IsisCB Explore

Article ID: CBB063608507

Some remarks concerning the trisection of an angle. Euclid between Pappus and Viète (2023)

Alvarez Jimenez, Carlos (Author)

Almagest
Volume: 14
Issue: 2
Pages: 76-97
Publication date: 2023
Language: English

DOI: 10.1484/J.ALMA.5.136760

URI: https://www.brepolsonline.net/doi/abs/10.1484/J.ALMA.5.136760

Outside Links

WorldCat

Google Scholar

JSTOR

Algebra Geometry 16th century Ancient France Greece Viète, François de la Bigotière Pappus of Alexandria Euclid

The trisection of an angle as an old geometric problem has been studied by historians of mathematics for a long time. In this paper we recover partially the history of this well-known geometric problem, trying to find not only a possible common ground under the different methods employed for its solution, through neusis procedures or using conic sections, but trying to show that the algebraic solution by means of cubic equation mainly provides an answer to another geometric problem posed by Euclid in Book I of the Elements.

...More

Included in

Article Vincent Jullien; Carmen Martínez-Adame (2023) Foreward. Almagest (pp. 6-14). unapi

Citation URI

data.isiscb.org/p/isis/citation/CBB063608507

This citation is part of the Isis database.

Citations Indexes

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” (/p/isis/citation/CBB000931646/)

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

Book Sefrin-Weis, Heike; (2010)
Pappus of Alexandria: Book 4 of the Collection (/p/isis/citation/CBB001024842/)

Thesis La Nave, Federica; (2005)
Belief Without Proof from Ancient Geometry to Renaissance Algebra (/p/isis/citation/CBB001560809/)

Article Høyrup, Jens; (2001)
On a Collection of Geometrical Riddles and their Role in the Shaping of Four to Six “Algebras” (/p/isis/citation/CBB000102557/)

Book Leo Corry; (2022)
British Versions of Book II of Euclid’s Elements: Geometry, Arithmetic, Algebra (1550–1750) (/p/isis/citation/CBB193067062/)

Article Acerbi, Fabio; (2009)
The Meaning of [Greek transliteration begin]plasmatikon[Greek transliteration end] in Diophantus' Arithmetica (/p/isis/citation/CBB000932071/)

Article Mateusz Hohol; Marcin Miłkowski; (2019)
Cognitive Artifacts for Geometric Reasoning (/p/isis/citation/CBB220742953/)

Article Vincenzo De Risi; (2022)
Euclid’s Fourth Postulate: Its authenticity and significance for the foundations of Greek mathematics (/p/isis/citation/CBB852153445/)

Article Webster, Colin; (2014)
Euclid's Optics and Geometrical Astronomy (/p/isis/citation/CBB001451440/)

Article Mueller, Ian; (2003)
Remarks on Euclid's Elements I, 32 and the Parallel Postulate (/p/isis/citation/CBB000740732/)

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

Article Aboav, David; (2008)
Euclid's Book on Divisions of Figures: A Conjecture as to Its Origin (/p/isis/citation/CBB000850606/)

Article Saito, Ken; (2012)
Traditions of the Diagram, Tradition of the Text: A Case Study (/p/isis/citation/CBB001211476/)

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

Book Euclid, ; (2001)
Euclide d'Alexandrie. Les Éléments. Traduit du texte de Heiberg, Volume 4, Livres XI-XIII: Géométrie des Solides (/p/isis/citation/CBB000101225/)

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

Book Suppes, Patrick; Moravcsik, Julius M.; Mendell, Henry; (2000)
Ancient & Medieval Traditions in the Exact Sciences: Essays in Memory of Wilbur Knorr (/p/isis/citation/CBB000101823/)

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

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