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

Best Sellers Rank: #71,495 in Books (See Top 100 in Books)
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M. J.

Great commentary on Euclid

Reviewed in the United States on November 6, 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.

7 people found this helpful

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Nona

A classic, but don't try to learn geometry from Euclid

Reviewed in the United States on June 7, 2009

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Euclid's "Elements" may very well be the most influential mathematical text in all of history. This fact alone justifies purchasing this book, which is the first of three volumes of Thomas L. Heath's English translation of this classic. This volume contains a lengthy introduction, and the actual mathematics covers plane geometry. Highlights include the construction of the regular 15-gon using straightedge and compass.

The actual text of Euclid's work is not particularly long, but this book contains extensive commentary about the history of the Elements, as well as commentary on the relevance of each of the propositions, definitions, and axioms in the book. As such, this book is a good scholarly reference for English readers interested in the historical evolution of Euclidean geometry. For example, there is considerable discussion on the well-known fifth postulate about parallel lines.

All this being said, do not try to learn geometry from this book. The content is more suited for readers who already know geometry and want to learn about the historical origins of the subject of geometry. There are many modern books written for readers new to geometry (some good, some bad). It's probably true that Abraham Lincoln studied the Elements as a young lawyer, but there are easier (if not better) ways to learn geometry nowadays. The Elements will be much more enlightening if the reader has a good grasp of the actual mathematics in the book prior to reading it.

24 people found this helpful

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Michael Buelow

Hard to read

Reviewed in the United States on December 21, 2018

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The type in this volume is very small. A larger volume with bigger text would be most useful. Original Greek text is of no benefit to anyone who doesn't read the language and adds nothing to the contents if you can't.

3 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

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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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Chris Kern

Features of Heath's translation and commentary

Reviewed in the United States on June 14, 2011

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I'm not sure that Euclid itself needs another review; its place in mathematics history is well established and other reviewers have done a good job explaining the Elements. I finished working through the "propositions" in the first two books (the contents of this volume) -- I recommend that if you are considering exploring the Elements, that you get out pen and paper and actually work through the steps. You don't necessarily need to draw every single line out using only a straightedge and compass, but without doing the work yourself it can be hard to appreciate how the proofs work.

What I mainly want to talk about is this edition specifically. Editions of the Elements are available online for free, and there are other printed editions that contain only the proofs and diagrams, without all the introduction and commentary. So the primary question should be whether the contents of this edition are worth it. In short, I think that if you are interested in Greek philosophy and the history of mathematics, this edition contains a great deal of useful information. If you are mainly interested in the Elements itself, you may do better to go with another edition.

Thomas Heath was writing in the early 20th century, and he may have expected his reading audience to be more familiar with Aristotelian philosophy and geometry in general than we are today. His 152-page introduction is divided into 9 chapters. The first chapter is a fairly accessible introduction to Euclid's life and the legends we have about him. Chapters 2-4 are about the work of previous Greek mathematicians and later commentators on Euclid; these chapters are more dense and probably not of interest to the general reader. Chapters 5-8 are a fairly tedious listing of various manuscripts, editions, translations, and adaptations of Euclid -- it's hard to imagine many people being interested in the content of these chapters unless they were specialist researchers. Chapter 9 is worth reading if you are interested in Greek philosophy, and especially if you have some understanding of Aristotle. In ancient Greece, philosophy often dealt with mathematics, and this chapter is a nicely detailed discussion of the philosophical underpinnings of Euclid's techniques, and explanations of terms such as "definition" and "axiom" (in terms of Greek philosophy).

The next 90 or so pages is about the definitions, postulates, and "common notions". Once again, these notes deal extensively with Greek philosophy and the philosophy of mathematics in general. For instance, the commentary on definition 1 (the point) discusses Aristotelian and pre-Euclidean definitions, criticism of Euclid's definition by later commentators, and "modern" (i.e. late 19th century) definitions. A lot of this content may not be accessible to someone without philosophy or geometry. Some of this may make more sense if you come back to it later -- for instance, the 20 pages of commentary on the infamous Postulate 5 are a lot easier to appreciate once you've worked through Propositions 29-32 (which use the Postulate).

This more or less applies to the commentary on the Propositions as well. A lot of the commentary is devoted to (a) Pre-Euclidean mathematics, (b) criticism of later commentators, and (c) modern treatments of the subject.

I suppose that anyone considering The Elements probably has some interest in the history of mathematics, and Heath's information is incredibly detailed and informative. But as I said earlier, unless you have some prior background in Aristotle and geometry in general, it may be difficult to digest.

16 people found this helpful

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Vassilios A.

Excellent classic book

Reviewed in the United States on March 24, 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.

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Jim Baird

A Hundred-Year-Old Classic

Reviewed in the United States on April 17, 2013

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This is a Dover reprint of a 1908 version of Euclid's Geometry. It contains the first two of
thirteen books of The Elements, and it's a treasure, assuming you're a scholar of Ancient
Greece or Greek mathematics. It combines extensive scholarly commentary along with
text and diagrams.

If you're looking to learn geometry, this book will be daunting. If you're looking to see
what textbooks looked like over 100 years ago, this will open your eyes.

There's a saying in Biblical Studies that students shouldn't take on Scripture without
commentary. The same goes for this deep and interesting volume. That goodness
for Dover Books, the publisher; everything they print is a treasure.

Five stars if you're a scholar. Four stars if you enjoy owning an early
20th Century gem. Two stars if you're a beginner in Geometry looking
for a textbook.

3 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

Wyatt Chanowski

Very descriptive

Reviewed in Canada on June 3, 2020

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

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

Robert Shutler

Five Stars

Reviewed in Canada on June 24, 2017

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You gotta love Math!

gary killeen

Three Stars

Reviewed in Canada on April 20, 2015

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im not einstein but im trying

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