| 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 |
図書
