I Need Help Understanding Euclid:

[spring kettle]

So, I am going to be in a class that has you memorize Euclid props, and then present them. We are supposed to have the entirety of Book I memorized by the end of the class.
I have memorized all of the first thirteen props, except for 4, 8, and 13. I can memorize them pretty easily, I just have to understand them, and then it is stuck in my head. But I am having trouble understanding said 4, 8, and 13. Can you guys help?

https://www.youtube.com/watch?v=GP6K-2nvZ-Q&list=PL2V76rajvC1I2TrbPMRLcTqhdcbha4sDE&index=5

https://www.youtube.com/watch?v=IuSdIB73AXQ&list=PL2V76rajvC1I2TrbPMRLcTqhdcbha4sDE&index=9

https://www.youtube.com/watch?v=veV5-j0f4eI&list=PL2V76rajvC1I2TrbPMRLcTqhdcbha4sDE&index=14

[west fulcrum]

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[spring kettle]

@modern ledge.

[modern ledge]

Okay, so.

How good are you with Cartesian geometry?

That is, geometry in the xy plane?

@spring kettle

[spring kettle]

Very horrible.
But you don't need Cartesian geometry to do these proofs.

[modern ledge]

It would actually make things a lot easier.

See, the reason Descartes invented this method, which is called formally analytic geometry, is because it allows you to convert geometric problems into algebraic problems and vice versa.

[spring kettle]

But I am learning geometry, not algebra.

[modern ledge]

...yes. And understanding this method will make you better at geometry.

[jaunty bison]

are you having a problem in understanding them?

[spring kettle]

Yes.

[little sage]

can u explain to me how we can use a cartesian plane for euclidean?
I'm interested, it can help me

[modern ledge]

Not here, it's rude to hijack other people's help threads.

[little sage]

ok I'll open my own thread then and ping u

[light sinew]

@spring kettle

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