On 7/28/2013 8:26 PM, Ken Pledger wrote: > In article <email@example.com>, > Thomas Nordhaus <firstname.lastname@example.org> wrote: > >> Am 28.07.2013 23:01, schrieb Ken Pledger: >>> .... >>> That's all. It's a traditional method in old text-books which aren't >>> read much any more, and it doesn't need any calculus. >> >> I think implicitly it does.... > > > It needs the fact that the shortest path from a point to a line is > along the perpendicular. My geometry students prove that as a little > exercise using Euclid I.16 and 19 - definitely no calculus. >
Have to love those old textbooks.
When I meet people having difficulties, I often advise them to seek some old texts from used bookstores. They often have better expositions.
When I read your post, I thought of a dusty old book on analytical geometry by W.K.Morrill.
No calculus needed. Just the definition of angle in terms of inner product.