Something New about the Line (Plato, Republic, Book VI -VII) (original) (raw)

Plato's Divided Line

Franco Trabattoni

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What Did Glaucon Draw?: A Diagrammatic Proof for Plato's Divided Line

Terry Echterling

Journal of the History of Philosophy, 2018

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From Plato's Rational Diameter to Proclus' Elegant Theorem

George Baloglou

2020

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"As if it were evident" : The mathematician in the Line ( Plato, Republic VI 510a-)

Gabrièle Wersinger Taylor

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Euclid's straight lines

Christer Kiselman

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The standard proof, the elegant proof, and the proof without words of tasks in geometry, and their dynamic investigation

Ruti Segal

International Journal of Mathematical Education in Science and Technology, 2016

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New Elements of Euclidean Geometry

Antonio Leon

New Elements of Euclidean Geometry, 2021

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Euclid's straight lines: An experience

Christer Kiselman

2015

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The Two Supreme Principles of Plato’s Cosmos—the One and the Indefinite Dyad—the Division of a Straight Line into Extreme and Mean Ratio, and Pingala’s Mātrāmeru

Maria Antonietta Salamone

Symmetry, 11(1) 98, 2019

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Mathematical Interpretation of Plato's Third Man Argument

George Chailos

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The Theorem of Pappus: A Bridge between Algebra and Geometry

Elena Marchisotto

The American Mathematical Monthly, 2002

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Plato on Geometrical Hypothesis in the Meno

Naoya Iwata

Apeiron, 2015

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Amicus Plato sed...': Fowler's New Mathematical Reconstruction of the Mathematics of Plato's Academy

Sabetai Unguru

Ann Sci, 2002

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Go(Φ)d is Number: Plotting the Divided Line & the Problem of the Irrational

Sandra Kroeker

Athens Journal of Philosophy, 2024

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Review: Theokritos Kouremenos. Plato's Forms, Mathematics and Astronomy. Boston/Berlin: De Gruyter, 2018

Leonid Zhmud

Syzetesis 6.2 (2019) 9-14, 2019

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Homeomeric Lines in Greek Mathematics

Fabio Acerbi

Science in Context, 2010

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An Introduction to the Modern Geometry of the Triangle and the Circle Altshiller Court N. College Geometry (Dover 2007)

Crizel Jean Reyes

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Athens Journal of Humanities and Arts Ideas of Plato in the Context of Contemporary Science and Mathematics

Mark Burgin

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Some Comments On: A Historical Note On The Proof Of The Area Of A Circle

JAIDEEP NAIDU

American Journal of Business Education (AJBE)

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Iconic Proofs more geometrico

Timm Lampert

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Faculty of Natural Sciences Constantine the Philosopher University in Nitra Acta Mathematica 17 49 Selected Geometrical Constructions

Michaela Holešová

2014

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THE FORMATION OF A MYTH: GREEK MATHEMATICS—OUR MATHEMATICS

Jens Hoyrup

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Is one proof enough? Travels with a mathematician of the baroque period

Jean Guy Dhombres

Educational Studies in Mathematics, 1993

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One Theorem, Two Ways: A Case Study in Geometric Techniques

John Little

Journal of humanistic mathematics, 2023

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Plato's Geometrical Logic

Mark Faller

2003

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Philosophical Reflections on the Geometric Proof of Incommensurability

Kevin Cales

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Plato's Use of Geometrical Logic

Mark Faller

2003

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“A Trivial Source of Wonder: Some Mathematical Examples in Plato’s Dialogues”. Archiv für Geschichte der Philosophie, 106.3, 2024, pp. 379–410. https://doi.org/10.1515/agph-2021-0161.

Laura Marongiu

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Advanced Plane Geometry Research 3: Alternative Proofs for the Standard Theorems in Plane Geometry

Indika Shameera Amarasinghe

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In Terms of Athens (Proofs)

Demetra Kasimis

Ramus, 2021

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On the History of Number Line

Galina Sinkevich

2015

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SP.2H3 / ESG.SP2H3 Ancient Philosophy and Mathematics, Fall 2006

Lee Perlman

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Euclidean geometry: foundations and paradoxes

George Mpantes

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A thirteenth century ?proof? of the parallel postulate

Sabetai Unguru

Historia Mathematica, 1978

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Textbooks revealing the development of a concept—the case of the number line in the analytic geometry (1708–1829)

Marcello Amadeo

ZDM: The International Journal on Mathematics Education, 2018

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