How to best read Euclid's Elements

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In summary, the conversation discusses the reader's interest in starting to read Euclid's Elements and asks for tips on how to approach the book. The conversation highlights the historical significance of the book and recommends additional resources to gain a better understanding of the time period and context in which Euclid lived. It also suggests using a computer geometry program to interactively follow along with Euclid's constructions.
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jack476
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I checked out a very nice copy of Euclid's Elements from my university library containing unabridged translations of all 13 books. Nice big book, one proof per page, lots of diagrams. It's been interesting so far to flip through and even work a couple of the proofs myself, but now I want to really get into it.

On the other hand, it doesn't seem like a normal textbook where you read through it a few times, take notes, and solve a few problems, and it certainly doesn't seem like an ordinary book one just reads cover to cover.

How do I most productively tackle this thing?
 
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The short answer is to get a toga and imagine you're a Greek student studying in Alexandria at the feet of Euclid.

http://en.wikipedia.org/wiki/Euclid

The best you can do now though is to get a modern geometry book and compare and contrast the proofs.
 
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  • #3
Congratulations for wanting to start Euclid. You are going to read a book which literally shaped the mathematical world. We would be far different (and far less advanced) if it weren't for Euclid's book. The book practically invented the theorem-proof-axiom style and it hasn't changed since. It was also the guide into mathematics for many past mathematicians, and it was a standard textbook in schools for centuries.

That said, math has definitely evolved a lot since Euclid. We have found many mistakes in Euclid, many incomplete proofs, and many things which are just easier when we do it the modern way. And then there's the problem of age. Like any thousands year old book, it's outdated. It gave answers to questions that are not asked anymore (likely because it's solved). So let me try to guide you a bit:

First it is important to get some grasp on the historic significance of Euclid. You should try to get a feel for the time in which Euclid lived, for the problems that they were facing, for the many (partial) solutions they had. For this, I recommend the first volume of this comprehensive text: https://www.amazon.com/dp/0195061357/?tag=pfamazon01-20 You only really need to read a few chapters, until you've covered the Greeks. This will help you appreciate Euclid significantly more. You will understand why some sentences in Euclid are so awkward (like the parallel postulate), why some solutions are what they are, what impact certain proofs had and what questions remained unsolved.

And then you're ready to read Euclid. You probably want some additional book which puts things into a more modern perspective. The best book is Hartshorne: https://www.amazon.com/dp/0387986502/?tag=pfamazon01-20 This book is meant to be read together with Euclid. So I suggest to read Euclid a bit, and then read Hartshorne to see a more modern (and in my opinion: better) treatment of the same materials. You will also cover some nice geometry that's not present in Euclid but could be. And you'll see the solution for several flaws in Euclid.

If you're ready and want some more history of geometry, you could always read the sequel of Kline, but there is also this awesome book: https://www.amazon.com/dp/3642291627/?tag=pfamazon01-20

Lastly, while reading Euclid, I recommend highly to use a computer geometry system to experiment. For this, I recommend geogebra: https://www.geogebra.org This is a free, easy to use, but also very powerful geometry program. I recommend making all constructions of Euclid on geogebra. For example if he says "draw a parellel line", then use the program to draw it. So you can really be interactive!

Please do ask if you want some more information!
 
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@micromass - thanks for the link to geogebra. I wasn't aware of this software. It's very cool and has a lot more features than I expected!
 

What is the best approach for reading Euclid's Elements?

The best approach for reading Euclid's Elements is to start with the first six books, which cover the fundamental principles of geometry such as points, lines, angles, and basic constructions. These books also introduce important concepts such as the parallel postulate and the Pythagorean theorem. It is important to read these books carefully and make sure you understand each proposition before moving on to the next one.

Do I need to have a strong background in mathematics to read Euclid's Elements?

While it is helpful to have a basic understanding of geometry and mathematical concepts, it is not necessary to have a strong background in mathematics to read Euclid's Elements. The book is written in a clear and logical manner, and with patience and dedication, anyone can understand and appreciate the concepts presented.

How should I approach the more difficult propositions in Euclid's Elements?

Some propositions in Euclid's Elements may be more challenging than others. It is important to read the proposition carefully and try to understand the logic behind it. If you are struggling, it may be helpful to consult a commentary or seek the guidance of a mathematics teacher or tutor.

Should I read Euclid's Elements in its entirety or focus on specific books?

It is recommended to read Euclid's Elements in its entirety, as each book builds upon the previous one and provides a comprehensive understanding of geometry. However, if you are only interested in certain topics, you can focus on specific books that cover those topics.

How can I apply the knowledge gained from reading Euclid's Elements?

The knowledge gained from reading Euclid's Elements can be applied to many areas, such as architecture, engineering, and physics. It also helps develop critical thinking and problem-solving skills. The principles and concepts presented in the book are still relevant and used in modern mathematics and sciences, making it a valuable read for any curious mind.

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