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Suny Series in Ancient Greek Philosophy Ser.: Metaphysics of the Pythagorean Theorem : Thales, Pythagoras, Engineering, Diagrams, and the Construction of the Cosmos Out of Right Triangles by Robert Hahn (2018, Trade Paperback)
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METAPHYSICS OF THE PYTHAGOREAN THEOREM, THE: THALES, PYTHAGORAS, ENGINEERING, DIAGRAMS, AND THE CONSTRUCTION OF THE COSMOS OUT OF RIGHT TRIANGLES (SUNY SERIES IN ANCIENT By Robert Hahn **BRAND NEW**.
- Buy It NowMETAPHYSICS OF THE PYTHAGOREAN THEOREM, THE: THALES, By Robert Hahn *BRAND NEW*
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About this product
Product Identifiers
PublisherSTATE University of New York Press
ISBN-101438464908
ISBN-139781438464909
eBay Product ID (ePID)240357543
Product Key Features
Number of Pages300 Pages
Publication NameMetaphysics of the Pythagorean Theorem : Thales, Pythagoras, Engineering, Diagrams, and the Construction of the Cosmos Out of Right Triangles
LanguageEnglish
SubjectHistory & Philosophy, Geometry / General, General, History & Surveys / Ancient & Classical
Publication Year2018
TypeTextbook
AuthorRobert Hahn
Subject AreaMathematics, Philosophy
SeriesSuny Series in Ancient Greek Philosophy Ser.
FormatTrade Paperback
Dimensions
Item Height1 in
Item Weight29.7 Oz
Item Length11 in
Item Width8.5 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2016-031414
TitleLeadingThe
Dewey Edition23
Reviews"Our understanding of the world in which Thales and Anaximander worked is sharpened by Hahn's discussion of contemporary design-techniques." -- Aestimatio "It is a mark of Hahn's generosity that he includes, in every chapter, clear analysis of the geometric problems together with a thorough history of both ancient sources and modern mathematical theory and interpretations before proposing his own extensions; this allows the non-specialist reader to perceive, if not participate in, the often quite divergent current debates about early Greek thought. The handsome production-values and clarity of organization of this book ... are exemplary, as are its general index and index of Greek terms." -- Bryn Mawr Classical Review "This book would be an excellent resource for anyone studying Euclidean geometry, or it could serve as a text for a geometry seminar ... Highly recommended." -- CHOICE, "This book would be an excellent resource for anyone studying Euclidean geometry, or it could serve as a text for a geometry seminar ... Highly recommended." -- CHOICE, "Our understanding of the world in which Thales and Anaximander worked is sharpened by Hahn's discussion of contemporary design-techniques." -- Aestimatio "It is a mark of Hahn's generosity that he includes, in every chapter, clear analysis of the geometric problems together with a thorough history of both ancient sources and modern mathematical theory and interpretations before proposing his own extensions; this allows the non-specialist reader to perceive, if not participate in, the often quite divergent current debates about early Greek thought. The handsome production-values and clarity of organization of this book are exemplary, as are its general index and index of Greek terms." -- Bryn Mawr Classical Review "This book would be an excellent resource for anyone studying Euclidean geometry, or it could serve as a text for a geometry seminar Highly recommended." -- CHOICE
Grade FromCollege Graduate Student
IllustratedYes
Dewey Decimal182
Table Of ContentPreface Acknowledgments Introduction: Metaphysics, Geometry, and the Problems with Diagrams A. The Missed Connection between the Origins of Philosophy-Science and Geometry: Metaphysics and Geometrical Diagrams B. The Problems Concerning Geometrical Diagrams C. Diagrams and Geometric Algebra: Babylonian Mathematics D. Diagrams and Ancient Egyptian Mathematics: What Geometrical Knowledge Could Thales have Learned in Egypt? E. Thales's Advance in Diagrams Beyond Egyptian Geometry F. The Earliest Geometrical Diagrams Were Practical: The Archaic Evidence for Greek Geometrical Diagrams and Lettered Diagrams G. Summary 1. The Pythagorean Theorem: Euclid I.47 and VI.31 A. Euclid: The Pythagorean Theorem I.47 B. The "Enlargement" of the Pythagorean Theorem: Euclid VI.31 C. Ratio, Proportion, and the Mean Proportional (μση νλογον) D. Arithmetic and Geometric Means E. Overview and Summary: The Metaphysics of the Pythagorean Theorem 2. Thales and Geometry: Egypt, Miletus, and Beyond A. Thales: Geometry in the Big Picture B. What Geometry Could Thales Have Learned in Egypt? B.1 Thales's Measurement of the Height of a Pyramid B.2 Thales's Measurement of the Height of a Pyramid C. Thales' Lines of Thought to the Hypotenuse Theorem 3. Pythagoras and the Famous Theorems A. The Problems of Connecting Pythagoras with the Famous Theorem B. Hippocrates and the Squaring of the Lunes C. Hippasus and the Proof of Incommensurability D. Lines, Shapes, and Numbers: Figurate Numbers E. Line Lengths, Numbers, Musical Intervals, Microcosmic-Macrocosmic Arguments, and the Harmony of the Circles F. Pythagoras and the Theorem: Geometry and the Tunnel of Eupalinos on Samos G. Pythagoras, the Hypotenuse Theorem, and the μση νλογος (Mean Proportional) H. The "Other" Proof of the Mean Proportional: The Pythagoreans and Euclid Book II I. Pythagoras's Other Theorem: The Application of Areas J. Pythagoras's Other Theorem in the Bigger Metaphysical Picture: Plato's Timaeus 53Cff K. Pythagoras and the Regular Solids: Building the Elements and the Cosmos Out of Right Triangles 4. Epilogue: From the Pythagorean Theorem to the Construction of the Cosmos Out of Right Triangles Notes Bibliography Image Credits Index
SynopsisBringing together geometry and philosophy, this book undertakes a strikingly original study of the origins and significance of the Pythagorean theorem. Thales, whom Aristotle called the first philosopher and who was an older contemporary of Pythagoras, posited the principle of a unity from which all things come, and back into which they return upon dissolution. He held that all appearances are only alterations of this basic unity and there can be no change in the cosmos. Such an account requires some fundamental geometric figure out of which appearances are structured. Robert Hahn argues that Thales came to the conclusion that it was the right triangle: by recombination and repackaging, all alterations can be explained from that figure. This idea is central to what the discovery of the Pythagorean theorem could have meant to Thales and Pythagoras in the sixth century BCE. With more than two hundred illustrations and figures, Hahn provides a series of geometric proofs for this lost narrative, tracing it from Thales to Pythagoras and the Pythagoreans who followed, and then finally to Plato's Timaeus . Uncovering the philosophical motivation behind the discovery of the theorem, Hahn's book will enrich the study of ancient philosophy and mathematics alike., Explores Thales's speculative philosophy through a study of geometrical diagrams. Bringing together geometry and philosophy, this book undertakes a strikingly original study of the origins and significance of the Pythagorean theorem. Thales, whom Aristotle called the first philosopher and who was an older contemporary of Pythagoras, posited the principle of a unity from which all things come, and back into which they return upon dissolution. He held that all appearances are only alterations of this basic unity and there can be no change in the cosmos. Such an account requires some fundamental geometric figure out of which appearances are structured. Robert Hahn argues that Thales came to the conclusion that it was the right triangle: by recombination and repackaging, all alterations can be explained from that figure. This idea is central to what the discovery of the Pythagorean theorem could have meant to Thales and Pythagoras in the sixth century BCE. With more than two hundred illustrations and figures, Hahn provides a series of geometric proofs for this lost narrative, tracing it from Thales to Pythagoras and the Pythagoreans who followed, and then finally to Plato's Timaeus . Uncovering the philosophical motivation behind the discovery of the theorem, Hahn's book will enrich the study of ancient philosophy and mathematics alike.
LC Classification NumberB188
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