Descriptive Geometry
Introduction
Descriptive geometry is a set of geometric techniques that allows representing three-dimensional space on a two-dimensional surface "Plane (geometry)"). Therefore, an adequate "reading" makes it possible to solve spatial problems in two dimensions in a way that guarantees the reversibility of the process.
In the current era, two models are recognized, in which they are considered: 1) “language” of representation and its applications; 2) treatise on geometry. Although it is not exactly the same, its development has been related to that of projective geometry.
Brief historical overview
Since Antiquity, as demonstrated by certain drawings found in prehistoric caves, man has always felt the need to graphically represent his environment, but it was not until the Renaissance that attempts were made to illustrate depth. Previously, builders needed to make faithful representations of the pieces they had to make. The best example of this is the stonework of the late Middle Ages and the Renaissance. The stonemasons performed complex three-dimensional stereotomies, particularly on the difficult stones at the junctions between arches "Arco (architecture)") or between vaults. The treatises of Alonso de Vandelvira, among others, remain as testimony to the level reached by stereotomy and its graphic tools. Other construction craftsmen such as carpenters had to master similar tools to make the complicated roofs of the large buildings of those times.
The new imperatives of representation of art and technology drive certain humanists to study geometric properties to obtain new methods that allow them to faithfully project reality. Figures such as Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Leone Battista Alberti, Piero della Francesca and many more are framed here. Along with them, Filippo Brunelleschi stands out, who codified the conical perspective based on medieval speculations on the reflection of mirrors.
By discovering perspective and the section "Section (geometry)"), all of them create the need to implement the formal bases on which the new modality of geometry that this implies is based: projective geometry, whose fundamental principles appear from the hand of Gérard Desargues in the 19th century. This new geometry was also studied by Blaise Pascal and Philippe de la Hire, but due to the great interest aroused by Cartesian geometry (analytical geometry) and its methods, it did not reach as much diffusion.