Incidence — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
The conic a circle becomes
A circle photographed is an ellipse, or a parabola, or a hyperbola, and which one is decided by a single incidence: whether the circle reaches the plane through the eye parallel to the picture. Not the lens, not the tilt, not how far away it is. The discriminant of the image agrees with that one test at every point of a sweep, and at the crossing it is zero to 1e-13.
The polar with a straightedge
Two secants through a point cut a conic at four places; the complete quadrangle they make has two more diagonal points; the line through those is the polar. Not one length, angle or midpoint is used, so the whole construction survives the projection that made the picture — and three unrelated pairs of secants land on the same line to 4.3e-13, while moving the point moves it by fifteen orders of magnitude more.
Named alongside it
The objects these essays reach for when they reach for this one.
centre of projectionConicHorizonProjective mapCircleComplete quadrangleCross ratioDiscriminantDualityEllipseHarmonic conjugateHyperbola