WebMath: geometry, length and angles

[Grand Bill]

Hi! I'm looking for information (books or an answer ... etc.).

My question is concerning a demonstration of the metric in Euclidian
geometry via
a geometric approach. It is easy to construct the quadric (or the
matrix) associated
with a given system of coordinate in 2D by using the cosine law (this
theorem can be
proven through purely geometric arguments). It is also easy to
iterate on the idea for 3D (or any dimension I gess). The problem is
that to find out
the length of the line from the origine to a point one needs the angle
between the
projection of the line on the plane XY (or YZ or ZX, the length of the
projection being
easily found using the above argument in 2D) and the original line.
While knowing the
angles between the XY lines the  YZ lines and the ZY it is not obvious
to me how to find
the disiered above angle. That is in a purely geometrical way. Knowing
this angle it is a
matter
of algebra to get the quadric (or the matrix). If any body has a book on
3D geometry to
sugest or any thing on the algebisation of the ruler and protractor in
2D or 3D (preferably
in 3D and based on basic geometry). I also would like any book on purely
geometrical area
and volume calculation (finding out the determinant finction througth
pure geometry).

Thanks for sharing your knowledge!

Alain Béliveau

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