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

/ mathoma
Heath's translation of Euclid's "Elements"
www.perseus.tufts.edu/hopper/t...
Greek-English parallel text plus diagrams:
archive.org/details/JL_Heiber...
This series is part of a larger project, part of which covers geometry.

[@rdbury507]

Surprisingly, I've never studied this proof before. The one I learned in high school involves similar triangles, but Euclid hasn't covered them yet. I was surprised by how elegant this is, using the tools available as efficiently as possible. The way this single proof puts together the most important results in Book I, and how these results were built painstakingly, brick by brick, from the axioms, is quite artistic. You might say it's classical architecture for the mind.

[@worldnotworld]

My reaction as well - I've somehow never come across it either. It's brilliant, and particularly appealing as a part of the unfolding sequence of results in the _Elements_.

[@thattimestampguy]

1:10 Square BDEC
1:25 More Squares.
Square GFBA
Square HACK
3:40 Two Adjacent Right Angles
5:00 DB = BC because all sides of a square are equal by nature of it's core square property that for a shape to be a square, all sides must be equal.
5:55 Side-Angle-Side means the Triangles are Congruent.
12:55 C^2 = A^2 + B^2

[@womb.w-o.2piR]

beautiful

[@comic4relief]

Seems like the diagram is a bit off-kilter,
as AL, BK, CF should meet in a point
(from Heath's note on 47).

[@zahydierodriguez1529]

Well that was fast