The Thirteen Books of the Elements

Volume 1 of 3-volume set containing complete English text of all 13 books of the Elements plus critical analysis of each definition, postulate, and proposition. Vol. 1 includes Introduction, Books I and II: Triangles, rectangles.

DOWNLOAD NOW »

Author: Euclid

Publisher: Courier Corporation

ISBN: 9780486158181

Category: Mathematics

Page: 464

View: 412

Volume 1 of 3-volume set containing complete English text of all 13 books of the Elements plus critical analysis of each definition, postulate, and proposition. Vol. 1 includes Introduction, Books I and II: Triangles, rectangles.

The Thirteen Books of the Elements Vol 1

This is the definitive edition of one of the very greatest classics of all time — the full Euclid, not an abridgement.

DOWNLOAD NOW »

Author: Euclid

Publisher: Dover Publications

ISBN: 0486600882

Category: Mathematics

Page: 464

View: 632

This is the definitive edition of one of the very greatest classics of all time — the full Euclid, not an abridgement. Using the text established by Heiberg, Sir Thomas Heath encompasses almost 2,500 years of mathematical and historical study upon Euclid. This unabridged republication of the original enlarged edition contains the complete English text of all 13 books of the Elements, plus a critical apparatus that analyzes each definition, postulate, and proposition in great detail. It covers textual and linguistic matters; mathematical analyses of Euclid’s ideas; classical, medieval, Renaissance, modern commentators; refutations, supports, extrapolations, reinterpretations, and historical notes, all given with extensive quotes. “The textbook that shall really replace Euclid has not yet been written and probably never will be.” — Encyclopaedia Britannica. Volume 1. 151-page Introduction: life and other works of Euclid; Greek and Islamic commentators; surviving mss., scholia, translations; bases of Euclid’s thought. Books I and II of the Elements, straight lines, angles, intersection of lines, triangles, parallelograms, etc. Volume 2. Books III-IX: Circles, tangents, segments, figures described around and within circles, rations, proportions, magnitudes, polygons, prime numbers, products, plane and solid numbers, series of rations, etc. Volume 3. Books X to XIII: planes, solid angles, etc.; method of exhaustion in similar polygons within circles, pyramids, cones, cylinders, spheres, etc. Appendix: Books XIV, XV, sometimes ascribed to Euclid.

The Thirteen Books of the Elements

(0-486-46899-2) MATHEMATICS: ITS CONTENT, METHODS AND MEANING, A. D. ALEKSANDROV, A. N. KOLMOGOROV, AND M. A. LAVRENT'EV. ... 1, EUCLID. EDITED BY THOMAS L. HEATH. (0-486-60088-2) THE THIRTEEN BOOKS OF THE ELEMENTS, VOL. 2, EUCLID.

DOWNLOAD NOW »

Author: Euclid

Publisher: Courier Corporation

ISBN: 9780486158198

Category: Mathematics

Page: 464

View: 684

Volume 2 of 3-volume set containing complete English text of all 13 books of the Elements plus critical analysis of each definition, postulate and proposition. Vol. 2 includes Books 3-9: Circles, relationships, rectilineal figures.

The Thirteen Books of Euclid s Elements

(0-486-46899-2) MATHEMATICS: ITS CONTENT, METHODS AND MEANING, A. D. ALEKSANDROV, A. N. KOLMOGOROV, AND M. A. LAVRENT'EV. ... 1, EUCLID. EDITED BY THOMAS L. HEATH. (0-486-60088-2) THE THIRTEEN BOOKS OF THE ELEMENTS, VOL. 2, EUCLID.

DOWNLOAD NOW »

Author: Euclid

Publisher: Courier Corporation

ISBN: 9780486600895

Category: Mathematics

Page: 464

View: 805

The definitive edition of one of the very greatest classics of all time--the full Euclid, encompassing almost 2500 years of mathematical and historical study. This unabridged republication of the original enlarged edition contains the complete English text of all 13 books of the ELEMENTS, plus analyses of each definition, postulate, and proposition.

CRC Concise Encyclopedia of Mathematics

Heath, T. L. The Thirteen Books of the Elements, 2nd ed., Vol. 1: ... 1 TRIANGLES 2 RECTANGLES 3 CIRCLES 4 POLYGONS 5 proportion 6 SIMILARITY 7Á/0 NUMBER THEORY 11 solid geometry 12 PYRAMIDS 13 PLATONIC SOLIDS Elevator Paradox A fact ...

DOWNLOAD NOW »

Author: Eric W. Weisstein

Publisher: CRC Press

ISBN: 9781420035223

Category: Mathematics

Page: 3252

View: 112

Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d

A Transition to Proof

Penguin Books, 1991. [18] Howard Eves. ... Euclid: The Thirteen Books of Elements, Volume 3, Books 10-13. Dover Publications, 1956. [27] Thomas L. Heath and Euclid. The Thirteen Books of the Elements, Volume 1: Books 1-2.

DOWNLOAD NOW »

Author: Neil R. Nicholson

Publisher: CRC Press

ISBN: 9780429522000

Category: Mathematics

Page: 450

View: 236

A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology

The Thirteen Books of the Elements

This unabridged republication of the enlarged Second Edition contains the complete English text of Volume One of this series, which includes the Introduction by Heath and Books I & II of the Elements.

DOWNLOAD NOW »

Author: Thomas L. Heath

Publisher:

ISBN: 1684224217

Category: Mathematics

Page: 448

View: 880

2019 Reprint of 1926 Second Edition. Volume One; Introduction by Heath and Books I & II. Full facsimile of the original edition, not reproduced with Optical Recognition software. This unabridged republication of the enlarged Second Edition contains the complete English text of Volume One of this series, which includes the Introduction by Heath and Books I & II of the Elements. The Elements is still considered a masterpiece in the application of logic to mathematics. In historical context, it has proven enormously influential in many areas of science. Scientists the likes of Nicolaus Copernicus, Johannes Kepler, Galileo Galilei, and Sir Isaac Newton were all influenced by the Elements, and applied their knowledge of it to their work. Mathematicians and philosophers, such as Thomas Hobbes, Baruch Spinoza, Alfred North Whitehead, and Bertrand Russell, have attempted to create their own foundational "Elements" for their respective disciplines, by adopting the axiomatized deductive structures that Euclid's work introduced. The success of the Elements is due primarily to its logical presentation of most of the mathematical knowledge available to Euclid. Contents: 151-page Introduction by Heath. Books I and II of the Elements, straight lines, angles, intersection of lines, triangles, parallelograms, etc.

A History of Folding in Mathematics

Math Intell 20(1):45–52 Epple M (1999) Die Entstehung der Knotentheorie: Kontexte und Konstruktionen einer ... The University Press, Cambridge Euclid (1908b) The thirteen books of the elements, vol 2: Books 3–9 (trans: Heath TL).

DOWNLOAD NOW »

Author: Michael Friedman

Publisher: Birkhäuser

ISBN: 9783319724874

Category: Mathematics

Page: 419

View: 787

While it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is cube root of 2 with these instruments – the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised? Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete. In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.

A Source Book in Mathematics

(0-486-46899-2) MATHEMATICS: ITs CONTENT, METHODS AND MEANING, A. D. ALEKSANDROV, A. N. KOLMOGOROV, AND M. A. LAVRENT'EV. ... 1, EUCLID. EDITED BY THOMAS L. HEATH. (0-486-60088-2) THE THIRTEEN BOOKS OP THE ELEMENTS, VOL. 2, EUCLID.

DOWNLOAD NOW »

Author: David Eugene Smith

Publisher: Courier Corporation

ISBN: 9780486158297

Category: Mathematics

Page: 736

View: 464

The writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others in a comprehensive selection of 125 treatises dating from the Renaissance to the late 19th century — most unavailable elsewhere.

Semiotics as a Tool for Learning Mathematics

Proceedings of the XXI International Conference of PME (Vol. 2, pp. 345–352). Stellenbosch, South Africa: PME. ... 1 & 2). New York, NY: Dover Publications. Heath, T. L. (1956). Euclid: The thirteen books of the elements (Vol. 1, Books ...

DOWNLOAD NOW »

Author: Adalira Sáenz-Ludlow

Publisher: Springer

ISBN: 9789463003377

Category: Education

Page: 232

View: 292

Semiotics as a Tool for Learning Mathematics is a collection of ten theoretical and empirical chapters, from researchers all over the world, who are interested in semiotic notions and their practical uses in mathematics classrooms. Collectively, they present a semiotic contribution to enhance pedagogical aspects both for the teaching of school mathematics and for the preparation of pre-service teachers. This enhancement involves the use of diagrams to visualize implicit or explicit mathematical relations and the use of mathematical discourse to facilitate the emergence of inferential reasoning in the process of argumentation. It will also facilitate the construction of proofs and solutions of mathematical problems as well as the progressive construction of mathematical conceptions that, eventually, will approximate the concept(s) encoded in mathematical symbols. These symbols hinge not only of mental operations but also on indexical and iconic aspects; aspects which often are not taken into account when working on the meaning of mathematical symbols. For such an enhancement to happen, it is necessary to transform basic notions of semiotic theories to make them usable for mathematics education. In addition, it is also necessary to back theoretical claims with empirical data. This anthology attempts to deal with such a conjunction. Overall, this book can be used as a theoretical basis for further semiotic considerations as well as for the design of different ways of teaching mathematical concepts.