Jump to ContentJump to Main Navigation

You are looking at 1-10 of 53 items

  • Keywords: geometrical x
Clear All Modify Search

View:

Introduction to Part II

Michael J. White

in The Continuous and the Discrete: Ancient Physical Theories from a Contemporary Perspective

Published in print:
1992
Published Online:
October 2011
ISBN:
9780198239529
eISBN:
9780191679940
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198239529.003.0009
Subject:
Philosophy, Ancient Philosophy, Philosophy of Science

Part II investigates two Hellenistic models of spatial magnitude, time, and motion — models that can be seen as conceptual alternatives to the Aristotelian model considered in some detail in Part I. ... More


Simple Shapes: Vision and Concepts

Marcus Giaquinto

in Visual Thinking in Mathematics

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199285945
eISBN:
9780191713811
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285945.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter focuses on the cognitive resources needed for basic geometry. It argues that the initial geometrical concepts of basic shapes depend on the way we perceive those shapes. In having ... More


Basic Geometrical Knowledge

Marcus Giaquinto

in Visual Thinking in Mathematics

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199285945
eISBN:
9780191713811
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285945.003.0003
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter shows how we might come by a simple geometrical belief without inferring it from other beliefs, in a way that is consonant with the apparent obviousness and cogency of the acquired ... More


Geometrical Discovery by Visualizing

Marcus Giaquinto

in Visual Thinking in Mathematics

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199285945
eISBN:
9780191713811
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285945.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter shows how, using basic beliefs, one can go on to make a geometrical discovery by visual means in a non-empirical manner. It focuses on a simple example in order to illustrate the general ... More


Egypt and Mesopotamia

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/9780691149059.003.0002
Subject:
Mathematics, History of Mathematics

This chapter explores the beginnings of algebra in Egypt and Mesopotamia. They are the earliest civilizations to have left written mathematical records, and they date back thousands of years. From ... More


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


Ancient Greek Mathematics: A Role for Diagrams

José Ferreirós

in Mathematical Knowledge and the Interplay of Practices

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167510
eISBN:
9781400874002
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167510.003.0005
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter focuses on the ancient Greek tradition of geometrical proof in light of recent studies by Kenneth Manders and others. It advances the view that the borderline of elementary mathematics ... More


<i>GL</i>(<i>n</i>) × <i>GL</i>(<i>n</i>) × … × <i>GL</i>(<i>n</i>) Examples

Nicholas M. Katz

in Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153308
eISBN:
9781400842704
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153308.003.0021
Subject:
Mathematics, Number Theory

This chapter investigates the question which begings as follows. Suppose we have a geometrically irreducible middle extension sheaf G on 𝔾ₘ/k which is pure of weight zero, such that the object N := ... More


The Inscrutability of Intrinsic Content

John Foster

in A World for Us: The Case for Phenomenalistic Idealism

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199297139
eISBN:
9780191711398
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199297139.003.0002
Subject:
Philosophy, Moral Philosophy

The realist view of the physical world represents it as something whose existence is logically independent of the human mind and philosophically fundamental. If we retain allegiance to this view, ... More


Locke on Powers: The Geometrical Model

Walter Ott

in Causation and Laws of Nature in Early Modern Philosophy

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199570430
eISBN:
9780191722394
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199570430.003.0021
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

Locke's ontology of relations and powers points to an alternative to the occasionalists' cognitive model of causality. So far, though, this is all it has done; it remains to be seen just how Locke ... More


View: