Hi! I enjoy your videos very much. But, I have a question that has been troubling for a while. Why do you say at this point, ie, proposition 35 of book I that the are of a rectangle with sides b and h is bxh? In what way does this formula for the area stems from Euclides axioms? Many thanks on any effort to make this clear. Greetings from Portugal
why cant the line be eb and cf be extended farther increasing the area of the bottom parallelogram cbdf keeping adbc constant would they not still have the same base but different area?
Thanks for the video - the translation I am reading is not clear on the definition of equality here (two parallelograms are equal - no mention of area) and if one assumes that equal parallelograms have equal sides and equal angles, this proof make no sense. If AREA is the equality sought, it makes perfect sense.
I am trying to stay true to Euclid's proofs, and he never ever mentions area. However, all of his proofs make sense when he says a triangle equals another triangle, or a square equals a rectangle, if we assume area.
EXCELLENT!!! THANK YOU! HALO FROM GREECE
what a clever proof! nice!
My favourite Euclid video so far.
Hi! I enjoy your videos very much. But, I have a question that has been troubling for a while. Why do you say at this point, ie, proposition 35 of book I that the are of a rectangle with sides b and h is bxh? In what way does this formula for the area stems from Euclides axioms? Many thanks on any effort to make this clear. Greetings from Portugal
This is a pretty cool proof. A small quibble I have is labeling the extra side as delta, since Greek letters are conventionally reserved for angles.
why cant the line be eb and cf be extended farther increasing the area of the bottom parallelogram
cbdf keeping adbc constant would they not still have the same base but different area?
Thanks for the video - the translation I am reading is not clear on the definition of equality here (two parallelograms are equal - no mention of area) and if one assumes that equal parallelograms have equal sides and equal angles, this proof make no sense. If AREA is the equality sought, it makes perfect sense.
I am trying to stay true to Euclid's proofs, and he never ever mentions area. However, all of his proofs make sense when he says a triangle equals another triangle, or a square equals a rectangle, if we assume area.