Chapter ID: CBB826243941

A Note on Lines and Planes in Euclid’s Geometry (2015)


The purpose of this note is to remind readers of information at times well-known and at times almost forgotten, namely that for several centuries in the modern West Euclid’s Elements was simultaneously regarded as the epitome of knowledge and as flawed and confused. It is well known that many mathematicians brought up on Euclid and other Greek geometers complained that they found themselves compelled to accept the conclusions but not instructed in how to do geometry, and the long struggle with the parallel postulate has also been frequently discussed. The confusion discussed here is different, and relates to the concepts of straightness and shortest distance. It will also be suggested that the growing awareness of the defects in Euclid’s presentation by the end of the 18th century contributed to the creation of the new geometries of the 19th century: projective geometry and non-Euclidean geometry.

Citation URI

Similar Citations

Book De Risi, Vincenzo; (2015)
Mathematizing Space: The Objects of Geometry from Antiquity to the Early Modern Age (/isis/citation/CBB843280666/)

Article Ambrosi, Gerhard Michael; (2012)
Pre-Euclidean Geometry and Aeginetan Coin Design: Some Further Remarks (/isis/citation/CBB001251104/)

Article Chen, Huiyong; (2011)
Study on the Approach to Realize the Thought of Gauss' Non-Euclidean Geometry (/isis/citation/CBB001210056/)

Article Slowik, Edward; (2003)
Conventionalism in Reid's “Geometry of Visibles” (/isis/citation/CBB000340889/)

Chapter Giulia Giannini; (2009)
Poincaré, la nozione di gruppo e il Programma di Erlangen di F. Klein (/isis/citation/CBB227666735/)

Article Daniele Pasquazi; Benedetto Scoppola; (2021)
Aritmetica euclidea e filosofia stoica (/isis/citation/CBB278285265/)

Article Le Meur, Guy; (2012)
Le rôle des diagrammes dans quelques traités de la Petite astronomie (/isis/citation/CBB001211449/)

Article De Groot, Jean; (2009)
Modes of Explanation in the Aristotelian “Mechanical Problems” (/isis/citation/CBB000932570/)

Article Solere, Jean-Luc; (2003)
L'ordre axiomatique comme modèle d'écriture philosophique dans l'Antiquité et au Moyen Age (/isis/citation/CBB000770963/)

Article Harari, Orna; (2003)
The Concept of Existence and the Role of Constructions in Euclid's Elements (/isis/citation/CBB000300433/)

Article Gunhan Caglayan; (2016)
Exploring the Lunes of Hippocrates in a Dynamic Geometry Environment (/isis/citation/CBB484034654/)

Book David S. Richeson; (2019)
Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity (/isis/citation/CBB243851906/)

Article Geymonat, Mario; (2009)
Arithmetic and Geometry in Ancient Rome: Surveyors, Intellectuals, and Poets (/isis/citation/CBB000933728/)

Article Mode, ; (2007)
A Study of the Editions of Euclid's Elements (II) (/isis/citation/CBB000760544/)

Article Siebert, Harald; (2014)
Transformation of Euclid's Optics in Late Antiquity (/isis/citation/CBB001450115/)

Article Krol, Z.; (2007)
Introduction to Ancient Theories of Proportion (/isis/citation/CBB000931652/)

Article Maria Alessandra Vaccaro; (2020)
Historical Origins of the Nine-Point Conic. the Contribution of Eugenio Beltrami (/isis/citation/CBB706274093/)

Authors & Contributors
Krol, Z.
Harari, Orna
Slowik, Edward S.
Solère, Jean-Luc
Shoji, Kota
Archive for History of Exact Sciences
Kwartalnik Historii Nauki i Techniki
Nuncius: Annali di Storia della Scienza
Studies in History and Philosophy of Science
Nei Menggu Shifan Daxue Xuebao (Ziran Kexue Ban)
Revue d'Histoire des Sciences
Princeton University Press
Springer, AIP Press
Non-euclidean geometry
Transmission of texts
Gauss, Carl Friedrich
Reid, Thomas
Killing, Wilhelm Karl Joseph
Time Periods
19th century
18th century
Alexandria (Egypt)

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment