BOOKS ON ARCHITECTURE
||Maniere universelle de Mr Desargues, pour pratiquer la perspective par petit-pied...
||Paris, P. Des Hayes, 1648
||Tours, CESR, 7159
The Maniere universelle de Mr Desargues, pour pratiquer la perspective par petit-pied comme le geometral is the result of a friendly and learned collaboration between Girard Desargues and Abraham Bosse. Desargues, the creator of projective geometry, “one of the great minds of this time” according to Blaise Pascal, would not truly be recognized for his mathematical work until two centuries later. At the beginning of the seventeenth century, he was nevertheless a protagonist that learned Europe, led in particular by Père Mersenne, listened to. As for Bosse, he was an accomplished engraver, popular with connoisseurs of engravings and artists. He was not satisfied merely to be a skilled engraver; he made many drawings, in particular genre scenes. Thus they were both interested in perspective, one to analyze the geometric constructions at play and the other to analyze how perspective contributed to “the satisfaction of the eye”. What’s more they had friends in common, like the painter Laurent de la Hire. In 1636 Desargues published a short opuscule on the new and universal method for practicing perspective (reproduced in this 1648 publication, pp. 321-334). Desargues did the promotion work for it, which allowed him to write in his Brouillon project of August, 1640, “The average person will be able to learn perspective in few days, and the intelligent in few hours, as have done among others in Paris, M. Buret, master joiner, M. Bosse, copper-plate engraver, and M. De La Hyre, painter, each one among the most excellent men of the time in his art”. Bosse was well enough informed in geometry to understand Desargues’ constructions in depth and even to adjust them to facilitate the draftsman’s task. They both shared equally the wish to find “shortened and infallible methods” to put at the disposal of “craftsmen” so that their work would be guided by reason and not misdirected by imitation, impulse or error. The Brouillon project on conic sections was published in 1639; it was a major mathematical book by Desargues which might have gone unnoticed if the author had failed to insert in the last pages of the 1648 book some mathematical propositions relating to it. The following year Desargues published two other booklets in which he applied “his own and distinctive thinking” to gnomonics and strereotomy. But Desargues’ writing style is elliptical, with a vocabulary he sometimes invented which discouraged the reader. Bosse, on the contrary, familiar with working groups and “Academies where one studies the art of portraiture”, was sensitive to more instructive approaches. And above all he had the power of illustration at his command. In 1642 the two boon companions stood together against the various controversies set off by Desargues’ publications. Desargues obtained a privilege to allow Bosse to publish his universal methods applied to stereotomy, gnomonics and perspective. The first two books on stonecutting (La pratique du trait a preuves...) and on sundials (La maniere universelle... pour poser l’essieu...) which came out in 1643 allowed Bosse to develop his teaching method. Unlike Desargues who implements only one discussion and a diagram encumbered with lines, Bosse makes an effort to “break up the diagram and its discussion into several fragments, which follow each other methodically, and to present them one after the other, in order to accustom the eyes and the understanding to possess all of it”.
The third publication, the Maniere universelle de Mr Desargues, pour pratiquer la perspective par petit-pied, comme le geometral, is certainly the one in which the two collaborators went into the greatest depth. It was dedicated to Michel Larcher, advisor to the King and a friend of Desargues’ and like him, a member of the Mersenne network. It opens on an acknowledgement of Desargues, dated October 1647, who makes the most of it, with his usual venom, to assail his detractors, especially Curabelle and Père Du Breuil. The following eighteen pages consist of a preface and foreword, copied identically in the three works, an assurance of coherence of the whole. Next come forty-one pages on the “particularity of this treatise” on perspective. In it Bosse reaffirms that the inventions belong entirely to Desargues but he claims four as his own discoveries, namely “La Conformité d’entre les pratiques des petits pieds Geometral & Perspectif. / La Demonstration de la Necessité d’affaiblir ou fortifier les touches ou teintes du Perspectif. / La Regle des places de ces fortes & faibles touches ou teintes. / Et la Regle de la pratique pour les affaiblir & fortifier”. In these pages he insists on the fact that all objects to be represented depend on perspective, for “to practice perspective, make a portrait or the representation of a thing, are the same”. He stresses that Arguesian construction regulates at the same time linear perspective, that of “the line” and chromatic perspective, that of the “place des fortes ou faibles touches teintes ou couleurs”. Above all he supports intensely the idea that using Desargues’ non-regular scales (homographic) in a drawing in perspective presents no more difficulties than using regular scales in a plane drawing.
After this long introduction, the treatise begins with optical explanations. The visual pyramid is made concrete with threads attached to the object and gathered together at the eye of the observor. They carry two sorts of information on the geometrical appearance of the subject and its colored appearance. Bosse shows his great artfulness as a draftsman in these plates many times reproduced since then, such as plate 3 copied in Bernard Lamy’s (1701) and Brook Taylor’s (1719) treatises on perspective. Then in small cognitive steps Bosse familiarizes his reader with the positioning of objects drawn to scale by means of axes bearing regular gradations or in a square grid pattern. In plane geometry he always locates a point in space. He repeats this study with receding axes bearing gradations which become shorter, without specifying their construction. The grids consist of trapezia.
After this pedagogical preparation, Bosse gives the actual construction of the Arguesian scales (pl. 28) which allow one to represent any object in perspective while taking into account the position of the eye in relation to the painting. He insists on the fact that this construction does not use distance points and that it functions only in the picture field. Then he goes back to his comparison between plane drawing and drawing in perspective, but with established scales, not arbitrary ones. In conformity with classical treatises Bosse introduces the notion of the angle of vision, then he gives examples of its use in some everyday and original situations (like plate 100 on perspective of a human body “fil de fer”). He finally concludes this part with a separate chapter on drawing shadows cast by a torch and by the sun. In it he criticizes Du Breuil (La perspective practique..., 1642) as well as Niceron, who gave a partially false demonstration concerning a source of light, infinitely far away. He shows that Desargues’ method settles the problem with constructions staying inside the painting (La perspective curieuse..., 1638).
Bosse adds a second part to this treatise, of 108 pages and with 15 plates entitled Règle de la pratique de la perspective pour les places et proportions des fortes & faibles touches, teintes ou couleurs. He attempts to theorize on chromatic perspective namely to ensure that the burin and the brush take distance into account in order to give more or less “softness” to objects. He comes up against the fact that it was impossible for him to mathematize the intensity of colors and that furthermore “drypoint etching and etching would only produce so to speak a sort of a rough draft of what the paint brush can do with colors”. He brings into a focus a law according to which drawing lines must, for the hue or the color, follow the ratio of the frontal scale. For example, if the vertical painting is at distance d from the observor, the hue or the color of the objects inside the painting must be two times stronger than that of the objects situated in a frontal plane at 2d from the observor (pl. 126-127). The account is rather muddled; Bosse would come back to this subject in his treatise on perspective on irregular surfaces (Moyen universel de pratiquer la perspective..., 1653).
The book is completed by Desargues’ work, in which Bosse intervenes modestly as a recorder. First of all, there is an astonishing interleaf quire made up of two pages of presentation, followed by eight pages numbered exceptionally from 112 to 119 (the diagrams are numbered according to the general order of the collection), perhaps the vestiges of a treatise written in 1643, where Bosse was presenting Desargues’ analyses addressed to theoreticians. It consists of solutions to perspective problems on directions and lengths, “a construction of a scale of angles from the thought of Monsieur Desargues” (pl. 146) and instructions on the optical compass and perspective for “cavaliers” to use (pl. 148). They are probably Desargues’ answers to the Perspective spéculative et pratiqueby Étienne Migon (who attributed Desargues’ inventions to the late Aleaume) and to the Abrégé ou raccourcy de la perspective par l’imitation, by Jean-Louis de Vaulezard. Then follows the reprint of Exemple de l’une des manières universelles... touchant la pratique de la perspective sans employer aucun tiers point..., an opuscule by Desargues which came out in 1636. The last nine pages of this work, illustrated by six plates, are absolutely essential in order to understand Desargues’ mathematical thought applied to perspective. Bosse presents demonstrations on the foundations of perspective and of the rule of the strong and the weak touches and colors. He explains the reasons for constructions using the optical compass. Finally he gives three geometric propositions whose theorem is called Desargues’ theorem, on homological triangles (pl. 154). It was these last pages which saved Desargues from oblivion. This whole work consacrated Bosse as an excellent illustrator, a learned man and a pedagogue, all of which opened the doors of the brand new Royal Academy of Painting and Sculpture to him, to teach perspective and geometry.
Jean-Pierre Manceau (Tours) – 2015
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R. Taton, L’œuvre mathématique de G. Desargues, Paris, PUF, 1951.