Projective transformation — where it appears
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
The second eye is a shear
A picture drawn from two eyes is a picture drawn from one, of a different room. The map that puts the second eye away holds the picture plane still point by point and carries one centre onto the other, and the member of its family that matters turns out to be affine — a shear along the line joining the eyes, growing with depth, which is the same operation an oblique drawing performs.
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.
DemonstrationAffine mapcentre of projectionCross-ratioDesarguesFixed pointFree parameterHarmonic conjugateHomologyline at infinityOblique projectionPencil