Greek Mathematical Works, Volume 2: Aristarchus to Pappus

Ivor Thomas, translator

Publisher:

Harvard University Press

Publication Date:

2018

Number of Pages:

683

Format:

Hardcover

Series:

Loeb Classical Library

Price:

26.00

ISBN:

9780674993990

Category:

Sourcebook

BLL Rating:

BLL*

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

MAA Review
Table of Contents

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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
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