左右，當時合成觀點已被公理化，解析觀點則與代數幾何交織在一起。

本書在歷史分析與技術精確性之間取得平衡，並深入洞察數學的演變，這本豐富插圖的書籍作為射影幾何歷史的核心參考資料。

作者簡介

Andrea Del Centina has been full professor at the University of Ferrara, where he taught Higher Geometry from 1990 to his retirement in 2012. Previously he taught Analysis and Geometry at the universities of Florence and Urbino. Del Centina has been working in Algebraic geometry until his retirement, and in this field he is author and co-author of many research articles published in international mathematics Journals. Since 2000, he has been also working in History of mathematics, and he has produced important research articles and books concerning the work and life of N. H. Abel, S. Germain, G. Libri. More recently he has turned his interest to the history of projective geometry, and he had published several papers which appeared in Archive for History of Exact Sciences and Historia Mathematica.

Alessandro Gimigliano (PhD, Queens'University, Kingston, CA) is full professor of Geometry at the University of Bologna since 2000, where he teaches Projective Geometry and History of Mathematics. Previously he taught at the universities of Genoa, Potenza and Rome Tor Vergata. His research is in the fields of Algebraic Geometry, Commutative Algebra and their Applications, with over 50 published research articles in international journals. He is also co-author of two university textbooks.

作者簡介(中文翻譯)

安德烈亞·德爾·琴塔納自1990年至2012年退休期間，擔任費拉拉大學的全職教授，教授高等幾何學。在此之前，他曾在佛羅倫斯大學和烏爾比諾大學教授分析學和幾何學。德爾·琴塔納在代數幾何領域工作至退休，並在該領域發表了多篇研究文章，這些文章刊登於國際數學期刊。自2000年以來，他也開始研究數學史，並撰寫了有關N. H. 阿貝爾、S. 傑曼和G. 利布里的重要研究文章和書籍。最近，他將興趣轉向射影幾何的歷史，並發表了幾篇文章，這些文章出現在《精確科學歷史檔案》和《數學史》期刊上。

亞歷山德羅·吉米利亞諾（博士，女王大學，金斯頓，加拿大）自2000年以來擔任博洛尼亞大學的幾何學全職教授，教授射影幾何和數學史。在此之前，他曾在熱那亞大學、波滕扎大學和羅馬托爾維爾大學任教。他的研究領域包括代數幾何、交換代數及其應用，並在國際期刊上發表了超過50篇研究文章。他也是兩本大學教科書的共同作者。

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