proof of Desargues’ theorem
are collinear) and conversely.
Since no three of are collinear, we can lay down homogeneous coordinates such that
By hypothesis, there are scalars such that
The equation for a line through and is
giving us equations for six lines:
As claimed, these three points are collinear, since the determinant
is zero. (More precisely, all three points are on the line
Since the hypotheses are self-dual, the converse is true also, by the principle of duality.
|Title||proof of Desargues’ theorem|
|Date of creation||2013-03-22 13:47:51|
|Last modified on||2013-03-22 13:47:51|
|Last modified by||drini (3)|