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1.

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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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
2.

図書

図書
Reviel Netz
出版情報: Cambridge ; New York : Cambridge University Press, 1999  xvii, 327 p. ; 24 cm
シリーズ名: Ideas in context / edited by Quentin Skinner (general editor) ... [et al.] ; 51
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Introduction: a specimen of Greek mathematics
The lettered diagram / 1:
The pragmatics of letters / 2:
The mathematical lexicon / 3:
Formulae / 4:
The shaping of necessity / 5:
The shaping of generality / 6:
The historical setting / 7:
Appendix: the main Greek mathematicians cited in the book
Introduction: a specimen of Greek mathematics
The lettered diagram / 1:
The pragmatics of letters / 2:
3.

図書

図書
translated from the text of Heiberg, with introduction and commentary by Sir Thomas L. Heath
出版情報: New York : Dover Publications, 1956  3 v. ; 20 cm
シリーズ名: Dover science books
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4.

図書

図書
[translated by Sir Thomas L. Heath] . [translated by Sir Thomas L. Heath] . by Apollonius of Perga ; [translated by R. Catesby Taliaferro] . by Nichomachus of Gerasa ; [translated by Martin L. D'Ooge]
出版情報: Chicago : Encyclopædia Britannica, c1952  xi, 848 p. ; 25 cm
シリーズ名: Great books of the Western World / Robert Maynard Hutchins, editor in chief ; 11
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5.

図書

図書
B. L. van der Waerden : English translation by Arnold Dresden with additions of the author
出版情報: Groningen : P. Noordhoff, [1954-74]  2 v ; 26 cm
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6.

図書

図書
Jacques Sesiano
出版情報: New York ; Heidelberg : Springer-Verlag, c1982  xii, 502 p. ; 25 cm
シリーズ名: Sources in the history of mathematics and physical sciences ; 3
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7.

図書

図書
by E.J. Dijksterhuis ; translated by C. Dikshoorn ; with a new bibliographic essay by Wilbur R. Knorr
出版情報: Princeton, N.J. : Princeton University Press, c1987  457 p. ; 24 cm
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8.

図書

図書
[translated by Thomas L. Heath] . [translated by Thomas L. Heath] . by Nichomachus ; [translated by Martin L. D'Ooge]
出版情報: Chicago : Encyclopædia Britannica, c1990  xi, 636 p. ; 24 cm
シリーズ名: Great books of the Western World / Mortimer J. Adler, editor in chief ; 10
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9.

図書

図書
Jacob Klein ; Translated by Eva Brann. With an appendix containing Vieta's Introduction to the analytical art, translated by J. Winfree Smith
出版情報: Cambridge, Mass. : M.I.T. Press, c1968  xv, 360 p. ; 21 cm
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10.

図書

図書
Proclus ; translated with introduction and notes by Glenn R. Morrow
出版情報: Princeton, N.J. : Princeton University Press, 1970  xlv, 355 p. ; 24 cm
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