Alternative Proofs To Euclid's Propositions

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SUMMARY

This discussion centers on the search for alternative proofs to Euclid's propositions, specifically proposition 37 from Book I, which states that triangles on the same base and within the same parallels are equal. The user expresses difficulty in locating a centralized directory for various proofs, unlike the abundance of resources available for the Pythagorean theorem. Recommendations include specific Amazon editions that compile Euclid's works, which may aid in finding alternative proofs. The conversation highlights the challenge of identifying proofs for unnamed theorems compared to those with established names.

PREREQUISITES
  • Understanding of Euclidean geometry principles
  • Familiarity with Euclid's Elements, particularly Book I
  • Basic knowledge of algebraic proof techniques
  • Experience with theorem identification and classification
NEXT STEPS
  • Research alternative proofs for Euclid's propositions
  • Explore resources like "The Elements of Non-Euclidean Geometry" for broader context
  • Investigate the Numberphile episode on prime numbers for related mathematical insights
  • Look into online databases or forums dedicated to mathematical proofs
USEFUL FOR

Mathematicians, educators, and students interested in deepening their understanding of Euclidean geometry and exploring various proof techniques beyond traditional methods.

moe darklight
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So lately I've been trying to start practicing proving things without being given a prompt (as in actually finding something out, not answering the question: "prove so and so"), which I'd never done before. -- But then the bummer is not knowing the name of what you've just proved :rolleyes:

So after searching I found out that one is a proof of Euclid's proposition 37 from book I (Triangles which are on the same base and in the same parallels equal one another). -- Is there a website where I can find alternative proofs from the one given in the actual book?

I used an algebraic proof and I want to find out who came up with it. -- I found websites with a bazillion (ok, more like 3 or 4) alternative proofs to the pythagorean theorem, but I can't find a website with proofs to the other propositions.

Is there like a proofs directory somewhere out there or something?
 
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I can only recommend https://www.amazon.com/dp/0486600882/?tag=pfamazon01-20 and the following volumes. If your theorem has a name, then it is very likely that many proofs can be found using that name on an internet search. But if it is just a theorem - number 37 - then it will be difficult to find it.
 

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