I agree that the exact form of an ellipse is not useful, but some general idea is.
Other example is the method for long multiplication. I think that it's not 1000 years old, but I can't find a source. One of the formed methods was to use square tables and the identity xy = ( (x+y)^2 - (x-y)^2) )/4. It guesses it was explained in schools, but now it's almost a curiosity. To use it, you must have a book with the tables of the squares, and the last edition of those books is from 1888: http://en.wikipedia.org/wiki/Multiplication_algorithm#Quarte...
Other example is the method for long multiplication. I think that it's not 1000 years old, but I can't find a source. One of the formed methods was to use square tables and the identity xy = ( (x+y)^2 - (x-y)^2) )/4. It guesses it was explained in schools, but now it's almost a curiosity. To use it, you must have a book with the tables of the squares, and the last edition of those books is from 1888: http://en.wikipedia.org/wiki/Multiplication_algorithm#Quarte...