Euclid - The Creation of Mathematics

Even if the material covered by Euclid may be considered elementary for the most part, the way in which he presents essential features of mathematics in a much more general sense, has set the standards for more than 2000 years. 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 how it enforces the strictly deductive presentation of a theory. We learn what creative definitions are and how the conceptual grasp leads to the classification of the relevant objects.

This is a book for all lovers of mathematics with a solid background in high school geometry, from teachers and students to university professors. For each of Euclid's thirteen Books, the author has given a general description of the contents and structure of the Book, plus one or two sample proofs.

Euclid's treatment of mathematics and the presentation of its essential features has set the standard which remains today, and which every mathematician should know Artmann reveals many pieces of beautiful mathematics from the Elements, which are easily accessible and can be studied in detail by anyone with a minimal training in math Each book of the Elements is clearly described in detail, and proofs are given for important results Modernized language is used to make the material more accessible to the reader Includes general remarks about typical mathematical procedures of the day, subjects of historical interest, and connections to philosophy

Inhalt
Preface *Notes to the reader *General historical remarks *The Origins of Mathematics I: The Testimony of Eudemus *Euclid: Book I *Origin of Mathematics 2: Parallels and Axioms *Origins of Mathematics 3: Pythagoras of Samos *Euclid: Book II *Origin of Mathematics 4: Squaring the Circle *Euclid: Book III *Origin of Mathematics 5: Problems and Theories *Euclid: Book IV *Origin of Mathematics 6: The Birth of Rigor *Origin of Mathematics 7: Polygons after Euclid *Euclid: Book V *Euclid: Book VI *Origin of Mathematics 8:Be Wise, Generalize *Euclid: Book VII *Origin of Mathematics 9: Nicomachus and Diophantus *Euclid:Book VIII *Origins of Mathematics 10: Tools and Theorems *Euclid: Book IX *Origin of Mathematics 11: Math is Beautiful *Euclid: Book X *Origins of Mathematics 12: Incommensurability and Irrationality *Euclid: Book XI *Origins of Mathematics 13: The Role of Defiinitions *Euclid: Book XII *Origins of Mathematics 14: The Taming of the Infinite *Euclid: Book XIII *Origin of Mathematics 15: Symmetry Through the Ages *Origin of Mathematics 16: The Origin of the Elements *Notes *Bibliography *Index

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