Euclid's Elements Book 1: Proposition 44, Constructing a Parallelogram 2

This is the forty fourth proposition in Euclid's first book of The Elements. This construction proof shows how to build a parallelogram equal to the area of a given triangle and containing an angle equal to a given angle. Also, one of the sides of the parallelogram must be equal in length to a side length that we start with.

[@davyn_u4144]

Your videos are amazing. They help me so much. I’m grateful for the time and effort you put into making these videos. Without you I most likely wouldn’t understand the class I’m taking.

[@EulersAcademy]

Thank you for the kind words, I appreciate it. I'm glad the videos have been helpful.

[@singforjoy7123]

This is great! I have one question: what are the requirements in the extension of FG to FG? Is it necessary for GH to be equal to AB, and if it only needs to be long enough to create AH parallel to GB, how should I word that requirement while presenting? Thank you!

[@patricktan3723]

first? 1

[@jakelm4256]

The wording of this proposition is lousy. It didn't say a "finite" straight line. And when it doesn't specify that, it means the line should be continuous. So constructing a parallelogram on it equal to C should just be a couple steps. Also, it doesn't make sense why you can just construct your first parallelogram GFEB off AB like that when in Proposition I.42 the parallelogram had to be constructed off the base of the given triangle. Why are we suddenly assumed to be able to just construct the equal parallelogram on a different line? And if that is just allowed, why not have the ability to do it off AB like it ultimately wants us to do?

[@singforjoy7123]

That makes sense, but I wouldn't call it lousy because it was very good in a lot of places. What would you recommend instead?

[@jakelm4256]

@@singforjoy7123 please note my comment isn’t a criticism of the creator of this video. The creator simply goes over Euclid’s proof. So my criticism is of the source material.

[@singforjoy7123]

@@jakelm4256 Are you saying that you're criticizing Euclid's demonstration? (That's totally ok if you are. I'm just trying to understand)

[@jakelm4256]

@@singforjoy7123 yes, the demonstration is flawed, and it’s quite clear it is if you’ve worked through the entire text line by line and understand completely. Not sure if it was Euclid himself or one of the scribes a thousand years down the line - it’s very hard to tell when it comes to the Elements.

[@ksol6675]

HRA y’all here?

[@EulersAcademy]

Thanks for watching. I'm just curious, what is HRA?

[@ksol6675]

@@EulersAcademy It’s our school. We get taught euclid.

[@EulersAcademy]

@@ksol6675 Thank you for letting me know. What does HRA stand for?

[@ksol6675]

@@EulersAcademy holy rosary academy. We’re a small school in anchorage.

[@cricketsucker6281]

@@ksol6675 found it 47 wasnt horrible