John Stillwell on Girard Desargues

“The discovery of a method for correct perspective is usually attributed to... Brunelleschi... The first published method appears in... On Painting [Della Pittura] by Alberti. ...Alberti's veil, used a piece of transparent cloth, stretched on a frame... viewing the scene with one eye... fixed... one could trace the scene directly onto the veil. ...The mathematical setting... is the family of lines ("light rays") through the point (the "eye"), together with the plane... (the "veil"). ...In this setting, the problems of perspective and anamorphosis were not very difficult, but the concepts were... a challenge to traditional geometric thought. Contrary to Euclid, one had... (i) Points at infinity ("vanishing points") where parallels met. (ii) Transformations that changed lengths and angles (projections). The first to construct a mathematical theory incorporating these ideas was Desargues,... although the idea of points at infinity had already been used by Kepler...”

“The book of Desargues (1639), Brouillon project d'une atteinte aux événemens des recontres du cône avec un plan (Schematic Sketch of What Happens When a Cone Meets a Plane), suffered an extreme case of delayed recognition, being completely lost for 200 years.”