Selections illustrating the history of greek mathematics. From Aristarchus to Pappus

Title page
XVI. ARISTARCHUS OF SAMOS
(a) General
(b) Distances of the sun and moon
(c) Continued fractions (?)
XVII. ARCHIMEDES
(a) General
(b) Surface and volume of the cylinder and sphere
(c) Solution of a cubic equation
(d) Conoids and spheroids
(i) Preface
(ii) Two lemmas
(iii) Volume of a segment of a paraboloid of revolution
(e) The spiral of Archimedes
(i) Definitions
(ii) Fundamental property
(iii) A verging
(iv) Property of the subtangent
(f) Semi-regular solids
(g) System of expressing large numbers
(h) Indeterminate analysis: the Cattle Problem
(i) Mechanics: centres of gravity
(i) Postulates
(ii) Principle of the lever
(iii) Centre of gravity of a parallelogram
(j) Mechanical method in geometry
(k) Hydrostatics
(i) Postulates
(ii) Surface of fluid at rest
(iii) Solid immersed in a fluid
(iv) Stability of a paraboloid of revolution
XVIII. ERATOSTHENES
(a) General
(b) On means
(c) The Platonicus
(d) Measurement of the earth
XIX. APOLLONIUS OF PERGA
(a) The conic sections
(i) Relation to previous works
(ii) Scope of the work
(iii) Definitions
(iv) Construction of the sections
(v) Fundamental properties
(vi) Transition to new diameter
(b) Other works
(i) General
(ii) On the Cutting-off of a Ratio
(iii) On the Cutting-off of an Area
(iv) On Determinate Section
(v) On Tangencies
(vi) On Plane Loci
(vii) On Vergings
(viii) On the dodecahedron and the icosahedron
(ix) Principles of mathematics
(x) On the Cochlias
(xi) On unordered irrationals
(xii) Measurement of a circle
(xiii) Continued multiplications
(xiv) On the Burning Mirror
XX. LATER DEVELOPMENTS lN GEOMETRY
(a) Classification of curves
(b) Attempts to prove the parallel postulate
(i) General
(ii) Posidonius and Geminus
(iii) Ptolemy
(iv) Proclus
(c) Isoperimetric figurcs
(d) Division of zodiac circle into 360 parts: Hypsicles
(e) Handbooks
(i) Cleomedes
(ii) Theon of Smyrna
XXI. TRIGONOMETRY
1. Hipparchus and Menelaus
2. Ptolemy
(a) General
(b) Table of sines
(i) Introduction
(ii) sin 18° and sin 36°
(iii) sin²θ + cos²θ = 1
(iv) Ptolemy's theorem
(v) sin(θ-φ) = sinθ cosφ - cosθ sinφ
(vi) sin²(θ/2) = (1 - cosθ)/2
(vii) cos(θ+φ) = cosθ cosφ - sinθ sinφ
(viii) Method of interpolation
(ix) The table
(c) Menelaus's theorem
(i) Lemmas
(ii) The theorem
XXII. MENSURATION: HERON OF ALEXANDRIA
(a) Definitions
(b) Measuremcnt of areas and volumes
(i) Area of a triangle given the sides
(ii) Volume of a spire
(iii) Division of a circle
(iv) Measurement of an irregular area
(c) Mechanics
(d) Optics: equality of angles of incidence and reflection
(e) Quadratic equations
(f) Indeterminate analysis
XXIII. ALGEBRA: DIOPHANTUS
(a) General
(b) Notation
(c) Determinate equations
(i) Pure determinate equations
(ii) Quadratic equations
(iii) Simultaneous equations leading to a quadratic
(iv) Cubic equation
(d) Indeterminate equations
(i) Indeterminate equations of the second degree
(α) Single equations
(β) Double equations
(ii) Indeterminate equations of higher degree
(e) Theory of numbers: sums of squares
(j) Polygonal numbers
XXIV. REVIVAL OF GEOMETRY: PAPPUS OF ALEXANDRIA
(a) General
(b) Problems and theorems
(c) The theory of means
(d) The paradoxes of Erycinus
(e) The regular solids
(f) Extension of Pythagoras's theorem
(g) Circles inscribed in the arbelos
(h) Spiral on a sphere
(i) Isoperimetric figures
(j) Apparent form of a circle
(k) The Treasury of Analysis
(l) Locus with respect to five or six lines
(m) Anticipation of Guldin's theorem
(n) Lemmas to the treatises
(i) To the Determinate Section of Apollonius
(ii) To the Porisms of Euclid
(o) Mechanics
INDEX
LIST OF ANCIENT TEXTS CITED
INDEX OF GREEK TERMS