Descriptive Geometry, The Spread of a Polytechnic Art

1. Front Matter

   Pages i-xxvi

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2. First Spreading in Southern Europe

   1. Front Matter

      Pages 1-1

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   2. Monge’s Descriptive Geometry: His Lessons and the Teachings Given by Lacroix and Hachette

      • Évelyne Barbin

      Pages 3-18

   3. Descriptive Geometry in France: Circulation, Transformation, Recognition (1795–1905)

      • Évelyne Barbin

      Pages 19-38

   4. Descriptive Geometry in Italy in the Nineteenth Century: Spread, Popularization, Teaching

      • Roberto Scoth

      Pages 39-55

   5. Luigi Cremona and Wilhelm Fiedler: The Link Between Descriptive and Projective Geometry in Technical Instruction

      • Marta Menghini

      Pages 57-68

   6. Descriptive Geometry in the Nineteenth-Century Spain: From Monge to Cirodde

      • Elena Ausejo

      Pages 69-80

   7. Descriptive Geometry in Spain as an Example of the Emergence of the Late Modern Outlook on the Relationship Between Science and Technology

      • Ana Millán Gasca

      Pages 81-96

   8. Portuguese Textbooks on Descriptive Geometry

      • Eliana Manuel Pinho, José Carlos Santos, João Pedro Xavier

      Pages 97-111

   9. In Pursuit of Monge’s Ideal: The Introduction of Descriptive Geometry in the Educational Institutions of Greece During the Nineteenth Century

      • Christine Phili

      Pages 113-135

3. Installation of Descriptive Geometry in Europe

   1. Front Matter

      Pages 137-137

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   2. A German Interpreting of Descriptive Geometry and Polytechnic

      • Nadine Benstein

      Pages 139-166

   3. Otto Wilhelm Fiedler and the Synthesis of Projective and Descriptive Geometry

      • Klaus Volkert

      Pages 167-180

   4. The Evolution of Descriptive Geometry in Austria

      • Hellmuth Stachel

      Pages 181-195

   5. The Vienna School of Descriptive Geometry

      • Christa Binder

      Pages 197-209

   6. At the Crossroads of Two Engineering Cultures, or an Unedited Story of the French Polytechnician Charles Potier’s Descriptive Geometry Books in Russia

      • Dmitri Gouzevitch, Irina Gouzevitch, Nikolaj Eliseev

      Pages 211-231

   7. Engineering Studies and Secondary Education: Descriptive Geometry in the Netherlands (1820–1960)

      • Jenneke Krüger

      Pages 233-253

   8. The Rise and Fall of Descriptive Geometry in Denmark

      • Jesper Lützen

      Pages 255-274

   9. Descriptive Geometry in Czech Technical Universities Before 1939

      • Vlasta Moravcová

      Pages 275-293

   10. The Love Affair with Descriptive Geometry: Its History in Serbia

       • Katarina Jevtić-Novaković, Snezana Lawrence

       Pages 295-311

This book seeks to explore the history of descriptive geometry in relation to its circulation in the 19th century, which had been favoured by the transfers of the model of the École Polytechnique to other countries. The book also covers the diffusion of its teaching from higher instruction to technical and secondary teaching. In relation to that, there is analysis of the role of the institution – similar but definitely not identical in the different countries – in the field under consideration. The book contains chapters focused on different countries, areas, and institutions, written by specialists of the history of the field. Insights on descriptive geometry are provided in the context of the mathematical aspect, the aspect of teaching in particular to non-mathematicians, and the institutions themselves. 

• History of Mathematics
• History of Mathematical Teaching
• Internationalization of Mathematics in 19th century
• Polytechnic schools
• Descriptive Geometry in France
• Descriptive Geometry in Italy
• Descriptive and Projective Geometry in Technical Instruction
• Descriptive Geometry in 19th Century Spain
• Late modern European outlook on science and technology
• Descriptive Geometry in Austria
• Otto Wilhelm Fiedler
• Engineering Studies and Secondary Education
• Descriptive Geometry in the Netherlands
• Descriptive Geometry in the Educational Institutions in Greece
• The Rise and Fall of Descriptive Geometry in Denmark
• Descriptive Geometry at Czech Technical Universities
• Descriptive Geometry in America and Africa
• The Myth of the Polytechnic School

“I learned much from this book and it caused me to reflect on various aspects of mathematics education in ways I would have not have before. … I warmly recommend mathematics educators to include Évelyne Barbin, Marta Menghini, and Klaus Volkert’s volume on their bookshelves.” (Michael N. Fried,Educational Studies in Mathematics, Vol. 106, 2021)

• UFR Sciences et Techniques, Nantes, France

  Évelyne Barbin

• Department of Mathematics, Sapienza–University of Rome, Rome, Italy

  Marta Menghini

• University of Wuppertal, Wuppertal, Germany

  Klaus Volkert

Evelyne Barbin was previously a professor of epistemology and history of sciences at the University of Nantes (France). Since 2014, she is now professor emeritus at the University of Nantes. She is a member of the Laboratory of Mathematics Jean Leray CNRS UMR 6629, where she is in charge of the research group on history of mathematics. She taught history of mathematics and sciences in all levels of teaching from licence to master. She was the director of 15 theses on the history of mathematics and sciences. Her research concerns three fields: history of mathematics, history of mathematics teachings, and relations between history and teaching of mathematics. The main themes of her historical research are: mathematical proofs in history, mathematics and sciences in the 17th and 19th centuries, and history of mathematics teaching from the 19th to the 20th century. She has worked at the IREM (Institute for Research on Mathematics Education) since 1975. As convenor of the National Committee of the IREM “Epistemology and History of Mathematics”, she has organized 20 national colloquia, 8 interdisciplinary Summer Universities on history and teaching mathematics, and the first European Summer University (ESU) "Epistemology and History in Mathematics Education" in 1993. She was chair of seven ESUs from 1996 to 2014. Since 1980, she has also been a member of the International Study Group on the Relations between History and Pedagogy of Mathematics (HPM). She was the chair of HPM from 2008 to 2012.

Marta Menghini is an associate professor in the Department of Mathematics of the University of Rome Sapienza. She is the author of numerous published works in the fields of Mathematics Education, History of Mathematics, and the History of Mathematics Education. She was in the Scientific Committee and chaired the Organizing Committee of the International Symposium held in Rome in March 2008, “The First Century of the InternationalCommission on Mathematical Instruction: Reflecting and Shaping the World of Mathematics Education”, and edited the volume published on this occasion by Enciclopedia Italiana. In 2012, she held a Regular Lecture at ICME 12 in Seoul. She wrote, with Evelyne Barbin, the Chapter on “History of Teaching Geometry” in the International Handbook on the History of Mathematics Education. She was involved in the translation of Felix Klein’s third volume on “Elementary Mathematics from a Higher Standpoint”, which appeared in 2016.

Klaus Volkert is a full professor at the University of Wuppertal; he lectures on mathematics, didactics, and history. His interests are mainly in the history of geometry and topology, and recently he started a project on Wilhelm Fiedler. He is Editor in Chief of the journal “Mathematische Semesterberichte” (together with J. Steuding) and editor of the series “Mathematik im Kontext” (with David Rowe).

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