Bosse, Abraham
Desargues, Girard

La maniere universelle de M.r Desargues Lyonnois, pour poser l’essieu... Par A. Bosse...
Imprint Paris, P. Des Hayes, 1643
Localisation Paris, Ensba, Les 108
Subject Gnomonic, Sundials


     In 1640, in Paris, Girard Desargues brought out two texts which demonstrate this great geometer’s mathematical inventivity in the already somewhat outmoded area of sundial construction (Brouillon project d’exemple d’une manière universelle... touchant la practique du trait à preuves pour la coupe des pierres en l’Architecture...; Brouillon project... touchant une maniere universelle de poser le style et tracer les lignes d’un Quadran aux rayons du Soleil...). As usual, using a very concise, even enigmatic style, he addresses theoreticians rather than artisans, warning “(this) sketch or preliminary draft is not a work to be examined in detail, as it will appear when finished; learned men are to consider it as only the basis of thought”. Three years later Abraham Bosse, a well-reputed engraver, a friend of the geometer and sufficiently learned to understand it well, put Desargues’s thought within the reach of all.
Desargues proposes a new method for determining, at any and all places, the direction of the world’s axis, viz. the axis of the celestial poles which controls the apparent motion of the stars around the earth. Taking into account astronomical distances, one can consider that any terrestrial point on the globe is located on that axis. That axis is in particular that of the cone created by solar rays reaching a given point during the daily motion of the sun. It is important that the maker of a sundial position the axis of the globe correctly, for the style (the gnomon or the axle) of the dial, in most sundials, is placed in the direction of that axis. According to tradition, during Desargues’s period, the style is embedded in one point of a plane surface by determining the meridian passing through this point and by using the latitude of the place.
Descartes was one of the learned men who examined the new method Desargues proposed. In a letter addressed to Mersenne dated January 28, 1641, he wrote, “I have just received your last (letter) of January 19, with M. Des Argues’s paper, which I have just read very promptly. The invention in it is very fine and all the more so as it is simpler”. In the next part of his comments Descartes even advises a small technical modification to render Desargues’s process more operational. Others were less flattering, for his method was theoretically impeccable, but difficult to realize, notably when the basic triangle of its construction degenerates practically into a segment during periods close to the equinoxes. An anonymous criticism of this method appeared in a collection of anti-Desargues pamphlets published in Paris in 1642, at the shop of Tavernier and Langlois, entitled Advis charitables sur les diverses œuvres et feuilles volantes du sieur Girard Desargues Lyonnois. Other criticisms, better argued, would be expressed again in January, 1644, by Jacques Curabelle, in his Examen des œuvres du Sieur Desargues.
Meanwhile, at the end of 1643, Bosse published Desargues’s treatise on gnomonics. The famous engraver and the learned man had known each other for several years; in 1639 certainly, because Desargues vouches for it, but probably two or three years earlier. In four years, Abraham Bosse published successively three books on Desargues’s trilogy, stereotomy (1643), gnomonics (1643) and perspective (1647), all printed in Paris by Pierre Des Hayes and protected by the same privilege dated November 3, 1642. La maniere universelle de MR Desargues lyonnois pour poser l’essieus is dedicated to Sublet des Noyers, Superintendent and Director-general of the King’s Buildings. Sublet was known for his zealous support of the arts, notably through the intermediary of the Fréart brothers, his cousins, close to Bosse themselves. He was also a patron of Desargues, and gave him the responsibility of working at the Louvre during 1639-1640 to experiment with his methods of stereotomy. The book written and illustrated by Bosse is fundamentally completely Arguesian, but in form very far from the “sketches or preliminary drafts” by Desargues. In fact, in this treatise Abraham Bosse implements an innovative pedagogy made explicit from page 1 to 16, which is the same as in his two other treatises. In particular he divides his readers into three categories. He brings short and learned explanations to theoreticians. For those acquainted with practical geometry he provides longer explanations. And for workers, without precise justification, he provides detailed descriptions of the methods used. This time, lastly, he writes particular explanations for all sorts of people, considering that “the wish to enjoy themselves by working on sundials could come to people who have no knowledge of practical Geometry and who have an aptitude for it”.
Whereas Desargues was stingy with diagrams, in order to avoid putting the aptitude of his readers in doubt, and, he said, to keep from distracting them from examining his geometry, Bosse, on the contrary, used his talent as engraver to multiply them. He made 28 different plates, some of which, like the basic plates 8 and 9, were used several times with comments matched to the various categories of reader. In fact Bosse’s treatise goes back over the essential part of Desargues’s writings. At first he explains the Arguesian method (pl. 1-12) for placing the style, with a judicious modification in the practical suggestion Descartes proposed (Bosse uses an espèce de piroüete, pl. 2). Once the style was in place, lines drawn indicating the hours (the day being divided into 24 hours of equal length, “equal hours in the French style”) are traced according to Desargues’s methods, hardly different from the classic methods of the period. Plates 13 to 21 demonstrate this. To amuse the curious, Bosse adds traditional elements of sundials, the signs of the zodiac for a solar calendar, the lines of Italic, Babylonian and antique hours (which correspond to particular hourly divisions of the day) and lastly, on the advice of Desargues, considerations on the height of the sun on the horizon and its orientation. In this last part, “des pièces à machiner”, plate 22 describes a few tools used to make various lines on the dial. Bosse often invented this sort of machine, but it is not known if they were really produced. They simply are examples of the richness of his imagination in working with the tangible and in reinforcing the pedagogy of his diagrams.
The work came out during a period when many works were coming out on sundials. It was rather, as Bosse indicates, a subject of curiosity for “ingenious contemplative men”. It was translated into English in 1659. For Desargues and Bosse, gnomonics was a minor topic but useful for illustrating the geometric invention of the former and the pedagogic capabilites of the latter. This work is an essay which prepared the way for the major works on perspective and architecture.

Jean-Pierre Manceau (Tours) – 2011

Critical bibliography

Abraham Bosse savant graveur, Tours, vers 1604-1676, Paris, Paris, Bibliothèque nationale de France/Musée des Beaux-Arts de Tours, 2004, n° 228.

Desargues en son temps, collective work published under the direction of J. Dhombres & J. Sakarovitch with the collaboration of the laboratory of the history of sciences, Cnrs, Paris, Blanchard, 1994.

A. Blum, L’œuvre gravé d’Abraham Bosse, Paris, Morancé, 1924, n° 206-228.

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.-P. Manceau, “Abraham Bosse, un cartésien dans les milieux artistiques et scientifiques du XVIIe siècle”, Abraham Bosse savant graveur, Tours, vers 1604-1676, Paris, Paris, Bibliothèque nationale de France/Musée des Beaux-Arts de Tours, pp. 53-63.

R. Taton, L’œuvre mathématique de G. Desargues, Paris, PUF, 1951.