- 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

- 1. Preface
- 2. Two Lemmas
- 3. Volume of a Segment of a Paraboloid of Revolution

- E. The Spiral of Archimedes

- 1. Definitions
- 2. Fundamental Property
- 3. A Verging
- 4. 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

- 1. Postulates
- 2. Principle of the Lever
- 3. Centre of Gravity of a Parallelogram

- J. Mechanical Method in Geometry
- K. Hydrostatics

- 1. Postulates
- 2. Surface of Fluid at Rest
- 3. Solid Immersed in a Fluid
- 4. 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

- 1. Relation to Previous Works
- 2. Scope of the Work
- 3. Definitions
- 4. Construction of the Sections
- 5. Fundamental Properties
- 6. Transition to New Diameter

- B. Other Works

- 1. General
- 2. On the Cutting-off of a Ratio
- 3. On the Cutting-off of an Area
- 4. On Determinate Section
- 5. On Tangencies
- 6. On Plane Loci
- 7. On Vergings
- 8. On the Dodecahedron and the Icosahedron
- 9. Principles of Mathematics
- 10. On the Cochlias
- 11. On Unordered Irrationals
- 12. Measurement of a Circle
- 13. Continued Multiplications
- 14. On the Burning Mirror

- A. The Conic Sections
- XX. Later Developments in Geometry

- A. Classification of Curves
- B. Attempts to Prove the Parallel Postulate

- 1. General
- 2. Posidonius and Geminus
- 3. Ptolemy
- 4. Proclus

- C. Isoperimetric Figures
- D. Division of Zodiac Circle into 360 Parts: Hypsicles
- E. Handbooks

- 1. Cleomedes
- 2. Theon of Smyrna

- XXI. Trigonometry

- 1. Hipparchus and Menelaus
- 2. Ptolemy

- A. General
- B. Table of Sines

- 1. Introduction
- 2. sin 180° and sin 360°
- 3. sin2 θ + cos2 θ = 1
- 4. Ptolemy’s Theorem
- 5. sin (θ – φ) = sin θ cos φ – cos θ sin φ
- 6. sin2 ½ θ = ½ (1 – cos θ)
- 7. cos (θ + φ) = cos θ cos φ – sin θ sin φ
- 8. Method of Interpolation
- 9. The Table

- C. Menelaus’s Theorem

- 1. Lemmas
- 2. The Theorem

- XXII. Mensuration: Heron of Alexandria

- A. Definitions
- B. Measurement of Areas and Volumes

- 1. Area of a Triangle Given the Sides
- 2. Volume of a Spire
- 3. Division of a Circle
- 4. Measurement of an Irregular Area

- XXIII. Algebra: Diophantus

- A. General
- B. Notation
- C. Determinate Equations
- D. Indeterminate Equations
- E. Theory of Numbers: Sums of Squares
- F. 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 ἄρβηλος
- 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
- O. Mechanics

- Index
- List of Ancient Texts Cited
- Index of Greek Terms

##### LOEB CLASSICAL LIBRARY

#### Loeb Classical Library 362

# Greek Mathematical Works, Volume II: Aristarchus to Pappus

#### Product Details

HARDCOVER

$28.00 • £19.95 • €25.00

ISBN 9780674993990

Publication Date: 01/01/1941