Euclid's Elements Book 1: Proposition 47, The Pythagorean Theorem

This is the forty seventh proposition in Euclid's first book of The Elements. This proposition is essentially the Pythagorean Theorem. With a right angled triangle, the squares constructed on each of the two sides next to the right angle are equal to the square constructed on the hypotenuse (the long side of the triangle opposite the right angle).

[@samfessler1586]

I missed the part where it makes sense

[@emmadaily8052]

Thank you for this video! Really simplified things for me!

[@mnic6292]

you know it’s a hard prop when the video is almost 10 minutes 😭🙏

[@hank_smith]

maya💀💀

[@EulersAcademy]

Thanks for watching. I hope the video was helpful. This one is arguably the most famous, but a bit difficult to prove using Euclid. Over 100 different proofs have been created around this theorem through the centuries since Euclid and many are much easier and simpler.

[@gracemiller4251]

Great channel! One of my classes is on Euclid’s elements and this really simplified things for me!

[@ksol6675]

Thank you so much. If it weren’t for this I would be a failing student lol.

[@EulersAcademy]

Thank you for the kind words. I'm glad to hear that the videos are helping.

[@MilciadesAndrion]

This is one of the most important theorem. Widely used. Great video.

[@bigprovola]

Since angles GAB and BAC are two right angles, GA is straight on to AC [I. 14], and GA is parallel to FB by construction. Then, BG and FBC are a parallelogram and a triangle between the same parallels. So BG is double FBC [I. 41].

[@michaelmihov1651]

A very subtle omission here is to also prove that points g,a and c and a, h,b respectively lie on the same line, according to proposition 1.14, anyway you did a great job :)

[@EulersAcademy]

Thank you for watching. I'm glad you enjoyed the video. I appreciate the correction. I will take a closer look at this soon.

[@fpell4256]

Why do you need to show the triangles are parallel?

[@peterfuerst3643]

Lord help me

[@jakelm4256]

If you learned the first 46 propositions this is very straightforward. Too many people try to skim through or skip over propositions then get confused when a proposition uses those propositions in the proof.

[@Paul-qm7ye]

big brain euclid

[@AgeofReason]

Listen to all of the 47 codes during the presidential debate

[@liltommy1]

Wow thx

[@EulersAcademy]

Thanks for watching. I'm glad you enjoyed it.

[@girlysoundy]

ha angle fba

[@andrew3912]

666

[@patricktan3723]

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[@jovanyleal8549]

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[@bdpv025]

101010

[@olafnunez2011]

22

[@vendonix]

33

[@rosenti]

Don, You're Italian and I'm Danish. How could it ever work?
Leondardo DA VINCI/SHIVA/SHIVA/LEONARDO DA VINCI..
Since when did that EVER matter, when it comes to brotherhood?