The Thirteen Books of the Elements, Vol. 1: Books 1-2 [Paperback]

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

Book Description

ISBN-10: 0486600882 | ISBN-13: 978-0486600888 | Publication Date: June 1, 1956 | Edition: 2

Volume 1 of 3-volume set containing complete English text of all 13 books of the Elements plus critical apparatus analyzing each definition, postulate, and proposition. Covers textual and linguistic matters; mathematical analyses of Euclid's ideas; commentators; refutations, supports, extrapolations, reinterpretations, and historical notes. Vol. 1 includes Introduction, Books I and II of Elements, lines, angles, intersections, etc.

Product Details

• Paperback: 464 pages
• Publisher: Dover Publications; 2 edition (June 1, 1956)
• Language: English
• ISBN-10: 0486600882
• ISBN-13: 978-0486600888
• Product Dimensions: 8 x 5.4 x 0.9 inches
• Shipping Weight: 14.9 ounces (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars  See all reviews (22 customer reviews)
• Amazon Best Sellers Rank: #138,183 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

68 of 72 people found the following review helpful:

5.0 out of 5 stars Euclid Alone Has Looked on Beauty Bare, August 5, 2001

By 

Timothy Haugh (New York, NY United States) - See all my reviews
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This review is from: The Thirteen Books of the Elements, Vol. 1: Books 1-2 (Paperback)

I have taught high school geometry for nearly ten years now. It is a subject of which I am very fond. And yet, even though we call the subject Euclidean geometry, very few people, even those of us who teach it, have a clear idea of what exactly it was that Euclid did. We might use the compass and straightedge occasionally but not with Euclid's methodology. I think that this is too bad.

Over the course of the past year or so, I have made it a quest to prove the propositions of The Elements in Euclid's style. Thus far (and at a leisurely pace), I have made it through the first two books outlined in this volume. It has been a wonderful experience that has deepened my knowledge of this subject and, hopefully, has made me a better teacher of it to my students. I am looking forward to going through the remaining eleven books of the last two volumes.

Some things of which a reader should be aware: this volume only contains Euclid's first two books which, in and of themselves, are not very long; however, this volume also contains 150 pages of introduction and significant commentary on nearly every definition, postulate and proposition by Sir Thomas L. Heath. I found much of this very enlightening and was glad to have it included. Still, this material could easily be a stumbling block for weaker students and people interested in Euclid alone. Heath's notes are very detailed and assume a knowledge of certain things (such as classical languages) that are not a common part of the modern curriculum. But, remember, this commentary was written nearly 100 years ago. Don't let it stand in your way. It can be a bonus but, if you have trouble connecting with it, skip it. The notes and commentary should be considered gravy for the prime component here: Euclid's text.

There has never been a writer of mathematics as successful as Euclid. For well over 2000 years the work that Euclid did in compiling The Elements has been the crowning achievement of geometry and it has only been in the twentieth century that his book has been replaced by other texts. There are good reasons for this but, on another level, it is sad that his genius is being diluted. Anyone with a decent handle on high school geometry could get a lot from Euclid himself. The propositions would be familiar and anyone truly interested in understanding how mathematics has become the powerful tool it is today would be remiss in not reading Euclid.

39 of 40 people found the following review helpful:

4.0 out of 5 stars Comprehensive English language review of _Elements I and II_, May 18, 1999

By A Customer

This review is from: The Thirteen Books of the Elements, Vol. 1: Books 1-2 (Paperback)

At the time of this writing, the sales summary points out "Vol. 1", but it does not point out that it is "Volume 1 of 3". Volume 1 provides a historical summary of work that followed _Elements_, along with a detailed translation of Book I and Book II. Heath includes bracketed references to justify each critical step of each proof. The text surrounding each Euclidean statement is detailed, but often very lengthy; at times, this detracts from the reading of the _Elements_ itself. This set is for the scholar of the history of _Elements_, and not the best source for a first-time reading of Euclid. Even with these minor quibbles, however, my copy of Volume I is a well-worn, beloved volume with frequently-annotated margins. All of the major "players" in the development of Geometry are detailed within, as well as their contributions.

I recommend it highly for any scholar that wishes to understand _Elements_ thoroughly, through a close reading of a detailed text.

42 of 45 people found the following review helpful:

5.0 out of 5 stars Reviewing editor Heath, not Euclid, August 17, 2004

By 

C. Jones "he reads" (Muncie, IN USA) - See all my reviews
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This review is from: The Thirteen Books of the Elements, Vol. 1: Books 1-2 (Paperback)

Euclid hardly needs reviews after two millennia of endorsements. Until the advent of mass-produced texts, endorsements came by way of large sums of money or time, or both. Therefore, if we do not understand what Euclid is writing about, there is overwhelming evidence that this failure is ours, not Euclid's. If we decry the unfamiliarity of Euclid's way of reasoning and his manner of writing his mathematics as being less clear or efficient than our own, we are simply expressing our faith--perhaps misplaced--in our own mathematical culture. Clearly, if one's purpose is to learn geometric techniques and results, other books may serve as well or better; if one's purpose is to understand mathematics, the thirteen books of the Elements are without equal.

The Heath edition of Euclid's Elements actually consists of three volumes: volume 1 has Euclid's Books I and II; Heath's volume 2 contains Euclid's Books III - IX; and his volume 3 encompasses Euclid's remaining Books X - XIII. Books VII, VIII, and IX are about "arithmetic," not "geometry"--a feature of the Elements often left unstated. Throughout, Heath intersperses his notes and comments, so the three volumes actually consist of as much Heath as Euclid. (Just Heath's translation, alone, is reproduced in the Great Books of the Western World, published in 1952 by University of Chicago.) Up until recently, maybe as late as the nineteenth century, a typical reader of Euclid would be quite familiar with Plato and therefore know that arithmetic and geometry are the philosophical branches of mathematics; music and astronomy are the remaining branches of mathematics, although somewhat contaminated since--in the Greek understanding as expressed by Plato--music and astronomy introduce motion, which is not strictly a mathematical topic.

Niceties such as these, and there are many others, would be lost to us if Euclid were transformed by using modern symbolism. Consider proposition 47 of Book I, the so-called Pythagorean theorem: Euclid talks about constructing squares on the sides of a triangle and never even hints at the possibility of the sides being "numbers." In fact, Euclid and all of his notable contemporaries and successors up to about the 15th century would consider the term "irrational number" as utter nonesensical babble--something more dangerous than an oxymoron such as a "square circle" because "square" and "circle" are not fundamental ideas. These comments may raise more questions than they purport to answer, but they give background to reviewing Heath, rather than Euclid.

Heath's edition, taken in toto, would have been very difficult to improve. His notes and collecting together of earlier commentaries represent a remarkable achievement in scholarship. He certainly made errors, but he provided nearly the best edition of Euclid possible at the opening of the last century. Heath made several efforts to explain the contents of Euclid by appealing to contemporary ideas and notations and, at least for me, these explanations simply reinforced the view that Euclid dealt with profound unanswerable questions that remain unanswered in contemporary mathematics.

Heath translated and edited several Greek primary sources, including Archimedes and Apollonius. Comparing his earlier translations with his later (in his career) Euclid, one immediately sees that Heath tried to preserve more faithfully Euclid's manner of speaking than he did Apollonius's or Archimedes'. This historigraphic point is important: if we are to respect the ancient Greeks by trying to understand or know their culture and values on their terms, we must have access to their culture with as few filters as possible. This line of arguing suggests that we should first study ancient Greek and then read Euclid, perhaps an ideal approach. Very few readers of Euclid take this approach. Hence, for an English reader (which includes readers of many other languages), a more faithful rendering of the Greek into English has greater importance because it does not filter the implicit culture as much as a less faithful rendering.

These views are my historian views. As a mathematician, I think of mathematics as timeless and critique any mathematical work on the basis of whether it represents good (read this as "my") mathematics. Heath knew his mathematics; he frequently calls on ideas from Cantor, who at this time is in the middle of his seminal publications. I would take the same critical approach if I were a philosopher--is Euclid good philosophy in that he provides answers to philosophical questions, regardless of whether many refinements have been formulated since Euclid? (By the way, there is no explicit philosophy in Euclid, but a lot of implicit philosophy.) In terms of editing a crucial historical document, Heath's work has withstood the test of about one century, and rightly so in my judgment. His Euclid is likely found among the personal books of people with a high regard for education.