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A Commentary on the First Book of Euclid's Elements

Author : Proclus

Publisher : Princeton University Press

Page : 432 pages

File Size : 35,57 MB

Release : 1992-11-08

Category : Mathematics

ISBN : 9780691020907

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Book Description

In Proclus' penetrating exposition of Euclid's methods and principles, the only one of its kind extant, we are afforded a unique vantage point for understanding the structure and strength of the Euclidean system. A primary source for the history and philosophy of mathematics, Proclus' treatise contains much priceless information about the mathematics and mathematicians of the previous seven or eight centuries that has not been preserved elsewhere. This is virtually the only work surviving from antiquity that deals with what we today would call the philosophy of mathematics.



Euclid's Elements

Author : Euclid

Publisher :

Page : 544 pages

File Size : 42,5 MB

Release : 2002

Category : Mathematics

ISBN :

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Book Description

"The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary" --from book jacket.



Proclus' Commentary on Plato's Parmenides

Author : Proclus,

Publisher : Princeton University Press

Page : 668 pages

File Size : 33,35 MB

Release : 1992-10-21

Category : Philosophy

ISBN : 9780691020891

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Book Description

This is the first English translation of Proclus' commentary on Plato's Parmenides. Glenn Morrow's death occurred while he was less than halfway through the translation, which was completed by John Dillon. A major work of the great Neoplatonist philosopher, the commentary is an intellectual tour de force that greatly influenced later medieval and Renaissance thought. As the notes and introductory summaries explain, it comprises a full account of Proclus' own metaphysical system, disguised, as is so much Neoplatonic philosophy, in the form of a commentary.



The Thirteen Books of Euclid's Elements

Author : Euclid

Publisher : Createspace Independent Publishing Platform

Page : 448 pages

File Size : 41,65 MB

Release : 2017-04-30

Category :

ISBN : 9781546376675

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Book Description

Euclid's Elements is a mathematical and geometric treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt circa 300 BC. It is a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover Euclidean geometry and the ancient Greek version of elementary number theory. The work also includes an algebraic system that has become known as geometric algebra, which is powerful enough to solve many algebraic problems, including the problem of finding the square root of a number. Elements is the second-oldest extant Greek mathematical treatise after Autolycus' On the Moving Sphere, and it is the oldest extant axiomatic deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science. According to Proclus, the term "element" was used to describe a theorem that is all-pervading and helps furnishing proofs of many other theorems. The word 'element' in the Greek language is the same as 'letter'. This suggests that theorems in the Elements should be seen as standing in the same relation to geometry as letters to language. Later commentators give a slightly different meaning to the term element, emphasizing how the propositions have progressed in small steps, and continued to build on previous propositions in a well-defined order.



Mathematical Commentaries in the Ancient World

Author : Karine Chemla

Publisher : Cambridge University Press

Page : 475 pages

File Size : 29,39 MB

Release : 2022-06-09

Category : History

ISBN : 1108839576

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Book Description

Comparative analysis of the techniques and procedures of important mathematical commentaries in five ancient cultures from China to Greece.



Euclid in China

Author : Engelfriet

Publisher : BRILL

Page : 502 pages

File Size : 41,52 MB

Release : 2021-11-01

Category : History

ISBN : 9004482792

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Book Description

As part of the Jesuits' programme of introduction to European culture, in 1607 the Elements of Euclid (± 300 BC) were translated for the first time into Chinese. The translation of this epoch-making ancient Greek textbook on deductive geometry meant a confrontation of contemporary Chinese and European cultures. Part I of Peter Engelfriet's work deals mainly with the European and Chinese backgrounds, part II with linguistic and textual matters. In part III the manner in which learned Chinese tried to integrate this new knowledge into their own, Chinese, mathematical and cultural traditions comes to the fore. This fascinating work explores in depth and at various levels the circumstances and mechanisms that shaped the transmission of a key work of science from one language and cultural context onto another. Consequently it offers often surprising insights into the ways of intercultural exchange and misunderstandings.



Proclus

Author : Radek Chlup

Publisher : Cambridge University Press

Page : 345 pages

File Size : 44,75 MB

Release : 2012-04-26

Category : History

ISBN : 0521761484

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Book Description

An introduction to the philosophical and religious thought of Proclus the Neoplatonist, one of the most complex thinkers of antiquity.



The Mathematics of Harmony

Author : Alexey Stakhov

Publisher : World Scientific

Page : 745 pages

File Size : 43,26 MB

Release : 2009

Category : Mathematics

ISBN : 9812775838

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Book Description

Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science."



Plato's Cretan City

Author : Glenn R. Morrow

Publisher : Princeton University Press

Page : 659 pages

File Size : 36,75 MB

Release : 2022-03-08

Category : Performing Arts

ISBN : 0691242852

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Book Description

Plato's Cretan City is a thorough investigation into the roots of Plato's Laws and a compelling explication of his ideas on legislation and social institutions. A dialogue among three travelers, the Laws proposes a detailed plan for administering a new colony on the island of Crete. In examining this dialogue, Glenn Morrow describes the contemporary Greek institutions in Athens, Crete, and Sparta on which Plato based his model city, and explores the philosopher's proposed regulations concerning property, the family, government, and the administration of justice, education, and religion. He approaches the Laws as both a living document of reform and a philosophical inquiry into humankind's highest earthly duty.