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.
...MoreBook De Risi, Vincenzo (2015) Mathematizing Space: The Objects of Geometry from Antiquity to the Early Modern Age.
Similar Citations
Article
Krol, Z.;
(2006)
Ancient Geometry and Plato's Philosophy on the Base of Pappus' “Comment on the Xth Book of Elements of Euclid”
(/isis/citation/CBB000931646/)
Chapter
Vitrac, Bernard;
(2012)
The Euclidean Ideal of Proof in The Elements and Philological Uncertainties of Heiberg's Edition of the Text
(/isis/citation/CBB001320139/)
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
Shoji, Kota;
(2006)
The Contact of Differential Geometry and Continuous Groups of Transformations: W. Killing's “Ueber die Grundlagen der Geometrie”
(/isis/citation/CBB000772578/)
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/)
Be the first to comment!