Projective duality — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Two triangles and the line nobody drew
Desargues' theorem is the reason a hand-drawn shadow construction closes. An object and its shadow are two figures in perspective from the lamp; the theorem says their corresponding sides meet, pairwise, on one line — which is the ground line. So the closure a draughtsman treats as confirmation that the work is accurate is a theorem they cannot violate.
Four lines have a cross-ratio
The cross-ratio is introduced as a property of four points on a line. Its dual — four lines through a point carry the same number, and any transversal reads it back — is not a second theorem. It is why the first one is true: four rays from an eye are a pencil, every picture of them is a section of that pencil, and a quantity belonging to the pencil cannot depend on which section was taken.
Named alongside it
The objects these essays reach for when they reach for this one.
DemonstrationDesarguesHarmonic conjugateline at infinityProjective invariantcentre of projectionCross ratioGround linenecessary, not sufficientPinholePoint lightProjective map