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1 of 1 people found the following review helpful
4.0 out of 5 stars
A Classic. But that does not make it excellent,
By
This review is from: The Thirteen Books of the Elements, Vol. 1 (Paperback)
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.
2 of 2 people found the following review helpful
3.0 out of 5 stars
There's a Better Way,
By A Customer
This review is from: The Thirteen Books of the Elements, Vol. 1 (Paperback)
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.
5.0 out of 5 stars
I think we're missing something here.,
By A Customer
This review is from: The Thirteen Books of the Elements, Vol. 1 (Paperback)
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 algebrait is highly abstract where geometry would treat the same problem concretely). "Euclid teaches us stepbystep 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.
5.0 out of 5 stars
one of the best scientific works,
By Carl Slim (the factory)  See all my reviews
This review is from: The Thirteen Books of the Elements, Vol. 1 (Paperback)
Heath does a better job than most in his notesalmost all commentary written in modern editions of great scientific works is hilarioususually 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 booksdon't worry. The principles of Math and Physics don't change, this book is as valid now as ever!
5.0 out of 5 stars
Eternal,
By A Customer
This review is from: The Thirteen Books of the Elements, Vol. 1 (Paperback)
There are two aspects that must be reviewed: Euclid's text itself and Heath's commentaries. I shall begin with the first.
The Elements can be understood by anyone, although appears to have been written for adults. It begins with a system of definitions, postulates and axioms (if you do not know then difference between a postulate and an axiom, Heath's commentary explains it), and proceeds to a logical development of the ideas that appear in connection with our intuition of space. The first book treats lines (intersections, parallels), triangles and paralelograms and most of it is contained in the elementary school curriculum. The second book is also taught at elementary level, but with algebraic symbols. It is interesting to see how the ancients, that didn't have such a good notation as ours, treated problems in general with the methods used in this second book. The third book contains the geometry of the circle; the fourth treats polygons inscribed and circunscribed in circles; again, both are taught at school. The fifth is not taught at elementary level and contains one of the most precious gems of the Greek thought: the theory of Eudoxus, that has many analogies with Dedekind theory of irrationals. Indeed, it has served as a general inspiration for nineteenth century mathematics because of its clear presentation of the meaning of a magnitude. So it's not surprising that, in its endeavours to understand what is a number, the mathematicians looked for light in this beautiful book. The sixth contains the theory of similar polygons and has a lot of features taught at school, but not all. The seventh, eight and ninth treats arithmetic, again without our notation, but are interesting for the same reasons as the second book. The tenth book aplies the theory of the fifth book to geometry and contains the theory of the incomensurables. The last three books contains the Greek version of Spatial Geometry, called by them Stereometry (there are some things that you learn in high school that were not treated by Euclid because they were not known yet, but not very much). Summing all up, you learn a lot of Euclid in school and high school, but probably not with the precision and beauty that he endeavours to treat in this monumental work. Few scientists and mathematicians after Euclid can be said not to have used his work. The beauty of all is that the work still can be classified as one of the most precise, elegant and understandable book of mathematics, even after two thousand years. You can only understand the why reading it. No reviewer can catch in words the essence of the Elements. Heath's commentary is very important because he explains in detail things that would appear difficult for us to understand. For example, why Euclid chooses the order of topics he chooses in his treatment, what is the meaning of every proposition to the whole of the thirteen books, the deficiencies of the work (in today's point of view) and how to correct them, and the history behind it all. It is possible to understand the Elements without his commentaries, but you will perhaps not appreciate all the subtle nuances (and there are many) that make us sometimes think difficult to accept that someone could write such monument to the human industry. Lastly, I can only say that eternity is little to this work.
5.0 out of 5 stars
Euclid Alone Has Looked on Beauty Bare,
By
This review is from: The Thirteen Books of the Elements, Vol. 1 (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.
4.0 out of 5 stars
Comprehensive English language review of _Elements I and II_,
By A Customer
This review is from: The Thirteen Books of the Elements, Vol. 1 (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 firsttime reading of Euclid. Even with these minor quibbles, however, my copy of Volume I is a wellworn, beloved volume with frequentlyannotated 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.
3 of 4 people found the following review helpful
5.0 out of 5 stars
I think we're missing something here.,
By Isaac (Fresno, CA United States)  See all my reviews
This review is from: The Thirteen Books of the Elements, Vol. 1 (Paperback)
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 algebrait is highly abstract where geometry would treat the same problem concretely). "Euclid teaches us stepbystep 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.
5.0 out of 5 stars
Order Your Thinking,
By A Customer
This review is from: The Thirteen Books of the Elements, Vol. 1 (Paperback)
Euclid teaches us stepbystep 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.
5.0 out of 5 stars
Royal Road to Geometry,
By Amazon Customer (Belem, Brazil)  See all my reviews
This review is from: The Thirteen Books of the Elements, Vol. 1 (Paperback)
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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The Thirteen Books of the Elements, Vol. 1 by Euclid (Paperback  June 1 1956)
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