Author	Artmann, Benno. author
Title	EuclidโThe Creation of Mathematics [electronic resource] / by Benno Artmann
Imprint	New York, NY : Springer New York : Imprint: Springer, 1999
Connect to	http://dx.doi.org/10.1007/978-1-4612-1412-0
Descript	XVI, 349 p. online resource

This book is for all lovers ofmathematics. It is an attempt to underยญ stand the nature of mathematics from the point of view of its most important early source. Even if the material covered by Euclid may be considered eleยญ mentary for the most part, the way in which he presents it has set the standard for more than two thousand years. Knowing Euclid's Elements may be ofthe same importance for a mathematician today as knowing Greek architecture is for an architect. Clearly, no conยญ temporary architect will construct a Doric temple, let alone organize a construction site in the way the ancients did. But for the training ofan architect's aesthetic judgment, a knowledge ofthe Greek herยญ itage is indispensable. I agree with Peter Hilton when he says that genuine mathematics constitutesone ofthe finest expressions ofthe human spirit, and I may add that here as in so many other instances, we have learned that language ofexpression from the Greeks. While presenting geometry and arithmetic Euclid teaches us esยญ sential features of mathematics in a much more general sense. He displays the axiomatic foundation of a mathematical theory and its conscious development towards the solution of a specific problem. We see how abstraction works and enforces the strictly deductive presentation ofa theory. We learn what creative definitions are and v VI ----=P:. . :re:. ::::fa=ce how a conceptual grasp leads to toe classification ofthe relevant obยญ jects

1 General Historical Remarks -- 2 The Contents of the Elements -- 3 The Origin of Mathematics 1: The Testimony of Eudemus -- 4 Euclid Book I: Basic Geometry -- 5 The Origin of Mathematics 2: Parallels and Axioms -- 6 The Origin of Mathematics 3: Pythagoras of Samos -- 7 Euclid Book II: The Geometry of Rectangles -- 8 The Origin of Mathematics 4: Squaring the Circle -- 9 Euclid Book III: About the Circle -- 10 The Origin of Mathematics 5: Problems and Theories -- 11 Euclid Book IV: Regular Polygons -- 12 The Origin of Mathematics 6: The Birth of Rigor -- 13 The Origin of Mathematics 7: Polygons After Euclid -- 14 Euclid Book V: The General Theory of Proportions -- 15 Euclid Book VI:Similarity Geometry -- 16 The Origin of Mathematics 8: Be Wise, Generalize -- 17 Euclid Book VII: Basic Arithmetic -- 18 The Origin of Mathematics 9: Nicomachus and Diophantus -- 19 Euclid Book VIII: Numbers in Continued Proportion, the Geometry of Numbers -- 20 The Origin of Mathematics 10: Tools and Theorems -- 21 Euclid Book IX: Miscellaneous Topics from Arithmetic -- 22 The Origin of Mathematics 11: Math Is Beautiful -- 23 Euclid Book X: Incommensurable Magnitudes 23.1 Commensurability and Its Relation to Other Notions 227 -- 24 The Origin of Mathematics 12: Incommensurability and Irrationality -- 25 Euclid Book XI: Solid Geometry -- 26 The Origin of Mathematics 13: The Role of Definitions -- 27 Euclid Book XII: Volume by Limits -- 28 The Origin of Mathematics 14: The Taming of the Infinite -- 29 Euclid Book XIII: Regular Polyhedra -- 30 The Origin of Mathematics 15: Symmetry Through the Ages -- 31 The Origin of Mathematics 16: The Origin of the Elements -- Notes

1. Mathematics
2. Geometry
3. Mathematics
4. Geometry