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Overview: This book is intended for all lovers of mathematics, offering an exploration of the nature of mathematics through the lens of its most significant early source.
While the material covered by Euclid may largely be considered elementary, his presentation has set a standard for more than two thousand years. Understanding Euclid’s *Elements* is as crucial for a mathematician today as knowledge of Greek architecture is for an architect. Although no contemporary architect would construct a Doric temple or organize a construction site as the ancients did, familiarity with the Greek heritage is essential for the development of an architect’s aesthetic judgment. In agreement with Peter Hilton, it is asserted that genuine mathematics represents one of the finest expressions of the human spirit. Furthermore, it is noted that, in this and many other cases, we have learned that language of expression from the Greeks.
While presenting geometry and arithmetic Euclid teaches us essential 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 of a theory. We learn what creative definitions are and how a conceptual grasp leads to the classification of the relevant objects. Euclid creates the famous algorithm that bears his name for the solution of specific problems in arithmetic, and he shows us how to master the infinite in its various manifestations.
In the Elements we still have a very distant historical text that needs interpretation. Here the present book takes a clear position: The Elements are read, interpreted, and commented upon from the point of view of modern mathematics.
Genre: Non-Fiction > Educational
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