Methodus Geometrica 1598 by Paul Pfintzing

Methodus Geometrica is a printed hand coloured treatise on geometry and surveying published in 1598 in Nuremburg, Germany. It is held in the SP Thompson Library, part of the Rare Book Collection at the IET Archives.

Perspective and Geometry

Methodus Geometrica-Linear Perspective

During the Renaissance, European artists began to paint with the goal of greater realism. Artists such as Brusnelleschi, Alberti, Piero Della Francesca and Leonardo da Vinci brought science to art, conducting investigations into the true nature of form. They learned to paint lifelike images and they became skilled at creating the illusion of depth and distance by using the techniques of linear perspective. Brunelleschi is credited with the first correct formulation of linear perspective in about 1413. 

He understood that there should be a single vanishing point to which all parallel lines in a plane converge and that scale was dependant on an objects distance behind the plane of the canvas. It was Alberti though, who first described these rules.

The most mathematical of all the works written on perspective was Italian Renaissance artist, Piero della Francesca's work, Trattato d'abaco (circa. 1450). It included a lengthy discussion on geometry and numerous illustrations drawn in perspective. In a later book Piero gives geometric theorems that relate to perspective along a plane. 

The mathematician Luca Pacioli embraced the work of Piero in his own texts, which were illustrated by Leonardo da Vinci. Leonardo himself developed an acute interest in perspective and the two continued to learn from each other. Leonardo who, more so than anyone else, meshed the study of art and mathematics, studied the converse problem of perspective, eventually making the distinction between artificial and natural perspective.

Methodus Geometrica-Studies in Perspective

These skills enabled surveyors and cartographers of the Renaissance  to provide realistic depictions of construction and nature. In Methodus Geometrica, Pfintzing gives a detailed discussion of this newly understood science of perspective.

The Methodus Geometrica also illustrates what sixteenth century surveyors would have worn on the next page: Elizabethan Clothing.