GENERAL EDITOR'S PREFACE PREFACE ACKNOWLEDGMENTS MATHEMATICS Introductory Note The Divisions of Mathematics Pure and Applied Arithmetic or the Theory of Numbers Proportions Figured Numbers Perfect Numbers Friendly (Amicable) Numbers Incommensurable Numbers The General Theory of Proportion and the Theory of Incommensurable Magnitudes Prime Numbers The Number of Primes is Infinite Some Additional Thcorems and Problems in the Theory of Numbers Right-Angled Triangles with Sides in Rational Nunbers The Summation of a Geometrical Series On Cubic Numbers Algebra Some Mathematical Problems in the Greek Anthology The Cattle Problem of Archimedes Problems from Diophantus Geometry The History of Geometry to the Time of Euclid Analysis and Synthesis in Geometry An Example of Analysis and Synthesis Note on Pythagorean Geometry Elementary Geometry Postulates The Parallel Postulate The Method of Exhaustion The "Pythagorean" Theorem The Golden Section The Horn-Angle The Three Famous Geometrical Problems of the Greeks 1. The Squaring of the Circle a. Early Attempts b. Hippocrates of Chios c. Higher Curves The Spiral The Quadratrix d. The Area of a Circle Approximations to x 2. The Duplication of the Cube 3. The Trisection of an Angle Solution by a "Verging Mechanical and Geometric Methods Contrasted Conic Sections The Problem of Pappus
An Anticipation of Guldin's Theorem On the Sagacity of Bees in Building Their Cells Trigonometry Application of Trigonom?try Some Numerical Problems in Mensuration ASTRONOMY AND MATHEMATICAL GEOGRAPHY Introductory Note ASTRONOMY The Scope of Astronomy Contrasted with that of Physics Some Early Theories Thales Anaximander Pythagoras Anaxagoras Oenopides Pythagorean Astronomy The Central Fire The Harmony of the Spheres Note on Plato's Astronomy Elementary Notions in Astronomy The Theory of Concentric Spheres An Objection to the Theory of Concentric Spheres The Rotation of the Earth on Its Axis The Revolution of Mercury and Venus about the Sun The Heliocentric Hypothesis The Sizes and Distances of the Sun and Moon The Precession of the Equinoxes The Motion of the Sun and the Planets On Day and Night The Month Hypotheses of Ptolemaic Astronomy On the Order of the Theorems That the Heaven Rotates as a Sphere The Absolute Immobility of the Earth Note on the Ptolemaic System The Star Catalogue of Ptolemy Some Astronomical Instruments and Their Use Sundials and Water Clocks Astronomical Applications of the Dioptra An Ancient Planetarium
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