An introduction to the history of mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia u.a.
Saunders College Publ.
1983
|
| Ausgabe: | 5. ed. |
| Schriftenreihe: | The Saunders series.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 593 S. Ill., graph. Darst. |
| ISBN: | 0030620643 |
Internformat
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| 100 | 1 | |a Eves, Howard W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to the history of mathematics |c Howard Eves |
| 250 | |a 5. ed. | ||
| 264 | 1 | |a Philadelphia u.a. |b Saunders College Publ. |c 1983 | |
| 300 | |a XVIII, 593 S. |b Ill., graph. Darst. | ||
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| 650 | 4 | |a Mathématiques - Histoire | |
| 650 | 4 | |a Geschichte | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics |x History | |
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Datensatz im Suchindex
| _version_ | 1804117267195101184 |
|---|---|
| adam_text | CONTEXTS
PREFACE V
INTRODUCTION XVI
Part One before the seventee th ceivtury i
ONE NUMERAL SYSTEMS 2
1 1 Primitive Counting; 1 2 Number Bases; 1 3 Written Number
Systems; 1 4 Simple Grouping Systems; 1 5 Multiplicative Group¬
ing Systems; 1 6 Ciphered Numeral Systems; 1 7 Positional Num¬
eral Systems; 1 8 Early Computing; 1 9 The Hindu Arabic Numeral
System; 1 10 Arbitrary Bases
Problem Studies 16
1.1 Number Words; 1.2 Written Numbers; 1.3 Alphabetic Greek
Numeral System; 1.4 Old and Hypothetical Numeral Systems; 1.5
Finger Numbers; 1.6 Radix Fractions; 1.7 Arithmetic in Other
Scales; 1.8 Problems in Scales of Notation; 1.9 Some Recreational
Aspects of the Binary Scale; 1.10 Some Number Tricks
Essay Topics 20
Bibliography 20
TWO BABYLONIAN AND EGYPTIAN MATHEMATICS 22
2 1 The Ancient Orient; BABYLONIA; 2 2 Sources; 2 3 Commer¬
cial and Agrarian Mathematics; 2 4 Geometry; 2 5 Algebra; 2 6
Plimpton 322; EGYPT: 2 7 Sources and Dates; 2 8 Arithmetic and
Algebra; 2 9 Geometry; 2 10 A Curious Problem in the Rhind
Papyrus
Problem Studies 36
2.1 Regular Numbers; 2.2 Compound Interest; 2.3 Quadratic Equa¬
tions; 2.4 Algebraic Geometry; 2.5 The Susa Tablets; 2.6 Cubics;
2.7 Square Root Approximations; 2.8 Duplation and Mediation; 2.9
Unit Fractions; 2.10 The Sylvester Process; 2.11 The Seqt of a Pyra¬
mid; 2.12 Egyptian Algebra; 2.13 Egyptian Geometry; 2.14 The
Greatest Egyptian Pyramid; 2.15 Some Problems from the Moscow
Papyrus; 2.16 The 3, 4, 5 Triangle
Essay Topics 43
Bibliography 44
VII
VIII Contents
THREE PYTHAGOREAN MATHEMATICS 45
3 1 Birth of Demonstrative Mathematics; 3 2 Pythagoras and the
Pythagoreans; 3 3 Pythagorean Arithmetic; 3 4 Pythagorean The¬
orem and Pythagorean Triples; 3 5 Discovery of Irrational Magni¬
tudes; 3 6 Algebraic Identities; 3 7 Geometric Solution of Quadratic
Equations; 3 8 Transformation of Areas; 3 9 The Regular Solids;
3 10 Postulational Thinking
Problem Studies 64
3.1 The Practical Problems of Thales; 3.2 Perfect and Amicable
Numbers; 3.3 Figurate Numbers; 3.4 Means; 3.5 Dissection Proofs
of the Pythagorean Theorem; 3.6 Pythagorean Triples; 3.7 Irrational
Numbers; 3.8 Algebraic Identities; 3.9 Geometric Algebra; 3.10
Geometric Solution of Quadratic Equations; 3.11 Transformation of
Areas; 3.12 Regular Solids; 3.13 Some Problems Concerning the
Regular Solids; 3.14 Golden Section; 3.15 An Interesting Relation
Essay Topics 72
Bibliography 72
FOUR DUPLICATION, TRISECTION,
AND QUADRATURE 74
4 1 The Period from Thales to Euclid; 4 2 Lines of Mathematical
Development; 4 3 The Three Famous Problems; 4 4 The Euclidean
Tools; 4 5 Duplication of the Cube; 4 6 Trisection of an Angle; 4 7
Quadrature of the Circle; 4 8 A Chronology of n
Problem Studies 90
4.1 Euclidean and Modern Compasses; 4.2 Duplication by Archytas
and Menaechmus; 4.3 Duplication by Apollonius and Eratosthenes;
4.4 The Cissoid of Diodes; 4.5 Some Seventeenth Century Duplica¬
tions; 4 6 Applications of the Insertion Principle; 4.7 The Conchoid
of Nicomedes; 4.8 Trisection by Conies; 4.9 Asymptotic Euclidean
Constructions; 4.10 The Quadratrix; 4.11 Approximate Rectification;
4.12 Lunes of Hippocrates; 4.13 Computation of tt; 4.14 The Snell
Refinement; 4.15 Mnemonics for n
Essay Topics 98
Bibliography 98
FIVE EUCLID AND HIS ELEMENTS 100
5 1 Alexandria; 5 2 Euclid; 5 3 Euclid s Elements ; 5 4 Content
of the Elements ; 5 5 The Theory of Proportion; 5 6 Regular Poly¬
gons; 5 7 Formal Aspect of the Elements ; 5 8 Euclid s Other
Works
Problem Studies 113
5.1 The Euclidean Algorithm; 5.2 Applications of the Euclidean Al¬
gorithm; 5.3 The Pythagorean Theorem; 5.4 Euclid s Book 0; 5.5
Applications of the Fundamental Theorem of Arithmetic; 5.6 The
Eudoxian Theory of Proportion; 5.7 Regular Polygons; 5.8 The
Angle Sum of a Triangle; 5.9 A Deductive Sequence Concerning
Areas; 5.10 A Deductive Sequence Concerning Angles; 5 il Ele¬
ments; 5.12 Data; 5.13 Constructions Employing Data; 5.14 Divisions
Contents IX
Essay Topics 119
Bibliography 119
SIX GREEK MATHEMATICS AFTER EUCLID 121
6 1 Historical Setting; 6.2 Archimedes; 6 3 Eratosthenes; 6 4 Apol
lonius; 6 5 Hipparchus, Menelaus, Ptolemy, and Greek Trigo¬
nometry; 6 6 Heron; 6 7 Ancient Greek Algebra; 6 8 Diophantus;
6 9 Pappus; 6 10 The Commentators
Problem Studies 140
6.1 Measurements by Aristarchus and Eratosthenes; 6.2 On the
Sphere and Cylinder; 6.3 The Problem of the Crown; 6.4 The
Arbelos and the Salinon; 6.5 The Theorem of the Broken Chord; 6.6
The Focus Directrix Property; 6.7 Tangencies; 6.8 Problems from
Apollonius; 6.9 Ptolemy s Table of Chords; 6.10 Stereographic Pro¬
jection; 6.11 Problems from Heron; 6.12 Simultaneous Equations;
6.13 Problems from the Greek Anthology ; 6.14 Type Problems
from the Greek Anthology ; 6.15 Diophantus; 6.16 Some Number
Theory in the Arithmetica ; 6.17 Problems from Pappus; 6.18 The
Centroid Theorems; 6.19 The Trammel Construction of an Ellipse; 6.20
The Theorem of Menelaus; 6.21 More on Means
Essay Topics 154
Bibiography 155
SEVEN CHIME SE, HINDU, AND
ARABIAN MATHEMATICS 156
CHINA; 7 1 Sources and Periods; 7 2 From the Chou to the Tang;
7 3 From the Tang through the Ming; INDIA: 7 4 General Survey;
7 5 Number Computing; 7 6 Arithmetic and Algebra; 7 7 Geome¬
try and Trigonometry; 7 8 Contrast Between Greek and Hindu Mathe¬
matics; ARABIA: 7 9 The Rise of Moslem Culture; 7 10 Arithmetic
and Algebra; 7 11 Geometry and Trigonometry; 7 12 Some Etymol¬
ogy; 7 13 The Arabian Contribution
Problem Studies 178
7.1 Some Problems from the Arithmetic in Nine Sections ; 7.2 The
Pythagorean Theorem; 7.3 Magic Squares; 7.4 Some Early
Hindu Problems; 7.5 Problems from Mahavira; 7.6 Problems from
Bhaskara; 7.7 Quadratic Surds; 7.8 Indeterminate Equations of
the First Degree; 7.9 The Diagonals of a Cyclic Quadrilateral;
7.10 Brahmagupta s Quadrilaterals; 7.11 Tabit ibn Qorra, al Karkhi,
and Nasir ed din; 7.12 Casting Out 9 s; 7.13 Casting Out ll s;
7.14 Double False Position; 7.15 Khayyam s Solution of Cubics;
7.16 A Geometric Solution of Cubics; 7.17 Geometrical Constructions
on a Sphere
Essay Topics 187
Bibliography 188
EIGHT EUROPEAN MATHEMATICS, 500 to 1600 189
8 1 The Dark Ages; 8 2 The Period of Transmission; 8 3 Fibonacci
and the Thirteenth Century; 8 4 The Fourteenth Century; 8 5 The
Fifteenth Century; 8 6 The Early Arithmetics; 8 7 Beginnings of
Algebraic Symbolism; 8 8 Cubic and Quartic Equations; 8 9 Frangois
Viete; 8 10 Other Mathematicians of the Sixteenth Century
X Contents
Problem Studies 209
8.1 Problems from the Dark Ages; 8.2 The Fibonacci Sequence;
8.3 Problems from the Liber abaci ; 8.4 Further Problems of
Fibonacci; 8.5 Star Polygons; 8.6 Tordanus and Cusa; 8.7 Diirer
and Magic Squares of Doubly Even Order; 8.8 Problems from Regio
montanus; 8.9 Problems from Chuquet; 8.10 Problems from Pacioli;
8.11 Early Commercial Problems; 8.12 The Gelosia and Galley Algo¬
rithms; 8.13 Gematria and Arithmography; 8.14 Cubic Equations;
8.15 Quartic Equations; 8 16 Sixteenth Century Notation; 8.17 Pro
lems from Viete; 8 18 Problems from Clavius; 8.19 Some Geometry
Essay Topics 220
Bibliography 221
Part Two the seventeenth century and after 223
NINE THE DAWN OF MODERN MATHEMATICS 224
9 1 The Seventeeth Century; 9 2 Napier; 9 3 Logarithms; 9 4 The
Savilian and Lucasian Professorships; 9 5 Harriot and Oughtred;
9 6 Galileo; 9 7 Kepler; 9 8 Desargues; 9 9 Pascal
Problem Studies 246
9.1 Logarithms; 9.2 Napier and Spherical Trigonometry;
9.3 Napier s Rods; 9.4 The Slide Rule; 9.5 Freely Falling Bodies;
9.6 Sector Compasses; 9.7 Some Simple Paradoxes from Galileo s
Discorsi ; 9.8 Kepler s Laws; 9.9 Mosaics; 9.10 Proving
Theorems by Projection; 9.11 Pascal s Youthful Empirical Proof ;
9.12 Pascal s Theorem; 9.13 Pascal s Triangle
Essay Topics 256
Bibliography 256
TEN ANALYTIC GEOMETRY AND OTHER
PRECALCULUS DEVELOPMENTS 258
10 1 Analytic Geometry; 10 2 Descartes; 10 3 Fermat; 10 4 Rober
val and Torricelli; 10 5 Huygens; 10 6 Some Seventeenth Century
Mathematicians of France and Italy; 10 7 Some Seventeenth Century
Mathematicians of Germany and the Low Countries; 10 8 Some Sev¬
enteenth Century British Mathematicians
Problem Studies 279
10.1 Geometric Algebra; 10.2 Descartes s La geometrie ; 10.3
Descartes s Rule of Signs; 10.4 Problems from Descartes; 10.5 Fer
mat s Theorems; 10.6 The Problem of the Points; 10.7 Problems from
Huygens; 10.8 Higher Plane Curves; 10.9 Recreational Problems
from Bachet; 10.10 Some Geometry; 10.11 Computation of Log¬
arithms by Series
Essay Topics 285
Bibliography 285
Contents XI
ELEVEN THE CALCULUS AND RELATED CONCEPTS 287
11 1 Introduction; 11 2 Zeno s Paradoxes; 11 3 Eudoxus Method of
Exhaustion; 11 4 Archimedes Method of Equilibrium; 11 5 The Be¬
ginnings of Integration in Western Europe; 11 6 Cavalieri s Method of
Indivisibles; 11 7 The Beginning of Differentiation; 11 8 Wallis and
Barrow; 11 9 Newton; 11 10 Leibniz
Problem Studies 311
11.1 The Method of Exhaustion; 11.2 The Method of Equilibrium; 11.3
Some Archimedean Problems; 11.4 The Method of Indivisibles; 11.5
The Prismoidal Formula; 11.6 Differentiation; 11.7 The Binomial
Theorem; 11.8 An Upper Bound for the Roots of a Polynomial Equa¬
tion; 11.9 Approximate Solution of Equations; 11.10 Algebra of
Classes
Essay Topics 316
Bibliography 317
TWELVE THE EIGHTEENTH CENTURY AND THE
EXPLOITATION OF THE CALCULUS 319
12 1 Introduction and Apology; 12 2 The Bernoulli Family; 12 3
De Moivre and Probability; 12 4 Taylor and Maclaurin; 12 5 Euler; 12 6
Clairaut, d Alembert, and Lambert; 12 7 Lagrange; 12 8 Laplace and
Legendre; 12 9 Monge and Carnot; 12 10 The Metric System; 12 11
Summary
Problem Studies 344
12.1 Bernoulli Numbers; 12.2 De Moivre s Formula; 12.3 Distribu¬
tions; 12.4 Formal Manipulation of Series; 12.5 A Conjecture and a
Paradox; 12.6 Euler and an Infinite Series; 12.7 Orbiform Curves;
12.8 Unicursal and Multicursal Graphs; 12.9 Some Differential
Equations; 12.10 Hyperbolic Functions; 12.11 Lagrange and Analytic
Geometry; 12.12 Buffon s Needle Problem; 12.13 Random Chord in a
Circle; 12.14 The Method of Least Squares; 12.15 Some Mongean
Geometry; 12.16 Sensed Magnitudes; 12.17 Carnot s Theorem
Essay Topics 355
Bibliography 356
THIRTEEN THE EARLY NINETEENTH CENTURY AND THE
LIBERATION OF GEOMETRY AND ALGEBRA 357
13 1 The Prince of Mathematicians; 13 2 Fourier and Poisson; 13 3
Cauchy; 13 4 Abel and Galois; 13 5 Jacobi and Dirichlet; 13 6 Non
Euclidean Geometry; 13 7 The Emergence of Algebraic Structure;
13 8 The Liberation of Algebra; 13 9 Hamilton, Grassmann, Boole,
and De Morgan; 13 10 Cayley, Sylvester, and Hermite; 13 11 Aca¬
demies, Societies, and Periodicals
Problem Studies 392
13.1 The Fundamental Theorem of Algebra; 13.2 Basic Properties of
Congruence; 13.3 Gauss and Numbers; 13.4 Fourier Series; 13.5
Cauchy and Infinite Series; 13.6 Group Theory; 13.7 Examples of
Groups; 13.8 Abelian Groups; 13.9 Saccheri Quadrilaterals; 13.10
The Hypothesis of the Acute Angle; 13.11 A Euclidean Model for
Hyperbolic Geometry; 13.12 Non Euclidean Geometry and Physical
Space; 13.13 Systems with a Common Algebraic Structure; 13.14
XII Contents
Algebraic Laws; 13.15 More on Algebraic Laws; 13.16 Complex
Numbers as Ordered Pairs of Real Numbers; 13.17 Quaternions; 13.18
Matrices; 13.19 Jordan and Lie Algebras; 13.20 Vectors; 13.21 An
Interesting Algebra; 13.22 A Point Algebra; 13.23 An Infinite Non
Abelian Group; 13.24 The Hamiltonian Game
Essay Topics 403
Bibliography 403
FOURTEEN THE LATER NINETEENTH CENTURY AND
THE ARTTHMETIZATION OF ANALYSIS 405
14 1 Sequel to Euclid; 14 2 Impossibility of Solving the Three Fa¬
mous Problems with Euclidean Tools; 14 3 Compasses or Straight¬
edge Alone; 14 4 Projective Geometry; 14 5 Analytic Geometry;
14 6 N dimensional Geometry; 14 7 Differential Geometry;
14 8 The Erlanger Programm of Felix Klein; 14 9 The Arithmetiza
tion of Analysis; 14 10 Weierstrass and Riemann; 14 11 Cantor,
Kronecker, and Poincare; 14 12 Sonja Kovalevsky and Emmy Noether;
14 13 The Prime Numbers
Problem Studies 437
14.1 The Feuerbach Configuration; 14.2 Commandino s Theorem;
14.3 The Altitudes of a Tetrahedron; 14.4 Space Analogs; 14.5
Isogonal Elements; 14.6 Impossible Constructions; 14.7 Some Ap¬
proximate Constructions; 14.8 Mascheroni Construction Theorem;
14.9 Constructions with Straightedge and Rusty Compasses; 14.10
Lemoine s Geometrography; 14.11 Principle of Duality; 14.12 A Self
Dual Postulate Set for Projective Geometry; 14.13 Principle of Duality
of Trigonometry; 14.14 Coordinate Systems; 14.15 Line Coordinates;
14.16 Dimensionality; 14.17 Abridged Notation; 14.18 Homoge¬
neous Coordinates; 14.19 Pliicker s Numbers; 14.20 N dimensional
Geometry; 14.21 Gaussian Curvature; 14.22 The Tractoid; 14.23
The Erlanger Programm; 14.24 Mysticism and Absurdity in the Early
Calculus; 14.25 Early Difficulties with Infinite Series; 14.26 Some
Paradoxes in Elementary Algebra; 14.27 Some Paradoxes in Calculus;
14.28 A Continuous Curve Having No Tangents; 14.29 Algebraic
and Transcendental Numbers; 14.30 Prime Numbers
Essay Topics 454
Bibliography 455
FIFTEEN ABSTRACTION AND THE TRANSITION INTO
THE TWENTIETH CENTURY 457
15 1 Logical Shortcomings of Euclid s Elements ; 15 2 Axiomatics;
15 3 The Evolution of Some Basic Concepts; 15 4 Transfinite Num¬
bers; 15 5 Topology; 15 6 Mathematical Logic; 15 7 Antinomies of
Set Theory; 15 8 Philosophies of Mathematics; 15 9 Computers;
15 10 The New Math and Bourbaki; 15 11 The Tree of Mathematics
Problem Studies 493
15.1 Tacit Assumptions Made by Euclid; 15.2 Three Geometrical Par¬
adoxes; 15.3 Dedekind s Continuity Postulate; 15.4 A Coordinate
Interpretation of Euclid s Postulates; 15.5 A Spherical Interpretation
of Euclid s Postulates; 15.6 Pasch s Postulate; 15.7 An Abstract
Mathematical System; 15.8 Axiomatics; 15.9 Associated Hypotheti¬
cal Propositions; 15.10 Intuition versus Proof; 15.11 A Miniature
Mathematical System; 15.12 A Set of Inconsistent Statements; 15.13 A
Contents XIII
Postulate Set Related to Relativity Theory; 15.14 Bees and Hives;
15.15 Metric Space; 15.16 Equivalent Segments; 15.17 Some De
numerable and Nondenumerable Sets; 15.18 Polynomials of Heights
1, 2, 3, 4, and 5; 15.19 The Measure of a Denumerable Set of Points;
15.20 Transfinite Numbers and Dimension Theory; 15.21 Circles
and Lines; 15.22 Homeomorphic Surfaces; 15.23 Sides and Edges;
15.24 Paradromic Rings; 15.25 Polyhedral Surfaces; 15.26 Faces
and Vertices of Polyhedral Surfaces; 15.27 Hausdorff Space;
15.28 Allied Propositions; 15.29 Three Valued Logics; 15.30 The
Russell Paradox; 15.31 A Paradox; 15.32 Some Dilemmas and Some
Questions; 15.33 Recreational Mathematics
Essay Topics 506
Bibliography 507
GENERAL BIBLIOGRAPHY 512
A CHRONOLOGICAL TABLE 514
ANSWERS AND SUGGESTIONS FOR THE SOLUTION
OF THE PROBLEM STUDIES 522
INDEX 553
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| genre | 1\p (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV002976663 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:51:41Z |
| institution | BVB |
| isbn | 0030620643 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001863581 |
| oclc_num | 8785912 |
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| physical | XVIII, 593 S. Ill., graph. Darst. |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Saunders College Publ. |
| record_format | marc |
| series2 | The Saunders series. |
| spelling | Eves, Howard W. Verfasser aut An introduction to the history of mathematics Howard Eves 5. ed. Philadelphia u.a. Saunders College Publ. 1983 XVIII, 593 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Saunders series. Geschichte gnd rswk-swf Mathématiques - Histoire Geschichte Mathematik Mathematics History Mathematik (DE-588)4037944-9 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Mathematik (DE-588)4037944-9 s Geschichte (DE-588)4020517-4 s DE-604 Geschichte z 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001863581&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Eves, Howard W. An introduction to the history of mathematics Mathématiques - Histoire Geschichte Mathematik Mathematics History Mathematik (DE-588)4037944-9 gnd Geschichte (DE-588)4020517-4 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4020517-4 (DE-588)4151278-9 |
| title | An introduction to the history of mathematics |
| title_auth | An introduction to the history of mathematics |
| title_exact_search | An introduction to the history of mathematics |
| title_full | An introduction to the history of mathematics Howard Eves |
| title_fullStr | An introduction to the history of mathematics Howard Eves |
| title_full_unstemmed | An introduction to the history of mathematics Howard Eves |
| title_short | An introduction to the history of mathematics |
| title_sort | an introduction to the history of mathematics |
| topic | Mathématiques - Histoire Geschichte Mathematik Mathematics History Mathematik (DE-588)4037944-9 gnd Geschichte (DE-588)4020517-4 gnd |
| topic_facet | Mathématiques - Histoire Geschichte Mathematik Mathematics History Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001863581&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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