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The Ancient Greek World

Victor J. Katz and Karen Hunger Parshall

in Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691149059
eISBN:
9781400850525
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149059.003.0003
Subject:
Mathematics, History of Mathematics

This chapter focuses on the mathematicians of Ancient Greece; more specifically, on the elements of geometrical algebra present in the works of Euclid and Apollonius, as well as the propositions of ... More


Knowledge and Non-Contradiction

Bryson Brown

in The Law of Non-Contradiction

Published in print:
2004
Published Online:
May 2010
ISBN:
9780199265176
eISBN:
9780191713989
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199265176.003.0009
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

This chapter examines the status of the Law of Non-Contradiction (LNC) by means of an examination of the epistemology of logic. It argues that reasoning that tolerates contradictions, in the sense of ... More


Frege on Knowing the Foundation (1998)

TYLER BURGE

in Truth, Thought, Reason: Essays on Frege

Published in print:
2005
Published Online:
May 2010
ISBN:
9780199278534
eISBN:
9780191706943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199278534.003.0010
Subject:
Philosophy, History of Philosophy, Philosophy of Language

In reasoning about justification of the basic principles of logic and mathematics, Frege combined a traditional Euclidean conception with a more modern pragmatic one. In thinking of the self-evidence ... More


The Science of Logic

Jonathan Barnes

in Truth, etc.: Six Lectures on Ancient Logic

Published in print:
2009
Published Online:
October 2011
ISBN:
9780199568178
eISBN:
9780191702037
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199568178.003.0005
Subject:
Philosophy, Ancient Philosophy, Logic/Philosophy of Mathematics

In his Elements, Euclid first sets down certain primary truths or axioms and then deduces from them a number of secondary truths or theorems. Before ever Euclid wrote, Aristotle had described and ... More


Diagram‐Based Geometric Practice

Kenneth Manders

in The Philosophy of Mathematical Practice

Published in print:
2008
Published Online:
February 2010
ISBN:
9780199296453
eISBN:
9780191711961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296453.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter provides a survey of issues about diagrams in traditional geometrical reasoning. After briefly refuting several common philosophical objections, and giving a sketch of diagram-based ... More


The Euclidean Diagram (1995)

Kenneth Manders

in The Philosophy of Mathematical Practice

Published in print:
2008
Published Online:
February 2010
ISBN:
9780199296453
eISBN:
9780191711961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296453.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter gives a detailed study of diagram-based reasoning in Euclidean plane geometry (Books I, III), as well as an exploration how to characterise a geometric practice. First, an account is ... More


Epilogue

Demetris Nicolaides

in In Search of a Theory of Everything: The Philosophy Behind Physics

Published in print:
2020
Published Online:
July 2020
ISBN:
9780190098353
eISBN:
9780190098384
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190098353.003.0016
Subject:
Physics, History of Physics

Our quest for knowledge began with our evolution as a species 200,000 years ago. We hunted and gathered, painted on caves, told stories, domesticated animals and plants, wondered about nature, gave ... More


Science and Mathematics in Ancient Greek Culture

C. J. Tuplin and T. E. Rihll (eds)

Published in print:
2002
Published Online:
February 2010
ISBN:
9780198152484
eISBN:
9780191710049
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198152484.001.0001
Subject:
Classical Studies, European History: BCE to 500CE

Ancient Greece was the birthplace of science, which developed in the Hellenised culture of ancient Rome. This volume locates science within ancient Greek society and culture, explores the cultural ... More


A Geometric Strategy

John P. Burgess and Gideon Rosen

in A Subject With No Object: Strategies for Nominalistic Interpretation of Mathematics

Published in print:
1999
Published Online:
November 2003
ISBN:
9780198250128
eISBN:
9780191597138
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198250126.003.0003
Subject:
Philosophy, Logic/Philosophy of Mathematics

Develops in some detail a strategy of nominalistic interpretation that assumes that points of spacetime are legitimate, concrete, physical entities. What makes the strategy possible is the fact that ... More


Proclus on Mathematics

Dominic J. O'Meara

in Pythagoras Revived: Mathematics and Philosophy in Late Antiquity

Published in print:
1990
Published Online:
April 2004
ISBN:
9780198239130
eISBN:
9780191600937
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198239130.003.0009
Subject:
Philosophy, Ancient Philosophy

Proclus's use, in his commentary on Euclid, of Iamblichus's work On Pythagoreanism book III is examined, as are his views on general mathematics, on the importance of geometry in relation to ... More


The imperial road to geometry: new Elements of geometry

Catherine Jami

in The Emperor's New Mathematics: Western Learning and Imperial Authority During the Kangxi Reign (1662-1722)

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199601400
eISBN:
9780191729218
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199601400.003.0009
Subject:
Mathematics, History of Mathematics

This chapter focuses on the French Jesuits' work as translators of a recent geometry textbook, which was substituted for the 1607 translation of Euclid in teaching Kangxi. Significantly, this book ... More


Euclid's Elements 9. 14 and the Fundamental Theorem of Arithmetic

C. M. Taisbak

in Science and Mathematics in Ancient Greek Culture

Published in print:
2002
Published Online:
February 2010
ISBN:
9780198152484
eISBN:
9780191710049
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198152484.003.0013
Subject:
Classical Studies, European History: BCE to 500CE

This chapter clarifies some unfamiliar concepts of Euclidean number theory and examines the bricks, constituents, and formative elements of numbers. It also considers three famous propositions from ... More


Geometry

Nicholas Griffin

in Russell’s Idealist Apprenticeship

Published in print:
1991
Published Online:
March 2012
ISBN:
9780198244530
eISBN:
9780191680786
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198244530.003.0004
Subject:
Philosophy, History of Philosophy

This chapter discusses Russell's fellowship dissertation on the philosophy of geometry. It has been stated in this chapter that Russell had no exceptional fondness for the topic, and that his ... More


Joyce and Geometry

Ciaran McMorran

Published in print:
2020
Published Online:
September 2020
ISBN:
9780813066288
eISBN:
9780813065267
Item type:
book
Publisher:
University Press of Florida
DOI:
10.5744/florida/9780813066288.001.0001
Subject:
Literature, 20th-century Literature and Modernism

Following the development of non-Euclidean geometries from the mid-nineteenth century onwards, Euclid’s system came to be re-conceived as a language for describing reality rather than a set of ... More


Early Ideas

John C. H. Spence

in Lightspeed: The Ghostly Aether and the Race to Measure the Speed of Light

Published in print:
2019
Published Online:
October 2019
ISBN:
9780198841968
eISBN:
9780191878084
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198841968.003.0001
Subject:
Physics, Atomic, Laser, and Optical Physics, History of Physics

Mankind’s early ideas about the speed of light, the Aether (supposed to fill the universe) and the instantaneous “action at a distance” theory, before the speed of light was first measured. Euclid’s ... More


Space: A History

Andrew Janiak (ed.)

Published in print:
2020
Published Online:
April 2020
ISBN:
9780199914104
eISBN:
9780190090579
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199914104.001.0001
Subject:
Philosophy, Metaphysics/Epistemology, History of Philosophy

This volume chronicles the development of philosophical conceptions of space from early antiquity through the medieval period to the early modern era, ending with Kant. The chapters describe the ... More


Allegory and Science: From Euclid to the Search for Fundamental Structures in Modern Physics

James J. Paxson

in Thinking Allegory Otherwise

Published in print:
2009
Published Online:
June 2013
ISBN:
9780804763806
eISBN:
9780804773508
Item type:
chapter
Publisher:
Stanford University Press
DOI:
10.11126/stanford/9780804763806.003.0012
Subject:
Literature, Criticism/Theory

In his 1993 study of Gottfried Wilhelm von Leibniz's monadology and baroque aesthetics entitled The Fold, Gilles Deleuze argues that mathematics is the inscription of the literal, indeed, that ... More


Geometry

Robin Wilson

in The Mathematical World of Charles L. Dodgson (Lewis Carroll)

Published in print:
2019
Published Online:
April 2019
ISBN:
9780198817000
eISBN:
9780191858697
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198817000.003.0002
Subject:
Mathematics, History of Mathematics

This chapter presents Dodgson’s geometrical work, and in particular his interest in Euclid’s Elements. It describes the contents and structure of this work and considers the various Victorian ... More


Non-Euclidean Geometry

Jeremy Gray

in Space: A History

Published in print:
2020
Published Online:
April 2020
ISBN:
9780199914104
eISBN:
9780190090579
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199914104.003.0013
Subject:
Philosophy, Metaphysics/Epistemology, History of Philosophy

Non-Euclidean geometry began as an inquiry into a possible weakness in Euclid’s Elements and became the source of the ideas that there are geometries of spaces other than the one imagined in ... More


The Elements

Nicholas Mee

in Celestial Tapestry: The Warp and Weft of Art and Mathematics

Published in print:
2020
Published Online:
September 2020
ISBN:
9780198851950
eISBN:
9780191886690
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198851950.003.0004
Subject:
Physics, History of Physics

Chapter 3 moves from the elements of the physical world to the elements of abstract geometry as set out in Euclid’s Elements. It looks at Euclid’s axiomatic method of building geometry step by step ... More


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