The Evolution Of The Euclidean Elements
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The Evolution Of The Euclidean Elements
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Author : W.R. Knorr
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Evolution Of The Euclidean Elements written by W.R. Knorr and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Philosophy categories.
The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitudes beginning from the first discoveries by fifth-century Pythago reans, advancing through the achievements of Theodorus of Cyrene, Theaetetus, Archytas and Eudoxus, and culminating in the formal theory of Elements X; (2) to correlate the stages of this developing theory with the evolution of the Elements as a whole; and (3) to establish that the high standards of rigor characteristic of this evolution were intrinsic to the mathematicians' work. In this third point, we wish to counterbalance a prevalent thesis that the impulse toward mathematical rigor was purely a response to the dialecticians' critique of foundations; on the contrary, we shall see that not until Eudoxus does there appear work which may be described as purely foundational in its intent. Through the examination of these problems, the present work will either alter or set in a new light virtually every standard thesis about the fourth-century Greek geometry. I. THE PRE-EUCLIDEAN THEORY OF INCOMMENSURABLE MAGNITUDES The Euclidean theory of incommensurable magnitudes, as preserved in Book X of the Elements, is a synthetic masterwork. Yet there are detect able seams in its structure, seams revealed both through terminology and through the historical clues provided by the neo-Platonist commentator Proclus.
Euclid S Elements
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Author : Euclid
language : en
Publisher:
Release Date : 2002
Euclid S Elements written by Euclid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
"The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary" --from book jacket.
The Evolution Of The Euclidean Elements
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Author : W. R. Knorr
language : en
Publisher:
Release Date : 1980-10-31
The Evolution Of The Euclidean Elements written by W. R. Knorr and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-10-31 with categories.
Encounters With Euclid
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Author : Benjamin Wardhaugh
language : en
Publisher: Princeton University Press
Release Date : 2023-11-14
Encounters With Euclid written by Benjamin Wardhaugh and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-14 with Mathematics categories.
A sweeping cultural history of one of the most influential mathematical books ever written Euclid's Elements of Geometry is one of the fountainheads of mathematics—and of culture. Written around 300 BCE, it has traveled widely across the centuries, generating countless new ideas and inspiring such figures as Isaac Newton, Bertrand Russell, Abraham Lincoln, and Albert Einstein. Encounters with Euclid tells the story of this incomparable mathematical masterpiece, taking readers from its origins in the ancient world to its continuing influence today. In this lively and informative book, Benjamin Wardhaugh explains how Euclid’s text journeyed from antiquity to the Renaissance, introducing some of the many readers, copyists, and editors who left their mark on the Elements before handing it on. He shows how some read the book as a work of philosophy, while others viewed it as a practical guide to life. He examines the many different contexts in which Euclid's book and his geometry were put to use, from the Neoplatonic school at Athens and the artisans' studios of medieval Baghdad to the Jesuit mission in China and the workshops of Restoration London. Wardhaugh shows how the Elements inspired ideas in theology, art, and music, and how the book has acquired new relevance to the strange geometries of dark matter and curved space. Encounters with Euclid traces the life and afterlives of one of the most remarkable works of mathematics ever written, revealing its lasting role in the timeless search for order and reason in an unruly world.
The Evolution Of The Euclidean Elements
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Author : Wilbur Richard Knorr
language : nl
Publisher:
Release Date : 1975
The Evolution Of The Euclidean Elements written by Wilbur Richard Knorr and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
The Elements
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Author : Euclid
language : en
Publisher:
Release Date : 1947
The Elements written by Euclid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1947 with Geometry categories.
The Thirteen Books Of Euclid S Elements
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Author : Euclid
language : en
Publisher:
Release Date : 1956
The Thirteen Books Of Euclid S Elements written by Euclid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with Geometry categories.
Euclid S Window
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Author : Leonard Mlodinow
language : en
Publisher: Simon and Schuster
Release Date : 2010-09-28
Euclid S Window written by Leonard Mlodinow and has been published by Simon and Schuster this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-28 with Science categories.
Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology. Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.
Numbers And Numeracy In The Greek Polis
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Author :
language : en
Publisher: BRILL
Release Date : 2021-12-20
Numbers And Numeracy In The Greek Polis written by and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-20 with History categories.
We tend to think of numbers as inherently objective and precise. Yet the diverse ways in which ancient Greeks used numbers illustrates that counting is actually shaped by context-specific and culturally-dependent choices: what should be counted and how, who should count, and how should the results be shared? This volume is the first to focus on the generation and use of numbers in the polis to quantify, communicate and persuade. Its papers demonstrate the rich insights that can be gained into ancient Greek societies by reappraising seemingly straightforward examples of quantification as reflections of daily life and cultural understandings.
The History Of Mathematical Proof In Ancient Traditions
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Author : Karine Chemla
language : en
Publisher: Cambridge University Press
Release Date : 2012-07-05
The History Of Mathematical Proof In Ancient Traditions written by Karine Chemla and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-05 with Philosophy categories.
This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.