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1.

図書

図書
by W.W. Rouse Ball
出版情報: London : Macmillan, 1888  xxiii, 464 p. ; 20 cm
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2.

図書

図書
by Florian Cajori
出版情報: New York : Macmillan, 1924, c1919  viii, 516 p. ; 22 cm
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3.

図書

図書
by E.T. Bell
出版情報: New York : McGraw-Hill, c1951  xx, 437 p. ; 21 cm
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4.

図書

図書
John Stillwell
出版情報: New York : Springer, c2002  xviii, 542 p. ; 24 cm
シリーズ名: Undergraduate texts in mathematics
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5.

図書

図書
by Henry B. Fine
出版情報: New York : G.E. Stechert, 1937  ix, 131 p. ; 20 cm
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6.

図書

図書
by Sir Thomas L. Heath
出版情報: Mineola, N.Y. : Dover Publications, 2003  xvi, 552 p. ; 22 cm
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目次情報: 続きを見る
Introductory / I.:
Classification of mathematical subjects
Mathematics in Greek education
Numerical Notation and Practical Calculation / II.:
The decimal system
Egyptian numerical notation
Babylonian systems
Greek numerical notation
The 'Herodianic' or 'Attic' system / (a):
The ordinary alphabetic numerals / (b):
Notation for large numbers / (c):
Archimedes' system for large numbers ('octads') / (d):
Fractions
Sexagesimal fractions
Practical calculation
The abacus / ([alpha]):
Addition and subtraction / ([beta]):
Multiplication / ([gamma]):
Division / ([delta]):
Extraction of square root / ([epsilon]):
Pythagorean Arithmetic / III.:
Definitions of the unit and of number
Classification of numbers
'Perfect' and 'Friendly' numbers
Figured numbers
Triangular numbers
Square numbers and gnomons
Gnomons of the polygonal numbers
Right-angled triangles with sides in rational numbers
Oblong numbers / (e):
The theory of proportion and means
Geometric Means
The irrational
Algebraic equations
Indeterminate equations of the second degree 2x[superscript 2] - y[superscript 2] = [plus or minus]1
Epanthema of Thymaridas
Equation xy = 2(x+y)
Manuals of 'Arithmetic'
Nicomachus of Gerasa
Sum of series of cube numbers
Theon of Smyrna
Iamblichus
The Earliest Greek Geometry. Thales / IV.:
The 'Summary' of Proclus
Egyptian geometry (mensuration)
Thales
Measurement of height of pyramid
Geometrical theorems
Thales as astronomer
From Thales to Pythagoras
Anaximander
Pythagorean Geometry / V.:
Sum of angles of any triangle equal to two right angles
The 'Theorem of Pythagoras'
Application of areas and geometrical algebra
The five regular solids
Pythagorean astronomy / ([zeta]):
Summary
Progress in the Elements Down to Plato's Time / VI.:
Anaxagoras
Oenopides of Chios
Democritus
Hippias of Elis
Hippocrates of Chios
Quadratures of lunes
Reduction of the problem of doubling the cube
The Elements as known to Hippocrates
Theodorus of Cyrene
Theaetetus
Archytas of Taras
Special Problems / VII.:
The Squaring of the Circle
The quadratrix of Hippias
The spiral of Archimedes
Solutions by Apollonius and Carpus
Ancient approximations to [pi]
The Trisection of any Angle
Reduction to a [characters not reproducible] solved by conics
The conchoids of Nicomedes
Another reduction to a [characters not reproducible]
Solution by means of conics
The Duplication of the Cube, or the Problem of the two Mean Proportionals
Archytas
Eudoxus
Menaechmus
Solution attributed to Plato
Eratosthenes
Nicomedes
Apollonius, Heron, Philon of Byzantium
Diocles and the cissoid
Sporus and Pappus
From Plato to Euclid / VIII.:
Plato and the philosophy of mathematics
The hypotheses of mathematics
Definitions
Summary of the mathematics in Plato
Geometric means
The two geometrical passages in the Meno
Solution in integers of x[superscript 2] + y[superscript 2] = z[superscript 2]
Incommensurables
Plato's astronomy
Successors of Plato
Heraclides of Pontus
Eudoxus of Cnidos
Hypothesis of concentric spheres
Theory of proportion
The Method of Exhaustion
Zeno's paradoxes
Aristotle
Sphaeric. Autolycus of Pitane
Euclid / IX.:
The Elements
Euclid's other Works
The Data
On Divisions (of Figures)
Pseudaria. Porisms
Conics. Surface-Loci
Phaenomena. Optics
Catoptrica
Musical treatises
Supposed mechanical works
Aristarchus of Samos / X.:
Anticipation of Copernicus
On the sizes and distances of the Sun and Moon
Archimedes / XI.:
Extant works
Other reputed works
Text and editions
The Method
On the Sphere and Cylinder
Measurement of a Circle
On Conoids and Spheroids
On Spirals
Plane Equilibriums
The Sand-reckoner
Quadrature of a Parabola
On Floating Bodies
The Cattle-Problem
On semi-regular solids
'Liber assumptorum'
On the regular heptagon in a circle
Measurement of the earth
Conic Sections / XII.:
Discovery of conics by Menaechmus
Euclid and Aristaeus
Apollonius of Perga
The Conics
Sectio Rationis
Sectio Spatii
On Determinate Section
Contacts or Tangencies
Circle touching three circles
Plane Loci
[characters not reproducible], Inclinationes
Other works
The Successors of the Great Geometers / XIII.:
Diocles
The Fragmentum mathematicum Bobiense
Perseus and 'spiric sections'
Zenodorus
Hypsicles
Dionysodorus
Posidonius
Geminus
Trigonometry: Hipparchus, Menelaus, Ptolemy / XIV.:
Theodosius' Sphaerica
Hipparchus
Discovery of precession
On the Length of the Year
Trigonometry
Menelaus of Alexandria
Sphaerica
Ptolemy
The Syntaxis
Preparation of Table of Chords
Mensuration: Heron of Alexandria / XV.:
Heron's date
List of works
Commentary on Euclid
Mensuration
The Metrica
Area of triangle in terms of sides
Approximations to surds
Areas of regular polygons
Measurement of solids
On divisions of figures
Quadratic equations
On the Dioptra
Mechanics
Pappus of Alexandria / XVI.:
Date and works
The Collection
Editions
On problem of two mean proportionals / Books I, II:
On Means
'Paradoxes' of Erycinus
On five regular solids
Extension of Pythagoras' Theorem / Book IV:
Problems on the [characters not reproducible]
On spirals, conchoids, and the quadratrix
A spiral on a sphere
On the trisection of any angle
On isoperimetry: digression on bees and honeycombs / Book V:
On the sphere and cylinder
Comparison of five regular solids
On astronomical treatises / Book VI:
On works forming 'Treasury of Analysis' / Book VII:
Extension of notion of locus with respect to three or four lines (Pappus' Problem)
'Theorem of Guldin' anticipated
Lemmas to treatises of Apollonius and Euclid
Mechanics: historical preface / Book VIII:
On centre of gravity
Construction of conic through five points
Problem of seven equal hexagons in a circle
Algebra: Diophantus of Alexandria / XVII.:
Egyptian anticipations of algebra
Problems in Anthology
Indeterminate problems, first degree
Indeterminate problems from MS. of Heron's Metrica
Diophantus
The Arithmetica
Lost Books. 'Porisms'
Commentaries and editions
Notation: sign for unknown and its powers
sign for minus
Diophantus' treatment of equations
Determinate Equations / A.:
'Pure' equations / (1):
'Mixed' quadratics / (2):
Simultaneous equations involving quadratics / (3):
Indeterminate equations / B.:
Equations of second degree
Single equation
Double equation
Of first degree
Of second degree
Equations of degree higher than second
Single equations
Expressions to be made squares / (i):
Expressions to be made cubes / (ii):
Double equations
Method of approximation to limits
Porisms and propositions in the theory of numbers
Numbers as the sum of two, three, or four squares
Characteristic examples and solutions
Rational right-angled triangles
Treatise on Polygonal Numbers
Commentators and Minor Writers / XVIII.:
Cleomedes
Serenus of Antinoeia
Theon of Alexandria
Hypatia
Proclus
Domninus of Larissa
Simplicius
Eutocius
Anthemius of Tralles
Additional Notes / Appendix:
Egyptian mathematics / 1.:
Ancient Babylonian mathematics / 2.:
Hipparchus and Chaldaean astronomy / 3.:
Indices
Greek
English
Introductory / I.:
Classification of mathematical subjects
Mathematics in Greek education
7.

図書

図書
Uta C. Merzbach, Carl B. Boyer
出版情報: Hoboken, N.J. : Wiley, c2011  xx, 668 p. ; 24 cm
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目次情報: 続きを見る
Foreword
Preface to the First Edition
Preface to the Second Edition
Traces / 1:
Concepts and Relationships
Early Number Bases
Number Language and Counting
Spatial Relationships
Ancient Egypt / 2:
The Era and the Sources
Numbers and Fractions
Arithmetic Operations
"Heap" Problems
Geometric Problems
Slope Problems
Arithmetic Pragmatism
Mesopotamia / 3:
Cuneiform Writing
Numbers and Fractions; Sexagesimals
Positional Numeration
Sexagesimal Fractions
Approximations
Tables
Equations
Measurements: Pythagorean Triads
Polygonal Areas
Geometry as Applied Arithmetic
Hellenic Traditions / 4:
Thales and Pythagoras
Numeration
Arithmetic and Logistic
Fifth Century Athens
Three Classical Problems
Incommensurability
Paradoxes of Zeno
Deductive Reasoning
Democritus of Abdera
Mathematics and the Liberal Arts
The Academy
Aristotle
Euclid of Alexandria / 5:
Alexandria
Lost Works
Extant Works
The Elements
Archimedes of Syracuse / 6:
The Siege of Syracuse
On the Equilibriums of Planes
On Floating Bodies
The Sand-Reckoner
Measurement of the Circle
On Spirals
Quadrature of the Parabola
On Conoids and Spheroids
On the Sphere and Cylinder
Book of Lemmas
Semiregular Solids and Trigonometry
The Method
Apollonius of Perge / 7:
Works and Tradition
Cycles and Epicycles
The Conics
Cross-Currents / 8:
Changing Trends
Eratosthenes
Angles and Chords
Ptolemy's Almagest
Heron of Alexandria
Decline of Greek Mathematics
Nichomachus of Gerasa
Diophantus of Alexandria
Pappus of Alexandria
The End of Alexandrian Dominance
Proclus of Alexandria
Boethius
Athenian Fragments
Byzantine Mathematicians
Ancient and Medieval China / 9:
The Oldest Known Texts
The Nine Chapters
Rod Numerals
The Abacus and Decimal Fractions
Values of Pi
Thirteenth-Century Mathematics
Ancient and Medieval India / 10:
Early Mathematics in India
The Sulbasutras
The Siddhantas
Aryabhata
Numerals
Trigonometry
Multiplication
Long Division
Brahmagupta
Indeterminate Equations
Bhaskara
Madhava and the Keralese School
The Islamic Hegemony / 11:
Arabic Conquests
The House of Wisdom
al-Khwarizmi
'Abd Al-Hamid ibn-Turk
Thabit ibn Qurra
Abu'l-Wefa and Al-Karkhi
Al-Biruni and Alhazen
Omar Khayyam
The Parallel Postulate
Nasir al-Din al-Tusi
Al-Kashi
The Latin West / 12:
Introduction
Compendia of the Dark Ages
Gerbert
The Century of Translation
Abacists and Algorists
Fibonacci
Jordanus Nemorarius
Campanus of Novara
Learning in the Thirteenth Century
Archimedes Revived
Medieval Kinematics
Thomas Bradwardine
Nicole Oresme
The Latitude of Forms
Infinite Series
Levi ben Gerson
Nicholas of Cusa
Decline of Medieval Learning
The European Renaissance / 13:
Overview
Regiomontanus
Nicolas Chuquet's Triparty
Luca Pacioli's Summa
German Algebras and Arithmetics
Cardan's Ars Magna
Rafael Bombelli
Robert Recorde
Geometry
Renaissance Trends
François Viète
Early Modern Problem Solvers / 14:
Accessibility of Computation
Decimal Fractions
Notation
Logarithms
Mathematical Instruments
The Infinite and Italian Curves / 15:
Infinitesimal Methods: Stevin
Johannes Kepler
Galileo's Two New Sciences
Bonaventura Cavalieri
Evangelista Torricelli
Analysis, Synthesis, and Numbers / 16:
Mersenne's Communicants
Descartes
Fermat's Loci
Gregory of St. Vincent
Theory of Numbers
Gilles Persone de Roberval
Girard Desargues and Projective Geometry
Blaise Pascal
Philippe de Lahire
Georg Mohr
Pietro Mengoli
Frans van Schooten
Jan de Witt
Johann Hudde
René François de Sluse
Christiaan Huygens
Newton and British Techniques / 17:
John Wallis
James Gregory
Nicolaus Mercator and William Brouncker
Barrow's Method of Tangents
Newton
Abraham De Moivre
Leibniz and Continental Methods / 18:
Leibniz: Early Career and Travels
The Bernoulli Family
Tschirnhaus Transformations
Solid Analytic Geometry
Michel Rolle and Pierre Varignon
The Clairauts
Mathematics in Italy
Divergent Series
Euler / 19:
Life of Euler
Foundation of Analysis
Logarithms and the Euler Identities
Differential Equations
Probability
Textbooks
Analytic Geometry
The Parallel Postulate: Lambert
Pre- to Post-Revolutionary France / 20:
Men and Institutions
The Committee on Weights and Measures
D?Alembert
B\x{0082}zout
Condorcet
Lagrange
Monge
Carnot
Laplace
Legendre
Aspects of Abstraction
Paris in the 1820s
Fourier
Cauchy
Diffusion
Gauss / 21:
Nineteenth-Century Overview
Gauss: Early Work
Number Theory
Reception of the Disquisitiones Arithmeticae
Astronomy
Gauss's Middle Years
Differential Geometry
Gauss's Later Work
Gauss's Influence
The School of Monge / 22:
Projective Geometry: Poncelet and Chasles
Synthetic Metric Geometry: Steiner
Synthetic Nonmetric Geometry: von Staudt
Non-Euclidean Geometry
Riemannian Geometry
Spaces of Higher Dimensions
Felix Klein
Post-Riemannian Algebraic Geometry
Algebra / 23:
British Algebra and the Operational Calculus of Functions
Boole and the Algebra of Logic
Augustus De Morgan
William Rowan Hamilton
Grassmann and Ausdehnungslehre
Cayley and Sylvester
Linear Associative Algebras
Algebraic Geometry
Algebraic and Arithmetic Integers
Axioms of Arithmetic
Analysis / 24:
Berlin and Göttingen at Mid-Century
Riemann in Göttingen
Mathematical Physics in Germany
Mathematical Physics in English-Speaking Countries
Weierstrass and Students
The Arithmetization of Analysis
Dedekind
Cantor and Kronecker
Analysis in France
Poincaé and Hilbert / 25:
Turn-of-the-Century Overview
Poincar\x{0082}
Hilbert
Twentieth Century Legacies: Pre-1930 / 26:
General Overview
Integration and Measure
Functional Analysis and General Topology
Differential Geometry and Tensor Analysis
Bounds and Approximations
Twentieth Century Legacies: Post-1930 / 27:
The 1930s and World War II
Homological Algebra and Category Theory
Bourbaki
Logic and Computing
Recent Trends / 28:
The Four Color Conjecture
Classification of Finite Simple Groups
Fermat's Last Theorem
Poincaré's Query
Future Outlook
References
General Bibliography
Index
Foreword
Preface to the First Edition
Preface to the Second Edition
8.

図書

図書
by George Sarton
出版情報: New York : Dover, c1936  112, 75 p. ; 21 cm
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9.

図書

図書
Kurt Reidemeister
出版情報: Berlin : Springer, 1957  vi, 151 p. ; 23 cm
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10.

図書

図書
by Wooster Woodruff Beman ... and David Eugene Smith ...
出版情報: Chicago : The Open court publishing company, 1900  xii, 333 p ; 21 cm
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