The Thirteen Books of Euclid's Elements

Author: Euclid
Publisher: Createspace Independent Publishing Platform
ISBN: 9781546376675
Category :
Languages : en
Pages : 448

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.

The Thirteen Books of Euclid's Elements

Author: Euclid
Publisher:
ISBN:
Category : Mathematics, Greek
Languages : en
Pages : 594

Book Description

The Elements

Author: Euclid
Publisher:
ISBN:
Category : Geometry
Languages : en
Pages : 558

Book Description

Euclid's Elements

Author: Euclid
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 544

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

The Thirteen Books of Euclid's Elements

Author: Thomas L. Heath
Publisher: Cambridge University Press
ISBN: 1107480507
Category : History
Languages : en
Pages : 555

Book Description
First published in 1926, this book contains the final volume of a three-volume English translation of the thirteen books of Euclid's Elements.

Books 3-9

Author: Euclid
Publisher:
ISBN:
Category : Mathematics, Greek
Languages : en
Pages : 456

Book Description

Elements of Information Theory

Author: Thomas M. Cover
Publisher: John Wiley & Sons
ISBN: 1118585771
Category : Computers
Languages : en
Pages : 788

Book Description
The latest edition of this classic is updated with new problem sets and material The Second Edition of this fundamental textbook maintains the book's tradition of clear, thought-provoking instruction. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory. All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing. The authors provide readers with a solid understanding of the underlying theory and applications. Problem sets and a telegraphic summary at the end of each chapter further assist readers. The historical notes that follow each chapter recap the main points. The Second Edition features: * Chapters reorganized to improve teaching * 200 new problems * New material on source coding, portfolio theory, and feedback capacity * Updated references Now current and enhanced, the Second Edition of Elements of Information Theory remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications.

Euclid's Elements with Exercises Instructor's Copy

Author: Kathryn Goulding
Publisher:
ISBN: 9780692925959
Category :
Languages : en
Pages :

Book Description
The instructor's edition of Euclid's Elements With Exercises is intended as a guide for anyone teaching Euclid for the first time. Although it could be used by anyone, it was assembled and written with small schools or homeschooling groups in mind. In addition to containing the first six books in exactly the format of the student edition (also available on Amazon), the instructor's edition provides a concise overview of the course, including suggestions for conducting the class, a discussion of the organization of the material, brief comments on supplemental and memory work, and other details about which a new instructor might have questions. It also has notes for the teacher on each of the six books of the Elements, notes on selected exercises, and an appendix explaining the basics of formal reasoning, including an explanation of the converse and contrapositive of a statement and the concept of an indirect proof, which occurs early in Book I. The primary difference between this work and Euclid's Elements as it is usually presented (aside from the fact that there are some exercises), is that, while all of Books I - VI are included in the book, some propositions are omitted in the main body of the text (all omitted propositions are in Appendix A). This was done in order to be able to finish in two semesters all the plane geometry that would normally be covered in a modern geometry class. It should be noted, of course, that the flow of logic of the propositions is never interrupted. This book was not designed for the purist. Although it is pure Euclid and contains all of the first six books, it may offend the sensibilities of some who love Euclid (as the assembler/author does) to fail to place Book II in the expected flow of the main body of the text. For anyone not under a time constraint, or anyone moving quickly through the text, the author strongly recommends the inclusion of Book II in the course flow.

The First Six Books of the Elements of Euclid

Author: John Casey
Publisher:
ISBN: 9781088465103
Category :
Languages : en
Pages : 212

Book Description
This edition of the Elements of Euclid, undertaken at the request of the principalsof some of the leading Colleges and Schools of Ireland, is intended tosupply a want much felt by teachers at the present day-the production of awork which, while giving the unrivalled original in all its integrity, would alsocontain the modern conceptions and developments of the portion of Geometryover which the Elements extend. A cursory examination of the work will showthat the Editor has gone much further in this latter direction than any of hispredecessors, for it will be found to contain, not only more actual matter thanis given in any of theirs with which he is acquainted, but also much of a specialcharacter, which is not given, so far as he is aware, in any former work on thesubject. The great extension of geometrical methods in recent times has madesuch a work a necessity for the student, to enable him not only to read with advantage, but even to understand those mathematical writings of modern timeswhich require an accurate knowledge of Elementary Geometry, and to which itis in reality the best introduction

Euclid's Elements Book One with Questions for Discussion

Author: Dana Densmore
Publisher: Green Cat Books
ISBN: 9781888009460
Category : Geometry
Languages : en
Pages : 0

Book Description
Presents Book One of Euclid's Elements for students in humanities and for general readers. This treatment raises deep questions about the nature of human reason and its relation to the world. Dana Densmore's Questions for Discussion are intended as examples, to urge readers to think more carefully about what they are watching unfold, and to help them find their own questions in a genuine and exhilarating inquiry.