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Loeb Classical Library 362

Greek Mathematical Works, Volume II: Aristarchus to Pappus

Translated by Ivor Thomas

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Product Details

HARDCOVER

$28.00 • £19.95 • €25.00

ISBN 9780674993990

Publication Date: 01/01/1941

Loeb

704 pages

4-1/4 x 6-3/8 inches

Indexes

Loeb Classical Library > Greek Mathematical Works

World

  • 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

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