The Thirteen Books of the Elements, Vol. 1: Books 1-2 2nd ed. Edition

by Thomas L. Heath (Author), Euclid (Author)

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ISBN-13: 978-0486600888

ISBN-10: 0486600882

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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.

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Product details

Publisher ‏ : ‎ Dover Publications; 2nd ed. edition (June 1, 1956)
Language ‏ : ‎ English
Paperback ‏ : ‎ 464 pages
ISBN-10 ‏ : ‎ 0486600882
ISBN-13 ‏ : ‎ 978-0486600888
Item Weight ‏ : ‎ 1.25 pounds
Dimensions ‏ : ‎ 5.5 x 1 x 8.4 inches

Best Sellers Rank: #122,238 in Books (See Top 100 in Books)
- #42 in Geometry (Books)
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Sir Thomas Little Heath

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M. J.

Great commentary on Euclid

Reviewed in the United States on November 7, 2013

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Very interesting work that takes a serious look at geometry building from the ultimate basic assumptions and building from there. I definitely love Thomas L. Heath's commentary. It is daunting to read the entire commentary as it is quite longer than Euclid's book; however, many times the commentary shows the depth of Euclid. Why did Euclid choose the proof he did and not an alternative, and what the alternatives are. I found those comments the most interesting, though he offers many more types of insights. For example he gives a history in the beginning and a discussion about axioms and proofs, with much much more.

12 people found this helpful

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Amazon Customer

A good book to learn English writing.

Reviewed in the United States on July 22, 2016

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I like the writing style. As a foreigner, Heath's English is kind of different from today's newspaper and blogs. For example, the first paragraph of the preface to second edition is just ONE sentence, but it takes nine lines. Such long sentences are here and there. Long sentence with complicated structure is elegant and an indicator that the writer is well educated. And Heath likes to use subjunctive mood, which many non-native speaker do not feel comfortable about. It is a good book to learn English writing.

12 people found this helpful

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Jimmy Verona

Required Reading

Reviewed in the United States on September 12, 2013

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This was the book that got me into mathematics. After years of being afraid of the subject, I did a little digging and decided to start here, at the very beginning. I was hooked. I went through the books, proof by proof, constantly being amazed at what I was learning, and how easy it was for me to comprehend. From these books I was able to springboard into many other areas of mathematics, but I owe it all to Euclid.
T.L. Heath's translation is quite perfect, and his explanations of the proofs and the historical background he provides make him the absolute authority on the subject. This is the best translation out there, hands down.

8 people found this helpful

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Ozzyng

As Advertised , No Problems

Reviewed in the United States on December 30, 2019

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As Advertised , No Problems

One person found this helpful

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Vassilios A.

Excellent classic book

Reviewed in the United States on March 25, 2018

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I love geometry and I recommend this book to anyone with young kids going through HS education. They will benefit from it significantly.

One person found this helpful

Helpful

A Blessing for Undergraduate Math History

Reviewed in the United States on December 13, 2012

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First of all, this book is a Dover, so you get tons for your dollar!

I used this book as a supplement for my math history class. It was very helpful! It shows all of the logic behind Euclid's definitions, postulates, common notions (axioms), and book-one propositions! It goes far beyond proposition-picture-proof. I benefited from the lengthy descriptions and alternate solutions following each proposition!

Good little book!

5 people found this helpful

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John Moore

Classic Euclid Translation

Reviewed in the United States on October 27, 2013

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While the print is somewhat small for aging eyes, the commentary alone is worth the price of the book. Of course, all this commentary means you need multiple volumes to cover all thirteen books.

One person found this helpful

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Deyanira

Great book on the foundation for Geometry

Reviewed in the United States on September 26, 2009

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Great study book. It is quite detailed...very, very informative
for Geometry teachers...great tool for learning about Geometry's
beginnings.

2 people found this helpful

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Alun Williams

All Greek to Me.

Reviewed in the United Kingdom on January 23, 2009

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Nobody with an interest in Geometry, or the history of Western Civilisation should be without a copy of this book. What you get is far more than just the theorems and proofs to be found in the first two books of Euclid. Indeed, if this is all you want, one of the online versions of Euclid will probably be more to your taste. The book contains a mass of scholarly but fascinating detail on topics such as Euclid's predecessors, contemporary reaction, commentaries by later Greek mathematicians, the work of Arab mathematicians inspired by Euclid, the transmission of the text back to Renaissance Europe, and a list and potted history of the various translations and editions of Euclid from then on. The section on the postulates and axioms (and of course the all-important parallel postulate) is wonderful.

When we come to the actual theorems the amount of detail is just as impressive - references to earlier results are annotated, and textual variations are noted (especially where the proofs may have been amended by later writers in an attempt to correct gaps). In many cases alternative proofs are given - sometimes several different ones, with the history and references for each.

22 people found this helpful

Cliente de Amazon

Volume I is a different size compared to Vol. II and III.

Reviewed in Mexico on June 2, 2021

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I'm just nit-picking here, just bear with me. (These books are great otherwise).

According to Dover Publication's website, these books should be 5 1/2 x 8 1/2.

Volume II and III are.

Volume I, however, is 5 1/4 x 8 1/2, one quarter of an inch narrower.

All three seem to have been manufactured by LSC Communications the same year 2020. Other differences are present: the name Euclid in the spine of Vol I and II are parallel to the spine of the book, while it is not in Vol. III. In the back cover, upper left corner, Vol. I says "Mathematics", Vol. II says "Mathematics/ History and Philosophy", and Vol. III says "Mathematics", but underlined. Dover logo is bigger in Vol. III too.

You can expect these kind of changes when several years have passed, between different editions of the same book by the same book publisher. But this is supposed to be the same edition, printed the same year, by the same company.

I wonder who green-lighted all those changes.

At least they're the same height, so in the bookshelf all three will look even.

Menno Rubingh

Beautiful and extremely interesting

Reviewed in Germany on December 24, 2008

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Full marks for this book also from me. I belong to those who, despite an
engineering education, had never read Euclid directly before. Having now
seen this book for the first time, I think that anyone who is interested
in mathematics and ancient Greek culture, can hardly fail to find Euclid's
Elements extremely interesting.

The mathematics itself in Euclid's Elements is beautiful. The style
of presentation used by Euclid is terse, and some of his mathematical
terms took me a few minutes to get used to (like "rectangle" for
"multiplication"); but Euclid's presentation is very exact and logical,
and is easy to follow. I think that no mathematical background is needed,
and that simple interest suffices to read the book and to understand
the mathematics. Speaking humorously, the book may even have a slightly
"dangerous" :-) side for those who like puzzles -- danger of addiction
to a mental play world of circles, lines, and angles :-). The topic of
Euclid is pure, not applied, mathematics.

I find Euclid's mathematics by no means "crude" or "simplistic".
Euclid's Elements, in the later books, goes well beyond elementary-school
geometry, and in my view this is a book clearly aimed at adult readers,
not children. It's of course clear that mathematics has expanded very
substantially beyond Euclid since the 1700s and 1800s -- for example,
to mention just one thing, there is no such thing in Euclid as numerical
computation of the ("Cartesian") coordinates of things; Euclid always
keeps within the world of straight unmarked ruler and compasses
(dividers). Having said this however, I'm amazed at how sophisticated
Euclid's mathematics gets in the later books. The basis in Euclid's
Elements is definitely plane geometry, but books XI - XIII (in Volume 3)
do expand things into 3D geometry ("solid geometry").

Reading this book, what I found also interesting to discover is that
Euclid was a scholar/scientist whose work is firmly based on the corpus of
geometrical theory that already existed at that time. That is, Euclid's
Elements is a presentation of the mainstream scientific geometry of the
time, not a work of a romantic "loner genius".

Euclid's presentation is extremely beautiful in some points. Each theorem
is proved by a simple diagram plus mostly just a few lines of text.
(Only very few theorems, in the later books, take him more than about 15
lines of text.) Heath indents Euclid's text in an agreeable way that
I think is helpful for following Euclid's formulations. Admittedly,
Euclid's later theorems often base very heavily on earlier theorems;
but on the other hand, there is definite beauty itself in the logical
structure of how Euclid derives his later theorems from earlier ones.

This edition (Heath, Dover) provides a "full scholarly apparatus" of
notes, introductions, identification of sources, literature references,
etc. This scholarly stuff is easy to skip if you want to go directly to
Euclid's maths, but I have to say I did find some of Heath's notes helpful
for some of the terms used by Euclid (like "rectangle" and "gnomon").
The introductions by Heath are somewhat voluminous, and occupy the first
45 % of Volume 1. (Euclid's books I and II, which occupy the rest of
Volume 1, end with the so-called "Pythagorean" theorem.) There is a
good keyword index in each volume.

Despite being an English translation, this edition does contain some
snippets of the original Greek: Aside from the translation and copious
notes, Heath provides the original Greek for all of Euclid's very terse
Definitions which begin most of the Books, plus also provides in each
volume an index of Greek mathematical terms (both in Greek script).
What I appreciated also is that Volume 1 has one "facsimile" image of one
page from a Greek manuscript from 888 AD. My impression is that armed
with Heath's book (plus a little basic knowledge of classical Greek),
it should be easy to read the original Greek.

Described edition: Dover, Heath, 2nd Ed. (1st printed 1956), 3 volumes.

6 people found this helpful

Wyatt Chanowski

Very descriptive

Reviewed in Canada on June 4, 2020

Verified Purchase

Excellent reproduction of a timeless classic. The notes certainly helped to make the text more understandable and explain how Euclid thought.

Melaine

Matemática pura

Reviewed in Brazil on September 2, 2021

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Livro excelente segundo meu filho que o está lendo

2 people found this helpful

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The Thirteen Books of the Elements, Vol. 1: Books 1-2 2nd ed. Edition

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