Sialaros, Michalis (Author)
Christianidis, Jean P. (Author)
The aim of this paper is to employ the newly contextualized historiographical category of “premodern algebra” in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on “geometrical algebra.” Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related to Elem. II.5 as a case study, we discuss Euclid's geometrical proofs, the so-called “semi-algebraic” alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing “premodern algebra,” and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition.
...More
Article
Vincenzo De Risi;
(2021)
Euclid’s Common Notions and the Theory of Equivalence
(/isis/citation/CBB348431913/)
Article
Nathan Sidoli;
(2018)
The Concept of Given in Greek Mathematics
(/isis/citation/CBB871621734/)
Article
Tybjerg, Karin;
(2004)
Hero of Alexandria's Mechanical Geometry
(/isis/citation/CBB000502305/)
Book
David S. Richeson;
(2019)
Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity
(/isis/citation/CBB243851906/)
Book
Folkerts, Menso;
(2006)
The Development of Mathematics in Medieval Europe: The Arabs, Euclid, Regiomontanus
(/isis/citation/CBB000610313/)
Book
Matthew Wickman;
(2016)
Literature After Euclid: The Geometric Imagination in the Long Scottish Enlightenment
(/isis/citation/CBB932449151/)
Article
De Young, Gregg;
(2012)
Mathematical Diagrams from Manuscript to Print: Examples from the Arabic Euclidean Transmission
(/isis/citation/CBB001211477/)
Article
Harari, Orna;
(2003)
The Concept of Existence and the Role of Constructions in Euclid's Elements
(/isis/citation/CBB000300433/)
Article
Vincenzo De Risi;
(2016)
The Development of Euclidean Axiomatics
(/isis/citation/CBB819223565/)
Article
Young, Gregg de;
(2004)
The Latin Translation of Euclid's Elements Attributed to Gerard of Cremona in Relation to the Arabic Transmission
(/isis/citation/CBB000931713/)
Article
Virginia Iommi Echeverría;
(2016)
Copernicus and the Problem of Elemental Proportion in Renaissance Cosmology
(/isis/citation/CBB912586648/)
Article
Marcella Giulia Lorenzi;
Mauro Francaviglia;
(2010)
Dal cosmo al numero e alla geometria euclidea
(/isis/citation/CBB384645759/)
Article
Fabio Bellissima;
(2011)
L'antanairesi e la teoria armonica greca
(/isis/citation/CBB718056038/)
Book
Berlinski, David;
(2013)
The King of Infinite Space: Euclid and His Elements
(/isis/citation/CBB001213232/)
Article
Fennane, Khalid Bouzoubaâ;
(2003)
Réflexions sur le principe de continuité à partir du commentaire d'ibn al-Haythem sur la proposition 1.7 Des Éléments d'Euclide
(/isis/citation/CBB000340503/)
Article
Webster, Colin;
(2014)
Euclid's Optics and Geometrical Astronomy
(/isis/citation/CBB001451440/)
Article
Johnston, Stephen;
(2012)
John Dee on Geometry: Texts, Teaching and the Euclidean Tradition
(/isis/citation/CBB001251143/)
Chapter
Rommevaux, Sabine;
(2004)
Les prologues aux éditions des Eléments d'Euclide au Moyen Age et à la Renaissance
(/isis/citation/CBB000640965/)
Book
Euclid, ;
Taisbak, Christian Marinus;
(2003)
Dedomena---Euclid's Data, or, The Importance of Being Given
(/isis/citation/CBB000301663/)
Article
Camerota, Filippo;
(2006)
Teaching Euclid in a Practical Context: Linear Perspective and Practical Geometry
(/isis/citation/CBB000671073/)
Be the first to comment!