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Customer Reviews (20)

Extensive copy!
This copy is intended for the reader who already knows The Elements, and wants to investigate the influences of Euclid, and a vigorous account of every single step of the translation.It is important to know that this is more of a commentary on the Elements, rather than The Elements itself.For those who want just The Elements, the copy you want is Euclid's Elements.

If this is the first time you are reading The Elements, this is probably not the copy for you.However, if you are pondering about the translations, or are curious about who might have influenced a certain proposition, this edition would be perfect.

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

The Fundamentals of Math AND Philosophy
For anyone looking for an introduction to math, geometry more specifically, or philosophy at large, this is THE book, and in my estimation, THE edition to get.Heath is no fly-by-night pop-philosopher.His notes are almost as worthwhile as the text itself... a truly monumental feat.

The rigors of geometry, the method of logic learned in these proofs, are one of the best ways to prepare the mind for real philosophy.Anyone can talk about the true and the good in a manner that inspires awe through vagueness and transcendent language, but that is a very different matter than the sort of philosophy that is built upon the real work of logic and hard-earned definitions.

If you have any interest in the latter, I heartily commend this book to you.

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

Profoundly humbling.
It is difficult to argue with the fact that Euclid stands as one of the founding figures of mathematics. The ability of the ancient Greeks to perform complex mathematical calculations using only logic, a compass and a straight edge is profoundly humbling. Euclid's 13 books cover an enormous swath of math, from planar geometry to trignometry to irrational numbers and root finding to 3D geometry.At one point you feel he is on the cusp of discovering the Calculus.Considering these pages were written more than two thousand years ago I stand in awe.

That said, I have some serious problems with the way Euclid's materials are presented in this Dover Mathematics book.The book itself (a three volume set actually) is a reproduction of Sir Thomas Heath's famous Elements of 1908.This is the second Dover edition and it is unabridged.Usually I'm not a fan of abridgements but this book could certainly use it.At the very least some modernization of the notes and introductory essays would seem to be in order.Of course, if you approach this book as amathematician, you will likely skip over the first hundred or so pages and be spared some pain.If you are a student of philosophy you aren't so lucky.Heath's notes are dense, tangential, and require the mastery of at least four languages, two of which are now dead.Latin and Greek quotes of considerable length are left untranslated as an exercise for the reader, and French and German receive similar treatment.At times the footnotes threaten to overwhelm the text and for every page of Euclid there must be at least 3 pages of commentary.References to obscure mathematical theory and little known Greek manuscripts abound.I understand that this is Victorian Age scholarly writing at its height but it makes it a tough read - and I say this as someone with a background in Latin, Greek and French as well as considerable mathematical (never got much past partial differential equations) background. Heath was a polymath of the highest order.

If you are brave enough to tackle this book you may want to grab just the volume that interests you.The first volume contains introductory remarks by Heath and most of the well known postulates related to geometry.Book I, postulate 5 (I.5) is the well know triangle inequality while I.47 is the geometric proof of the Pythagorean theorem - a thing of rare beauty.In the second volume, Books III and IV deal with circles and arcs while Book V deals with ratios.I found the proofs with respect to ratios difficult to follow owing partially to the language in which they are couched. Book VI applies the theory of ratios to geometric figures while books VII and VIII deal with factorization, multiples and primes.Book IX deals with prime numbers, perfect numbers and odd and even numbers.The third volume begins with Book X which deals at length with rational and irrational numbers.It is here that the Greek methods seem to be a little weak, requiring rather clumsy proofs which would be much simpler in modern notation.Still, it is amazing to see the math they did with what they had.Books XI and XII deal with solids - spheres, prisms, parallelpipeds and pyramids - while Book XIII deals with the platonic solids.It is here that Euclid approaches calculus with his method of proof by exhaustion.The persistent reader will, by this point, also be quite exhausted but, as a bonus, Heath throws in the sometimes attributed Books XIV and XV, both of which are brief and neither of which are by Euclid.

If you are planning on buying this book I would recommend you consider the reason carefully.If you are looking for a math text there must surely be something more modern with a more concise commentary available.If you are a student of Greek philosophy you may find the first volume useful for its introductory notes but the last two volumes are likely unhelpful.If you are fluent in Latin, Greek, French, German and English, have a background in ancient greek literature, Renaissance and 19th century mathematical theory, and love geometric proofs then this is the book for you ... Read more

Product Description
This Elibron Classics book is a facsimile reprint of a 1921 edition by the Clarendon Press, Oxford. ... Read more

Customer Reviews (2)

more than just history
It should be noted that this is one of a two volume set. This author also compiled and commented upon The Elements ofEuclid in three volumes [also available here].

Theseworkswere first brought to my attention by my Greeklanguage professor nearly 40 years ago as the best English language source on Greek Mathematics.

Just as the Greeks did not view `pure' mathematics or geometry as a lifes-work so to younger readers [through collage] the methods of logic may prove most useful.

For we retired `geezers' not quite ready for Oprah reruns and made for T.V. `romances' it may be the stimulation ofthe brain by the problems [which are documented and solved infull], the history andthe `awe' of how much these did `without computers';

Academically great
This is not a terribly exciting book to read, but it is a superior reference for looking up Greek mathematicians.It is apparent that the author is partial to Euclid, as his section is close to a third of the book, (see the author's version of the Elements)but being a Euclid fan myself I can forgive this easily.Even the most obscure mathematicians are covered in good detail along with what they proved, as well as how they proved it.For those interested in historical mathematics, this book is invaluable. Note:This is a two volume set.I thought it was only one and I only purchased the second.Be sure to get both. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is a reproduction of the original edition including imperfections. Included with the purchase of this book is free trial access to Million-Books.com where you can read more than a million books for free, including many of the greatest books of all time like: * The complete works of Shakespeare, Charles Dickens, Mark Twain * Swift's Gulliver's Travels * Defoe's Robinson Crusoe * Thackeray's Vanity Fair * Jane Austen's Sense and Sensibility and Pride and Prejudice * Sigmund Freud's Interpretation of Dreams * Albert Einstein's Relativity * F. Scott Fitzgerald's Great Gatsby * George Orwell's 1984 * Milton's Paradise Lost * Smith's Wealth of Nations * Darwin's Origin of Species * Aristotle's Ethics * Plato's Dialogues * Thos. à Kempis' Imitation of Christ * Hume's History of England * Carlyle's French Revolution * Gibbon's Decline and Fall of the Roman Empire * . . .and more than a million more books These books have been a source of inspiration, joy and enlightenment to millions through the ages. Now they can all be yours. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
The Bones, a concise overview of Euclid's Elements, provides all the propositions and diagrams without the detailed proofs. Readers can use it to see the scope and structure of Elements, identify exactly what Euclid covers and what he doesn't, and to find the location of remembered propositions. The Table of Contents lists the subject matter of each book, number of propositions, and locations of definitions, to further assist the reader in seeing the scope and structure of Elements and to examine Euclid's treatment of specific areas. Equally at home in backpack or pocket, on desk or bedside table, it has enjoyable possibilities limited only by your imagination. ... Read more

Customer Reviews (4)

Euclid: The Bones

If you have any interest in Euclid's Elements of Geometry, then this will, I believe, interest you also. It is the Elements without the proofs. It is Heath's translation without his commentary. The design of the book is elegant. The layout is clear and clean. The diagrams have been redrawn and the fonts are crisp and inviting. The cover is durable and the pages are sewn in. The book fits well in the hands. It is a paperback the way paperbacks ought to be made. And it is Euclid. What more do you want?

Great reviewing tool for the Elements
I love the elements, but because of its size, I can only read it at home, which slows me down a lot.
With this book you can bring the Elements with you everywhere. It's quite small, and thin too. I've found it very useful as a learning and reviewing tool; The format (diagram and enunciation without the proof), let you see right away if you understand each proposition. For those you understand, it's immediately obvious as the proof comes to your mind while looking at the diagram. For those you don't, it's really fun to try and come up with the proof, given the diagram is a major tip. whether you succeed or fail, it's a thrill to go back to the Full Elements, and read Euclid's proof, As your understanding is deeper. Another fun exercise when you are familiar with a proposition is trying to prove it in your mind with just the proposition. So many way to use this book, I'm wondering why no one had the idea before. With, this you Can master this timeless classic in a fun way.

A great companion to a great book
Euclid's "Elements" is easily one of the most important books ever assembled and "Bones" is a summary whose quality is unlikely to be surpassed. The diagrams and text are logically laid out, the printing is clear, and the cover and binding are very sturdy. Obviously a lot of effort and care went into producing this companion volume, and any fan of Euclid would be well-served by it.

Arguably the most significant 200 pages of published mathematics now in existence
This is one of those books that should be in every mathematical library, academic and personal. It contains a distillation of "Euclid's Elements"; all the common notions, definitions, postulates, and propositions. All that is missing are the proofs. As such, it is the best quick geometry reference in existence and has been placed on my reference shelf where it will remain until it is wore out and I need to purchase another copy. I would argue that it is the most significant 200 pages of published mathematics now in existence.

Published in Journal of Recreational Mathematics, reprinted with permission. ... Read more

Product Description
This is a detailed exposition of Aristotelian mathematics and mathematical terminology. It contains clear translations of all the most important passages on mathematics in the writings of Aristotle, together with explanatory notes and commentary by Heath. Particularly interesting are the discussions of hypothesis and related terms, of Zeno's paradox, and of the relation of mathematics to other sciences. The book includes a comprehensive index of the passages translated. ... Read more

Product Description
The definitive edition of one of the very greatest classics of all time--the full Euclid, encompassing almost 2500 years of mathematical and historical study. This unabridged republication of the original enlarged edition contains the complete English text of all 13 books of the ELEMENTS, plus analyses of each definition, postulate, and proposition. ... Read more

Customer Reviews (4)

books 3-9, not 3-4
Contrary to the reviewer who says it is not clear that this is only one volume of 3, I thought there was 6 or 7 volumes altogether. The title clearly says "The Thirteen Books of the Elements, Vol.2: Books 3-4", so obviously this is volume 2 of a collection. Knowing that the original Elements had 13 books, my assumption was there must be several more volumes in this new edition. Actually, Amazon's title of the book is wrong! If you look at the front cover, or the index of this book, you can see that it says "Vol.2 (Books III-IX)". And if you are interested to know, volume 1 covers books I and II, and volume 3 covers books X through XIII so altogether they cover the original Elements entirely.

Update (10/14/2010):

At the time I wrote the previous review, the book's title was "The Thirteen Books of the Elements, Vol.2: Books 3-4". Obviously Amazon must have realized the mistake and corrected the title to "...: Books 3-9")

Euclid's Elements Volume 2
This unabridged republication of the 2nd enlarged edition originally published by Cambridge University Press contains the complete English text...together with a critical aparatus which analyzes each defintion, postulate, and proposition in great detail. It covers textual and linguistic matters; mathematical analysis of Euclid's ideas; classical, medieval, renaissance, modern commentators and their interpretations; refutation, supports, extrapolations, reinterpretations, historical notes, all given with extensive quotes.

Book III to IX of the Elements. Circles, their properties, tangents, segments, figures described around and within circles, ratios, proportions, magnitudes of lines; of triangles; polygons and their parts; prime numbers, products, ordinary numbers, plane numbers, solid numbers, series of ratios, etc.
--- excerpts from book's back cover

Classic = Elegant, if not for the notation!
We, the children of this new age, are deprived of major classics and beautiful mathematics because of the tediousness of the notation. Oh, do not be optimistic, this is not the only book with forbidding notation, see Artin's Galois theory, which is an excellent book if someone just tries to update its notation.

Aside from that the book was a merry one. It contains more books than the first one. It contains the books 3 up to 9 of Euclid's 13 books of the elements.

Book 3 is a delightful one. Its sole purpose is to characterize circles. It goes with the same style of the first two books given the first volume. Books 4 continues in the same fashion and studies circumscribing and inscribing figures by others.

Book 5 is the first attempt to bring geometry near to algebra. It deals with proportions. The notation started getting more and more cumbersome. He continues giving us things that we know already. And all through the volume until book 9 we see results commonly given in simple college algebra in the most tedious fashion.

I praise this volume only for the material on circles and I see that it is worth reading if you have a strong constitution. As for me I am not going to read the third one about the out of date commensurable numbers.

CAUTION
This is a word of warning to potential purchasers of this volume; it is only one of three volumes.This is not made clear in the presentation so just be aware.Look for the other two volumes if your intent is to acquireall thirteen books of Euclid's, The Elements. ... Read more

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Superb scholarly study documents extraordinary contributions of Pythagoras, Aristarchus, Hipparchus, Anaxagoras, many other thinkers in laying the foundations of scientific astronomy. Essential reading for scholars and students of astronomy and the history of science. Accessible to the science-minded layman. Introduction.
... Read more

Customer Reviews (1)

A doxography
I had to look up "Doxography" in the Oxford English Dictionary - it is a collection of philosophical opinions. The book "Greek Astronomy" is a Dover reprint of a book written in 1932. It consistsof a long (57 pages) introduction followed by a great many quotes (renderedinto English) from ancient Greek authors. The selection emphasizes generalquestions, such as "Does the Earth move?" - according to Ptolemyit does not. Perhaps useful as a souce book. But then again, perhaps not. ... Read more

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"Hyde Park, and its various characters, 16. Sir F----s B---- tt, 22, Delightful reverie, 23. " ... Read more

Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

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Aristarchus of Samos was the first man to suggest that the sun, and not the earth, is the real centre of our system, and thus for the first time to assign to the earth a subordinate rank. In this volume, Heath gives us a translation of that work, plus a detailed history of Greek astronomy. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more