Rating: 
Summary: Reviewing editor Heath, not Euclid
Review: 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.
Rating:
Summary: Order Your Thinking
Review: Euclid teaches us step-by-step how to prove the most fundamental and complex concepts of geometry in such a systematic and understandable way. By learning Euclid's propositions, we also find ourselves thinking and speaking in a more ordered fashion. I recommend these books to anyone interested in math as well as those who want to improve their debating and reasoning skills.
Rating:
Summary: Order Your Thinking
Review: Grab a protractor and a compass and go to work. Heath did a wonderful job in explaining the details and history of Euclid's work.
Rating:
Summary: one of the best scientific works
Review: Heath does a better job than most in his notes-almost all commentary written in modern editions of great scientific works is hilarious-usually some half brite clown trys to find a million faults in the writing of someone who is obviously one hell of a lot more intelligent. Heath just gives the likely facts surrounding Euclid's life, works, and the evolution of the math contained in The Elements.
This is math that is accesible if you're willing to put in the time, because it starts with principles we're all familiar with and can agree on (such as the whole being greater than the part), and slowly and methodically works it's way to comparisons of the 5 Platonic solids. Along the way he covers number theory, plane and solid geometry, and provides an early basis for calculus and even certain branches of physics, although the terminology is obscure if you're familiar with more modern methods. Approach this work as a puzzle book, and try to solve the proofs yourself, or even try to disprove them; proceed slowly, it will take more than a year to work through all 13 books, but you will understand these things much better than the average math teacher when you're done. It's also more fun to try to understand the work of one of the greats than it is to study from one of those overpriced college calculus books-don't worry. The principles of Math and Physics don't change, this book is as valid now as ever!
Rating: 
Summary: A Classic. But that does not make it excellent
Review: I am pretty much interested in geometry. I am, in fact, enthusiastic, and enthusiastic people usually do have strange habits regarding their subjects of enthusiasm. I, for one, like to buy all of the geometry books I can lay my hand on regardless of its relevance to my studies or usefulness for reading.And this book, being a classic, was on top of my demanded books list until I bought it around 1998. As usual with these books, I postponed its reading until the new millennium. But when I read it I was very disappointed. The material of this book is one of the most beautiful afforded by a mathematics book. It is very interesting, but, alas, it is written in a forbidding notation. I can understand high level math books in Algebra and Analysis, but this book confused me with words. Frankly, I do not see why a math book is supposed to explained in words after all this development of mathematics. Unfortunately, most historian mathematicians disagree with my view. They see that writing the elements of Euclid (The first rigorous set of axioms and lemmas) in the modern notation is unfaithful to the original manuscript. Well, I have got no problem with that, but at least try to make it up to date so that people could go through it. You see that I gave it 4 stars. Yes the material of the book was excellent, and it rather deserved 5 stars, but for this tedious presentation. One other thing I hated a bout this volume was the introduction. It had taken about one third of the book, and after the definitions of the first book, there are notes on the definitions and postulates that take another third of the book. These notes are not all that easy and at a higher level than the postulates of Euclid, and I found them irrelevant. I do not understand here why did not the author, who made notes on the definitions, make a section explaining all the postulates in modern notation. As for the material, the volume covers Books I and II of Euclid's 13 books of the elements. The first book introduces a set of definitions and goes on characterizing triangles. It, even, proves the Pythagorean theorem. This proof was a bit difficult, a simpler proof can be found else where, but, after all, it is amazing how mathematicians could have solved such a problem thousands of years ago. He introduced the famous constructions of straight edge and a compass, he would construct an isosceles triangle starting from a given segment by merely using a straight edge and a compass. Later on, Galois studied this construction in his famous Galois theory (try Artin's Galois theory, although I do not guarantee it). The second books deals with areas of triangles and rectangles, and Euclid's notation shows it incompetence when he uses the same name for two different things. For in the first book he used to say that two triangles are equal if all their angles and sides are equal, but in the second book he would define two triangles to be equal if they had the same area! All in all, I enjoyed the book, and would have enjoyed it more if not for the drawbacks.
Rating:
Summary: Euclid Alone Has Looked on Beauty Bare
Review: 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.
Rating:
Summary: I think we're missing something here.
Review: I read most of the twelve reviews. I gleaned from them several quotes which demonstrate my point. First, the quotes: "The principles of Math and Physics don't change, this book is as valid now as ever!" from the review by Carl Slim [I disagree. Neither math, nor physics are unchangable. They evolve, expand, modify, and make new discoveries regularly.] "I can understand high level math books in Algebra and Analysis, but this book confused me with words. Frankly, I do not see why a math book is supposed to explained in words after all this development of mathematics.These notes are not all that easy and at a higher level than the postulates of Euclid, and I found them irrelevant....It even, proves the Pythagorean theorem. This proof was a bit difficult, a simpler proof can be found elsewhere, but, after all, it is amazing how mathematicians could have solved such a problem thousands of years ago."
according to the reviewer from Qatar [This is a lengthy quote, however, it points out the misunderstanding regarding Euclid's treatment of the Pythagorean Theorem. Euclid's Prop. 47 gives a visual representation and proof, whereas the equation used in algebra is abstract (this is why many struggle with algebra--it is highly abstract where geometry would treat the same problem concretely). "Euclid teaches us step-by-step how to prove the most fundamental and complex concepts of geometry in such a systematic and understandable way. By learning Euclid's propositions, we also find ourselves thinking and speaking in a more ordered fashion. I recommend these books to anyone interested in math as well as those who want to improve their debating and reasoning skills."
according to a reader/reviewer in Eastern Pennsylvania (bless you) What's missing from the first two altogether, but pointed to in the third, is this: Euclid,his contemporaries, and many who followed in his footsteps were philosophers as well as mathematicians. Both math and philosophy try to produce certainty through systematic methodology. Euclid's Elements therefore, are not only profitable for developing an understanding of geometry, it can also aid in the development of disciplined and logical thought. Just listen to philosophy students; they use terminology similar to that of mathematicians. In fact, this is one reason classical home schoolers are sometimes taught Euclid; it compliments the study of the Great Books, logic, philiosophy, and forensics.
I actually heard recently that a new translation is coming out real soon, if it's not out already.
I hope I don't come off as a smartypants, writing essentially a review of the reviewers. I don't have advanced degrees in math, physics, or philosophy, but I believe the reviews are incomplete without this understanding of the historical relationship between math and philosophy and the use of Euclid. Blessings.
Rating: 
Summary: There's a Better Way
Review: I read most of the twelve reviews. I gleaned from them several quotes which demonstrate my point. First, the quotes: "The principles of Math and Physics don't change, this book is as valid now as ever!" from the review by Carl Slim [I disagree. Neither math, nor physics are unchangable. They evolve, expand, modify, and make new discoveries regularly.] "I can understand high level math books in Algebra and Analysis, but this book confused me with words. Frankly, I do not see why a math book is supposed to explained in words after all this development of mathematics.These notes are not all that easy and at a higher level than the postulates of Euclid, and I found them irrelevant....It even, proves the Pythagorean theorem. This proof was a bit difficult, a simpler proof can be found elsewhere, but, after all, it is amazing how mathematicians could have solved such a problem thousands of years ago."
according to the reviewer from Qatar [This is a lengthy quote, however, it points out the misunderstanding regarding Euclid's treatment of the Pythagorean Theorem. Euclid's Prop. 47 gives a visual representation and proof, whereas the equation used in algebra is abstract (this is why many struggle with algebra--it is highly abstract where geometry would treat the same problem concretely). "Euclid teaches us step-by-step how to prove the most fundamental and complex concepts of geometry in such a systematic and understandable way. By learning Euclid's propositions, we also find ourselves thinking and speaking in a more ordered fashion. I recommend these books to anyone interested in math as well as those who want to improve their debating and reasoning skills."
according to a reader/reviewer in Eastern Pennsylvania (bless you) What's missing from the first two altogether, but pointed to in the third, is this: Euclid,his contemporaries, and many who followed in his footsteps were philosophers as well as mathematicians. Both math and philosophy try to produce certainty through systematic methodology. Euclid's Elements therefore, are not only profitable for developing an understanding of geometry, it can also aid in the development of disciplined and logical thought. Just listen to philosophy students; they use terminology similar to that of mathematicians. In fact, this is one reason classical home schoolers are sometimes taught Euclid; it compliments the study of the Great Books, logic, philiosophy, and forensics.
I actually heard recently that a new translation is coming out real soon, if it's not out already.
I hope I don't come off as a smartypants, writing essentially a review of the reviewers. I don't have advanced degrees in math, physics, or philosophy, but I believe the reviews are incomplete without this understanding of the historical relationship between math and philosophy and the use of Euclid. Blessings.
Rating:
Summary: There's a Better Way
Review: If you like long, tedious introductions and the need to sort through endless words to find what you're looking for, then you might want this version of Euclid's work. On the other hand, if you want to get to the point and prefer a clear resource for study, the version published by Green Lion is FAR superior to this one.
Rating:
Summary: Royal Road to Geometry
Review: Sure, there is no royal road to geometry, the master said. But this edition, from Heath, bring to our days the pleasure and intellectual enlightment of admiring Euclid's master work, the geometry textbook for the centuries, in our own language. If you love math, read it for fun.
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