Applied Geometry

Thus far we have considered the academic tradition of geometry. It is clear that Desargues’ Rough Draft on Conics must be seen as related to (indeed derived from) this tradition. None the less, in attempting to relate the Rough Draft on Conics to other works by Desargues we shall be obliged to examine a different tradition, the practical tradition of applied geometry, to which all Desargues’ other works belong—with the exception of a few pages about teaching the reading and writing of music, which were published in Mersenne’s Harmonie Universelle (1636).1 Since we are particularly interested in the ideas we find in Desargues’ work on conics, we shall concentrate chiefly upon studies of linear perspective, for linear perspective was the subject of the only geometrical work Desargues seems to have published before he wrote his Rough Draft on Conics. However, at the very end of the main body of the text of his short work on perspective, published in 1636,2 Desargues refers briefly to solutions of two other groups of geometrical problems: those associated with the cutting of stones for use in architecture and those associated with setting up the gnomon of a sundial. He in fact went on to publish treatises on each of these two groups of problems. The one concerned with the cutting of stones, published in 1640, is entitled Brouillon project d’exemple d’une maniere universelle du S.G.D.L. touchant la practique du trait a preuves pour la coupe des pierres en l’Architecture... (A rough draft of an example showing a universal method of Monsieur Girard Desargues of Lyon for employing guide lines in cutting stones for Architecture...).