Re: button-hole problem

>  > So is a perspective projection of a conic section always a conic
>  > section?
> 
> I don't know now how the greeks liked to prove this this.  But an
> algebraic proof valid in all dimensions is essentially this:
> 
> Lemma.  If A:R^n --> R^n is a non-degenerate R-linear map of vector
> spaces and q:R^n --> R is a homogeneous quadratic function, then
> the composition qA: :R^n --> R is a homogeneous quadratic function.
> 
> Maybe someone will elaborate...

I hope so, because I don't understand it.
Actually, I have a vague idea about vector spaces and maps (if that's the
English term for _Abbildungen_).  Did the Greeks invent (or discover, if you
prefer) projective geometry?  I thought it was either Descartes, or followed 
Descartes.  Doesn't one need a coordinate system for projections?

Thanks.

Laurence