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9. Ideal and Achievement

9. Ideal and Achievement  

Jonathan Barnes

in Aristotle: A Very Short Introduction

Print Publication Year: 
Oct 2000
Published Online: 
Nov 2015
eISBN: 
9780191822322
DOI: 
10.1093/actrade/9780192854087.003.0009
Item type: 
chapter
ISBN: 
9780192854087
Some scholars have disputed that Aristotle was a system-builder. For them, Aristotle’s philosophy is ‘aporetic’: it consists in posing, and developing solutions to, particular puzzles. This ... More
8. Three Specimens of a Method

8. Three Specimens of a Method  

Tom Sorell

in Descartes: A Very Short Introduction

Print Publication Year: 
Oct 2000
Published Online: 
Sep 2013
eISBN: 
9780191776632
DOI: 
10.1093/actrade/9780192854094.003.0008
Item type: 
chapter
ISBN: 
9780192854094
‘Three Specimens of a Method’ discusses three essays: Dioptrics, Meteors, and Geometry, published, together with the Discourse on Methods, in 1637. The literary form of the Discourse and ... More
9. A New ‘Logic’

9. A New ‘Logic’  

Tom Sorell

in Descartes: A Very Short Introduction

Print Publication Year: 
Oct 2000
Published Online: 
Sep 2013
eISBN: 
9780191776632
DOI: 
10.1093/actrade/9780192854094.003.0009
Item type: 
chapter
ISBN: 
9780192854094
‘A New Logic’ points out that the Dioptrics, Meteors, and Geometry were not free-standing treatises but advertisements for a novel method of reasoning in the sciences. The Discourse on ... More
1. Why?

1. Why?  

Glen Van Brummelen

in Trigonometry: A Very Short Introduction

Print Publication Year: 
Jan 2020
Published Online: 
Jan 2020
eISBN: 
9780191851896
DOI: 
10.1093/actrade/9780198814313.003.0001
Item type: 
chapter
ISBN: 
9780198814313
‘Why?’ considers some of the mathematical problems faced by scientists in the past: Hipparchus of Rhodes trying to predict the times of eclipses; Maurice Bressieu, the 16th-century French ... More
5. Dimension

5. Dimension  

Timothy Gowers

in Mathematics: A Very Short Introduction

Print Publication Year: 
Aug 2002
Published Online: 
Sep 2013
eISBN: 
9780191776397
DOI: 
10.1093/actrade/9780192853615.003.0005
Item type: 
chapter
ISBN: 
9780192853615
A notable feature of advanced mathematics is that much of it is concerned with geometry in more than three dimensions. ‘Dimension’ looks at high-dimensional geometry, which is best ... More
6. Geometry

6. Geometry  

Timothy Gowers

in Mathematics: A Very Short Introduction

Print Publication Year: 
Aug 2002
Published Online: 
Sep 2013
eISBN: 
9780191776397
DOI: 
10.1093/actrade/9780192853615.003.0006
Item type: 
chapter
ISBN: 
9780192853615
‘Geometry’ begins with the Euclidean geometry, the geometry with which most people are familiar. Euclid's Elements, written in around 300bc, started with five axioms from which Euclid ... More
Introduction

Introduction  

Ian Stewart

in Infinity: A Very Short Introduction

Print Publication Year: 
Mar 2017
Published Online: 
Mar 2017
eISBN: 
9780191816574
DOI: 
10.1093/actrade/9780198755234.003.0001
Item type: 
chapter
ISBN: 
9780198755234
Why do we need to think about the infinite—a concept we never encounter directly? There are many reasons. Even in elementary mathematics, we encounter aspects of infinity, but more ... More
16. Body

16. Body  

Tom Sorell

in Descartes: A Very Short Introduction

Print Publication Year: 
Oct 2000
Published Online: 
Sep 2013
eISBN: 
9780191776632
DOI: 
10.1093/actrade/9780192854094.003.0016
Item type: 
chapter
ISBN: 
9780192854094
Just as Descartes conceived the mind without attributes involving a body as complete, so a conception of body that omits all properties dependent on a mind was also considered complete. ... More
3. One Science, One Method

3. One Science, One Method  

Tom Sorell

in Descartes: A Very Short Introduction

Print Publication Year: 
Oct 2000
Published Online: 
Sep 2013
eISBN: 
9780191776632
DOI: 
10.1093/actrade/9780192854094.003.0003
Item type: 
chapter
ISBN: 
9780192854094
‘One Science, One Method’ recounts Descartes' growing awareness of the unity under mathematics of many sciences that had previously been regarded as distinct. He became increasingly ... More
1. What is combinatorics?

1. What is combinatorics?  

Robin Wilson

in Combinatorics: A Very Short Introduction

Print Publication Year: 
Apr 2016
Published Online: 
Apr 2016
eISBN: 
9780191790324
DOI: 
10.1093/actrade/9780198723493.003.0001
Item type: 
chapter
ISBN: 
9780198723493
Combinatorics can loosely be described as the branch of mathematics concerned with selecting, arranging, constructing, classifying, and counting or listing things. ‘What is combinatorics?’ ... More
5. To infinity …

5. To infinity …  

Glen Van Brummelen

in Trigonometry: A Very Short Introduction

Print Publication Year: 
Jan 2020
Published Online: 
Jan 2020
eISBN: 
9780191851896
DOI: 
10.1093/actrade/9780198814313.003.0005
Item type: 
chapter
ISBN: 
9780198814313
‘To infinity … ’ looks at how infinite trigonometric series are used to compute π. It shows how Machin’s formula used the inverse tangent series to compute π to a hundred places. Lord ... More
7. Spheres and more

7. Spheres and more  

Glen Van Brummelen

in Trigonometry: A Very Short Introduction

Print Publication Year: 
Jan 2020
Published Online: 
Jan 2020
eISBN: 
9780191851896
DOI: 
10.1093/actrade/9780198814313.003.0007
Item type: 
chapter
ISBN: 
9780198814313
‘Spheres and more’ considers the ten formulas for right-angled spherical triangles (and how they can be generated), the spherical Pythagorean theorem, and Napier’s rules. Spherical ... More
2. Sines, cosines, and their relatives

2. Sines, cosines, and their relatives  

Glen Van Brummelen

in Trigonometry: A Very Short Introduction

Print Publication Year: 
Jan 2020
Published Online: 
Jan 2020
eISBN: 
9780191851896
DOI: 
10.1093/actrade/9780198814313.003.0002
Item type: 
chapter
ISBN: 
9780198814313
‘Sines, cosines, and their relatives’ begins by defining the basic trigonometric functions—sine, cosine, and tangent—and explaining their use. These functions are geometric quantities ... More
Trigonometry: A Very Short Introduction

Trigonometry: A Very Short Introduction  

Glen Van Brummelen

Print Publication Year: 
Jan 2020
Published Online: 
Jan 2020
eISBN: 
9780191851896
DOI: 
10.1093/actrade/9780198814313.001.0001
Item type: 
book
ISBN: 
9780198814313
Trigonometry: A Very Short Introduction draws together the full history of trigonometry, stretching across two millennia and several cultures such as ancient Greece, medieval ... More
Mathematics: A Very Short Introduction

Mathematics: A Very Short Introduction  

Timothy Gowers

Print Publication Year: 
Aug 2002
Published Online: 
Sep 2013
eISBN: 
9780191776397
DOI: 
10.1093/actrade/9780192853615.001.0001
Item type: 
book
ISBN: 
9780192853615
The aim of Mathematics: A Very Short Introduction is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we ... More
7. The nature of things

7. The nature of things  

Julia Annas

in Plato: A Very Short Introduction

Print Publication Year: 
Feb 2003
Published Online: 
Sep 2013
eISBN: 
9780191775505
DOI: 
10.1093/actrade/9780192802163.003.0007
Item type: 
chapter
ISBN: 
9780192802163
‘The nature of things’ examines Plato's understanding of the natural world. In the Timaeus, Plato describes the creation of the world as work done by a divine Craftsman, who does the job by ... More
5. Geometric infinity

5. Geometric infinity  

Ian Stewart

in Infinity: A Very Short Introduction

Print Publication Year: 
Mar 2017
Published Online: 
Mar 2017
eISBN: 
9780191816574
DOI: 
10.1093/actrade/9780198755234.003.0006
Item type: 
chapter
ISBN: 
9780198755234
Much of the philosophical and mathematical fun comes from trying to tease the different meanings apart, and deciding which make sense, and why. A clear example occurs in ‘Geometric ... More
3. Zeno's tortoise

3. Zeno's tortoise  

Catherine Osborne

in Presocratic Philosophy: A Very Short Introduction

Print Publication Year: 
Apr 2004
Published Online: 
Sep 2013
eISBN: 
9780191776267
DOI: 
10.1093/actrade/9780192840943.003.0004
Item type: 
chapter
ISBN: 
9780192840943
‘Zeno's tortoise’ examines Zeno's best-loved paradox, Achilles and the tortoise. Zeno's great innovation, for which he is justly famous, lies in how he persuades us to accept unwelcome ... More
4. ‘Absolutes’, Simple Natures, and Problems

4. ‘Absolutes’, Simple Natures, and Problems  

Tom Sorell

in Descartes: A Very Short Introduction

Print Publication Year: 
Oct 2000
Published Online: 
Sep 2013
eISBN: 
9780191776632
DOI: 
10.1093/actrade/9780192854094.003.0004
Item type: 
chapter
ISBN: 
9780192854094
‘Absolutes, Simple Natures and Problems’ deals mainly with the Regulae, an incomplete treatise which anticipated some of the innovations of the Geometry, and which adapted, in outline, some ... More
Descartes: A Very Short Introduction

Descartes: A Very Short Introduction  

Tom Sorell

Print Publication Year: 
Oct 2000
Published Online: 
Sep 2013
eISBN: 
9780191776632
DOI: 
10.1093/actrade/9780192854094.001.0001
Item type: 
book
ISBN: 
9780192854094
Descartes: A Very Short Introduction explores the life and work of a man who made fundamental contributions to physics, mathematics, and optics, and reported useful ... More

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