Examen des oeuvres de Sr. Desargues. Paris: de l'imprimerie de M. & I. Henault, et se vendent, chez F. l'Anglois dit Chartres, 1644. [Bound with:] Foiblesse pitoyable du Sr. Desargues employée contre l'examen fait de ses oeuvres. Par I. Curabelle.

[Colophon:]  Imprimé à Paris: ce 16 Juin, 1644.

First edition, very rare, complete with its even rarer supplement, of this polemic against Girard Desargues (1591-1661), “the greatest perspectivist and projective geometer of his generation” (Kemp, p. 120). The importance of Curabelle’s work, a key text in the infamous ‘perspective wars’ of the 1640s, is that, in the process of attacking Desargues, he includes extracts from two of Desargues’s lost works, on perspective and on gnomonics. “One of [Desargues’s] first works to appear [in 1636] was a manual describing a new method for perspective construction … Desargues had long been promising to write a book on perspective. If Desargues really had a plan of a more comprehensive work on the subject than [his 1636 work], he never carried it out. He seems, however, to have produced a booklet that Jacques Curabelle referred to as Livret de perspective addressé aux théoriciens [pp. 70-77 of the Examen], claiming that it appeared it 1643. No copies of this booklet are known” (Andersen, pp. 428 & 437). In 1639, Desargues published his most important work, Brouillon projet d'une atteinte aux événemens des rencontres du Cone avec un Plan, a treatise on conics regarded as the birth of projective geometry. “In August 1640, Desargues published … an essay on techniques of stonecutting and gnomonics. While refining certain points of his method of perspective presented in 1636, he gives an example of a new graphical method … In attempting thus to improve the graphical procedures employed by many technicians, Desargues was in fact attacking an area of activity governed by the laws of the trade guilds; he also drew the open hostility of those who were attached to the old methods and felt they were being injured by his preference for theory rather than practice” (DSB). One of these technicians was Curabelle, who published in the present work a violent attack on Desargues' methods, “finding nothing in them but mediocrity, errors, plagiarism and information of no practical use” (ibid.). Desargues replied with a pamphlet defending his work, to which Curabelle responded with Foiblesse pitoyable. In Oeuvres de Desargues (II, p. 389), Poudra notes that the Foiblesse pitoyable is bound at the end of the Examen and, because of its rarity, transcribes it in full.Several of Desargues’s original works are lost, and those which are extant are of extreme rarity, often surviving in just one or two copies, so that Curabelle’s commentary on Desargues is the only information we have about some of the latter’s works. ABPC/RBH records the sale of only one other copy (de Vitry), which was in a modern binding (Zisska & Lacher, July 21, 2020, lot 589, €6,400 = $7,353; Sotheby’s, 2002, lot 165, £5,287 = $7,630).

Provenance: The Earls of Macclesfield, Shirburn Castle (bookplate on front paste-down and blind-stamp on first three leaves).

Girard Desargues (1591-1661) was born into a wealthy bourgeois family in Lyons. When he inherited the estate of his older brother Christophe, he immediately put all his assets in the hands of another brother, Antoine, and thereafter devoted himself to his passions, especially geometry and its applications. In 1630, Desargues, then living in Paris, obtained a royal license for the publication of several of his writings. At about this time Desargues became friendly with several of the leading mathematicians, including Mersenne, Gassendi, Mydorge, and perhaps Roberval. Mersenne cites him, in 1635, as one of those who regularly attended the meetings of his Académie Parisienne, in which, besides Mersenne, the following participated more or less regularly: Étienne Pascal, Mydorge, Claude Hardy, Roberval, and soon Carcavi and the young Blaise Pascal.

In 1636 Desargues published a 12-page booklet with one double plate entitled Exemple de l’une de manières universelles touchant la practique de la perspective sans employer aucun tiers point, de distance, ny d’autre nature, qui soit hors du champs de l’ouvrage (Example of one of the universal methods concerning the practice of perspective without using any third point, the distance point, or any other kind [of vanishing point], which is outside the field of the picture). “Moreover, after presenting his rules of practical perspective, Desargues gave some indication of the vast program he had set for himself, a program dominated by two basic themes: on the one hand, the concern to rationalize, to coordinate, and to unify the diverse graphical techniques by his ‘universal methods’ and, on the other, the desire to integrate the projective methods into the body of mathematics by means of a purely geometric study of perspective, several elements of which are presented in an appendix. This publication appears not to have excited a great deal of immediate interest among artists and draftsmen, who were hardly anxious to change their technique; in contrast, Descartes and Fermat, to whom Mersenne had communicated it, were able to discern Desargues’s ability … Desargues’s goal was at once to breathe new life into geometry, to rationalize the various graphical techniques, and, through mechanics, to extend this renewal to several areas of technique. His profound intuition of spatial geometry led him to prefer a thorough renewal of the methods of geometry rather than the Cartesian algebraization; from this preference there resulted a broad extension of the possibilities of geometry” (DSB).

In 1640 Desargues published his stonecutting leaflet, Brouillon projet d’exemple d’une manière universelle … touchant la practique de trait a preuves pour la coupe des pierres en l’architecture (Draft project as an example of a universal system about the practice of tracing for stonecutting in architecture). “It explained a radically different way of tacking the stereotomic problems involving intersections of cylinders with oblique planes, that is, skew arches, arches opened in battered walls and sloping barrel vaults. Instead of using parallels to a reference plane, as usual up to this moment, he devised an idiosyncratic system using different axes named as essieu, sous-essieu, contre-essieu and traversieu and involving the use of two slanted projection planes …

“Professional stonecutters were infuriated by this unexpected intrusion in their field by an idle bourgeois. Jacques Curabelle (b. 1585), known as the best stonecutter of the period in Paris, published several pamphlets with such Baroque titles as Foiblesse pitoyable du Sr. Desargues employée contre l'examen fait de ses œuvres and a more substantial Examen des oeuvres de Sr. Desargues in 81 pages. Desargues answered with Recit au vray de ce qui a este la cause de faire cet escrit (1644). Both sides went so far as to paste posters about the issue in the streets of Paris, agreeing finally on a singular challenge. Two teams of masons, instructed by Desargues and Curabelle, were to erect arches according to the theories of their respective leaders; the winner was to be awarded a prize of the substantial sum of 200 pistoles. Ultimately, the duel did not take place since the contenders could not agree on the choice of a jury. It seems that Curabelle took it for granted that the panel of judges would be composed of masons, but Desargues retorted bluntly that ‘the geometers … should not go to the school nor the lessons of the masons; quite the contrary, masons … should go to the school and the lessons of geometers; that is to say, the geometers are the masters, and the masons are the pupils.’ This incident marks a crucial paradigm shift in the field: for Desargues actual arches or vaults are no longer the criterion of validity of stereotomic procedures; stonecutting methods should be tested against the abstract concepts of rational geometry.

“Desargues’s original leaflet includes four drawings and four pages of fine print; its circulation seems to have been quite limited, and his position did not gain immediate acceptance … As for Curabelle (pp. 19, 21, 22, 27, 31, 55, 63, 78, 81), his booklet is the first one to introduce the word stéréotomie, that is, ‘section of solids’ into the debate: the stonecutter, not wishing to be set back by the scientist, resorted to learned language. The controversy caused a sudden renewal of interest in the matter, fostering the publication of a remarkable number of books along the seventeenth century” (Calvo-López, pp. 88-89).

At the end of 1640 Desargues published a brief commentary on the principles of gnomonics presented in his Brouillon project [on stonecutting]; this text is known only through several references, in particular the opinion of Descartes, who found it a ‘very beautiful invention and so much the more ingenious in that it is so simple’” (DSB). The most detailed description we have of the work is that given by Curabelle towards the end of his Examen (p. 78).

“After 1644 evidence of [Desargues’s] scientific and polemic activity becomes much rarer … It seems that while remaining in close contact with the Paris scientists, Desargues had commenced another aspect of his work, that of architect and practitioner. There was no better reply to give to his adversaries, who accused him of wanting to impose arbitrary work rules on disciplines that he understood only superficially and theoretically. Probably, as Baillet states, he had already been technical adviser and engineer in Richelieu’s entourage, but he had not yet had any real contact with the graphical techniques he wished to reform. It seems that his new career as an architect, begun in Paris about 1645, was continued in Lyons, to which he returned around 1649–1650, then again in Paris, to which he returned in 1657. He remained there until 1661, the year of his death” (DSB).

Curabelle’s work was published at the height of the ‘perspective wars’ of the 1640s. “Desargues’s work on conics had been the subject of a limited polemic in 1640. Two years later the perspective wars began in earnest on a larger scale. The immediate cause was the publication of Perspective practique by a ‘Jesuit of Paris’ (actually Jean Dubreuil). This was a substantial, effective and not overly technical introduction for artists, which imprudently contained a bowdlerised version of Desargues’s Manière (i.e., Exemple de l’une de manières universelles touchant la practique de la perspective …). The mathematician’s response was immediate. He issued two posters (or hand bills) accusing the anonymous author of ‘incredible error’ and ‘enormous mistakes and falsehoods’. Dubreuil’s answer, in a pamphlet entitled Diverses methods universelles … was to accuse Desargues of having plagiarised the ideas of Vaulezard and Aleaume (which does not seem to have been the case). The Jesuit’s publishers also issued a collected edition of anti-Desargues pamphlets under the ironic title Avis charitables sur les diverses oueivres et feuilles volantes du Sieur Girard Desargues Lyonnais (Charitable opinions of the various works and leaflets of Mr. Girard Desargues of Lyons). Desargues replied with pamphlets devoted to Six errors on Pages 87, 118, 124, 128, 132 and 134 in the Book entitled thePerspective practique’ … and a Response to the Sources and Means of Opposition … Such terms as ‘imbecility’ and ‘mediocrity’ were used with undisguised venom by both parties.

“In the next year, [Abraham] Bosse brought out the first of the publications in which he expounded Desargues’s views … These attracted new assaults, this time from an expert in stonecutting, Curabelle, who devoted three pamphlets to the criticism of Desargues’s works and of the ‘public feebleness’ with which the mathematician had reacted. At this distance in time it is perhaps difficult to understand the vehemence, but we should remember that these disagreements were not simply keen disputes over geometrical solutions or theoretical issues; they related directly to the cherished practices of professional groups who were as protective then as such bodies are today” (Kemp, pp. 122-123).

The supplement, Foiblesse pitoyable…, is extremely rare. It is not present in the BNF copy of the Examen digitized on Gallica, nor in the Bayerische Staatsbibliothek copy digitized on BSB. We have been able to locate only one copy of Desargues’s 1636 pamphlet on perspective (BNF), and one of his 1640 pamphlet on stonecutting (Institut de France, Paris). It is known that Desargues’s pamphlet on conics was published in an edition of just 50 copies; his other pamphlets were probably issued in similar numbers.

Macclesfield 581 (this copy); Vagnetti EIIIb39. Andersen, The Geometry of an Art, 2007. Calvo-López, Stereotomy: Stone Construction and Geometry in Western Europe 1200–1900, 2020. Kemp, The Science of Art, 1990. For a detailed account of Desargues’s work, see Field & Gray, The geometrical work of Girard Desargues, 1987.

Two works in one vol., 4to (285 x 206 mm). Examen: pp. [1-2], 3-81, [1, blank] with 16 engravings printed in the text (several full-page); Foiblesse: pp. 9, [1] with an engraving printed on one page (lower inner corner of the first eight pages with some damage but not affecting the printing area). 18th century vellum-backed blue paper boards (calf spine showing under the vellum which is cracking).

Item #3085

Price: $12,500.00

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