Author(s) Desargues, Girard
Bosse, Abraham
Title La pratique du trait a preuves, de Mr Desargues Lyonnois...
Imprint Paris, P. Des Hayes, 1643
Localisation Tours, Musée des Beaux-Arts, 1950-7-1
Subject Stereotomy


     In 1643 Abraham Bosse and Girard Desargues had been friends for a very long time.  They were already considered by their contemporaries as "excellents" in their fields, copper plate engraving for the former, mathematics for the latter.  By that date, Girard Desargues (1591-1661) had published the essentials of his scientific work and Abraham Bosse (c. 1604-1676) had engraved his most famous prints.  Their friendship, beyond the sincere feelings of two men of strong character, was sealed by common views on the primacy of reason in every purview.  They both took part in the general movement of rational thought, which, in France, attempted to reform workshop practices, notably those of stone-cutters, of sun dial tracers, painters and engravers.  By recommending new solutions, mathematical and universal, to problems which had already been solved (admittedly by a tradition of trial and error), they were to contribute, consciously for Bosse, perhaps less so for Desargues, to modifying the status of these trades compared with "mechanical arts" and to raising them to the rank of "liberal arts".  The creation of various academies during the second half of the 17th century would be the outcome of this intellectualizing strategy in which they participated fully.
In 1563 Desargues published a very short opuscule (12 pp., 1 double plate) on the practice of perspective.  In 1640 he brought out two other even more succinct works, one on gnomonics (1 p.), the other on stereotomy, Brouillon projet d'exemple d'une manière universelle du S.G.D.L. [Sieur Girard Desargues Lyonnais] touchant la pratique du trait à preuves pour la coupe des pierres en l'Architecture… (4 pp., 5 pl.). Even if these three subjects seem very different, in Desargues' mind they fell within the province of the same geometrical treatment.
Bosse kept this fundamental unity.  In this 1643 treatise, (his first), he indicates, "dans mon Privilège qui est du mois de novembre 1642, il y a, que j'ai tout prêt à mettre en lumière des exemples du trait, pour la coupe des Pierres, des Cadrans, et de la Perspective, par les manières universelles de Monsieur Desargues…". Consequently after this Arguesian treatise on stereotomy, he published a second treatise, still in 1643, also Arguesian, on gnomonics. On the other hand, the best-known works of Bosse, in which he brought to light not only Desargues' universal method of practising perspective, but also more personal developments, appeared quite a bit later.  The third treatise, announced as early as 1642, was published in 1647-1648 under the title Manière universelle de M. Desargues pour pratiquer la perspective par petit pied, comme le géométral… It would be followed by two other works on perspective, one published in 1653, the other in 1665.
Desargues' opuscule on stereotomy presented a universal method of stone-cutting set forth in a single example ("une descente biaise dans un mur en talus") which was sufficiently complex to prevent the method from being polluted by particular situations, too simplistic.  He was addressing "des savants géomètres", "des excellents contemplatifs" and not "des ouvriers de la main".
"Si Monsieur Desargues eût voulu", wrote Bosse in his work, "je vous assure qu'il avait moyen de vous donner la pratique du trait par des manières particulières de son invention, en des pièces précises détachées et sans suite, comme les ouvriers ont été accoutumés jusqu'ici de l'apprendre entre-eux; et vous en verrez ici quelques-unes seulement en passant: mais il a jugé que cette façon-là d'enseigner n'était pas la meilleure pour instruire promptement et pleinement de cette matière, et il en a fait une manière universelle et méthodique à mon avis autant qu'il se peut".  But Monsieur Desargues didn't want to!
Bosse, persuaded that the Arguesian method brought intellectual relief and quicker implementation to practitioners, proposed to draft a treatise which would be more accessible to them.  To this end, he used a very Cartesian method of teaching (developed more fully in the following treatises).  Starting with the basic knowledge of a master mason, he draws his reader by degrees toward more complex knowledge by dividing each difficulty met up with into small fragments in which each elementary problem is resolved in almost obvious terms.  Therefore he decomposed in successive stages what Desargues tried to present globally.  "Puisque les géomètres et les ouvriers de plusieurs arts ne parlent pas souvent le même langage", he translated the universal mathematical language of scholars into craftsman's terms.  For example he points out, "ce que les géomètres nomment l'inclinaison de deux plans entre-eux, ces ouvriers le nomment beveau, etc.".  But this linguistic work was not socially innocent.  As Christèle Assegond points out, Bosse, "en ramenant la langue technique à un folklore local, en insistant sur le caractère normalisé et universel du langage scientifique, engage un travail de recomposition des valeurs".  Thus through this work appeared a new master craftsman, more speculative, who foreshadowed the modern architect.
That would already have been enough to justify the controversies, sometimes sharp, which put Desargues and Bosse in opposition with Parisian stone workers and master masons, and notably with Jacques Curabelle (one can find a weak echo of it in the "Reconnaissance de Monsieur Desargues" inserted in this book).  But there are other reasons for the reticence regarding the Arguesian method.  As Joël Sakarovitch points out, Desargues destabilizes his reader "en l'obligeant à raisonner à partir d'un plan qui, dans l'espace, n'est ni horizontal ni vertical.  Or pour un objet pesant – et qu'y a-t-il de plus pesant qu'une pièce d'architecture clavée? – une telle gymnastique intellectuelle est beaucoup plus délicate que pour une figure géométrique abstraite".
To simplify the conceptual effort imposed by the Arguesian method, Bosse used his talents as an engraver.  It is well known that he was one of the finest copper-plate engravers of the first part of the 17th century, and his mastery of drawing in perspective is exceptional.  Thus he multiplied the explanation plates, one hundred fourteen in all, of which some have fine artistic value. In spite of his pedagogical efforts, practitioners received this book with mediocre enthusiasm.  They were more worried about construction feasibility than the pertinence of geometrical procedures.  If one compares the lot of this treatise on stereotomy to the good fortune, still current, of the Traité des manières de graver en taille douce written by Bosse in 1645, one could even say that it was a failure.
Desargues and Bosse were not worried about it.  They continued to work together to aim at resolving complex stereotomic problems, along the way requesting the advice of a young talented mathematician, Philippe de la Hyre, the son of the painter Laurent de la Hyre.  If we believe Fontenelle, "Desargues, qui était du petit nombre des mathématiciens de Paris, et Bosse, fameux graveur, avaient fait une première partie d'un traité de la coupe des pierres, matière alors toute neuve; mais quand ils voulurent travailler à la seconde partie, ils sentirent que leur géométrie s'embarrassait; et ils s'adressèrent à de la Hyre, qui, dans leur besoin, les secourut de sept propositions tirées de la théorie des coniques.  Bosse les fit imprimer en 1672 dans une brochure "in-folio".
Bosse was always interested in architecture, even if it was only as "dépendance de l'art de la portraiture".  If he first studied architecture through the stereotomic preoccupations of Desargues, he did not confine himself to this area.  In 1659, 1664 and 1666 he brought out five treatises on architecture, notably on the orders of columns, of which some had real success and were reedited several times.  In 1671, five years before his death (February 14, 1676), he was still planning his "seconde partie de la coupe des pierres et un traité d'architecture".

Jean-Pierre Manceau (Tours) – 2005

Critical bibliography

C. Assegond, Socialisation de savoir, socialisation du regard. Les usages techniques et sociaux du savoir géométrique et de la stéréotomie chez les compagnons tailleurs de pierre, Tours, France, Doctoral thesis in sociology, Université François Rabelais, 2002.

A. Blum, D’acide et d’encre. Abraham Bosse, Paris, Morancé, 1924, n° 206-228.

J. Dhombres & J. Sakarovitch (ed.), Desargues en son temps, Paris, Blanchard, 1994.

G. Duplessis, "Catalogue de l’œuvre d’Abraham Bosse", Revue universelle des arts, Paris, 1859, n° 356-472.

M. Le Blanc, D'acide et d'encre. Abraham Bosse (1604?- 1676) et son siècle en perspective, Paris, CNRS Éditions, 2004.

J. Lothe, "Les livres illustrés par Abraham Bosse", S. Join-Lambert & M. Préaud (ed.), Abraham Bosse savant graveur, Tours, vers 1604-1676, Paris, Paris/Tours, Bibliothèque nationale de France/Musée des Beaux-Arts de Tours, 2004, pp.41-52.

J.-P. Manceau, "Abraham Bosse, un cartésien dans les milieux artistiques et scientifiques du XVIIe siècle", S. Join-Lambert & M. Préaud (ed.), Abraham Bosse savant graveur, Tours, vers 1604-1676, Paris, Paris/Tours, Bibliothèque nationale de France/Musée des Beaux-Arts de Tours, 2004, pp. 53-63.

J.-P. Manceau, notice 228 of the exhibition catalogue Abraham Bosse savant graveur, Tours, vers 1604-1676, Paris, S. Join-Lambert & M. Préaud (ed.), Paris/Tours, Bibliothèque nationale de France/Musée des Beaux-Arts de Tours, 2004.

R.-A. Weigert, Inventaire du fonds français. Graveurs du XVIIe siècle, 1, Paris, Bibliothèque nationale, 1939, pp. 471-534.