## 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