DESARGUES, Girard.

Six erreurs des pages 87. 118. 124. 128. 132. & 134. du livre intitulé La Perspective practique nécessaire à tous peintres, sculpteurs, graveurs, architectes, orphevres, brodeurs, tapissiers, et autres se servans du dessein. Paris: Melchior Tavernier, hydrographe, graveur & imprimeur du Roy, pour les cartes geographiques, & autres tailles douces, et Franc̜ois L’Anglois, dit Chartres, 1642. [Bound after:] DUBREUIL, Jean. La perspective practique … [With:] Diverses méthodes universelles … pour faire des perspectives … Ce qui servira de plus de response aux deux affiches du Sieur Desargues contre ladite perspective pratique. [With:] Advis Charitables sur les diverses oeuvres et feuilles volantes du Sr. Girard Desargues Lyonois publiées sous les titres: I. De Brouillon projet d’une atteinte aux événements des rencontres du Cone avec un Plan: & des contrarietez d'entre les actions des puissances ou forces. II. De Brouillon projet d’exemple d’une manière universelle, touchant la pratique du traicts à preuves, pour la couppe des pierres en l'Architecture. III. D’une manière de tracer tous quadrans d’heures égales au Soleil, au moyen du style pose: & d'une maniere universelle de poser le style, & tracer les lignes d'un quadran, &c ... [and four other works]. Ibid. La Perspective practique … Deuxième Partie [- Troisième Partie], Seconde édition.

Paris: Antoine Dezallier, 1679.

First and only edition, incredibly rare, of the last (surviving) contribution published by the brilliant French mathematician Girard Desargues in the notorious ‘perspective wars’ – Desargues was “the greatest perspectivist and projective geometer of his generation” (Kemp, The Science of Art, p. 120). Desargues published his works in very small editions, mostly for his friends and scientific colleagues. Today more than half of them are lost, and the survivors are of the greatest rarity, most known in just one or two copies. Desargues’ bio-bibliographer Poudra believed the Six erreurs to be lost, but two other copies are known today, both in the Bibliothèque nationale de France. It is likely that our copy of Six erreurs is the only work published by Desargues now in private hands. We know of no copy of any original work of Desargues having appeared on the market for at least a century. In 1636 Desargues (1591-1661), published Exemple de l'une des manières universelles . . . touchant la pratique de la perspective, describing a ‘universal technique’ which, he claimed, subsumed all previous methods of perspective drawing. Although this work appears not to have excited a great deal of interest among practitioners, “Descartes and Fermat, to whom Mersenne had communicated it, were able to discern Desargues’s ability” (DSB). “Through his own efforts as a polemicist and with the conspicuous assistance of Abraham Bosse in the [Académie Royale de Peinture et de Sculpture], the Manière became the centre of a noisily prominent controversy … The immediate cause was the publication of Perspective pratique … 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' Manière. The mathematician’s response was immediate. He issued two hand bills [both now lost] accusing the anonymous author of ‘incredible error’ and ‘enormous mistakes and falsehoods.’ Dubreuil’s answer, in a pamphlet entitled Diverses méthodes universelles …, was to accuse Desargues of having plagiarized the ideas of Vaulezard and Aleaume (which does not appear 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 oeuvres et feuilles volantes du Sieur Girard Desargues. Desargues replied with pamphlets devoted to Six errors in Pages 87, 118, 124, 128, 132, and 134 in the Book Entitled the Perspective Pratique … [the offered work] and a Response to the Sources and Means of Opposition … [the latter now lost]. Such terms as ‘imbecility’ and ‘mediocrity’ were used with undisguised venom by both parties” (Kemp, pp. 120 & 122). The dispute continued until 1679, drawing in other mathematicians and practitioners, notably Desargues’ supporter Bosse and his opponents Jean Beaugrand and Jacques Curabelle. It cannot be said that Desargues prevailed, at least initially. Dubreuil’s ‘practical perspective’ was popular until the 18^th century; in England his book became known as the ‘Jesuit perspective’. Desargues was far ahead of his time and it was not until the 19^th century that the importance of his work was fully understood. Our copy of the Six erreurs is bound after the first edition of the first volume of Dubreuil’s La perspective practique, which includes the Diverses méthodes universelles and Advis charitables. This is accompanied by the third edition of the second and third volumes (despite the ‘seconde édition’ on their titles – another edition appeared in 1663).

Provenance: François du Verdus (1621-75) (signature on title of Dubreuil, ‘Du Verdus’). Du Verdus was a student of Gilles Personne de Roberval (1602-75). Based upon Roberval’s lectures, in 1643 Du Verdus wrote Observations sur la composition des mouvemens, et sur le moyen de trouver les touchantes des lignes courbes (first published in 1693), which contained Roberval’s independent discovery of the method of tangents, a precursor to the differential calculus. Du Verdus was a correspondent of many of the leading European savants, including Evangelista Torricelli whom he met in Rome in 1644; while there he communicated Torricelli’s ideas on the vacuum to Marin Mersenne. “With Du Verdus [Thomas] Hobbes seems to have been particularly close. When Hobbes came to write his autobiography it was addressed to ‘this candid friend,who knew his ways so well.’ While in France he seems to have thought at one point of remaining permanently in exile and going to stay with Du Verdus in Languedoc. Both men always professed the highest regard for each other; this was to lead Du Verdus to translate one of Hobbes’ works, the De Cive; it was to lead Hobbes to dedicate one of his own works to Du Verdus, the mathematical Examinatio et Emendatio” (Skinner). This copy of Six erreurs was probably given to Du Verdus by Desargues – both men were members of Mersenne’s circle; Du Verdus became one of the leaders of its successor, the Montmor Academy.

Little is known of Desargues’ early life. He was born in Lyons in 1591, the youngest son in a large family. It is probable that, some time in the late 1620s, he was employed as an engineer by Cardinal Richelieu. We know that, about 1630, Desargues entered the cadre of savants with whom Marin Mersenne (1588-1648) surrounded himself. This gave Desargues ready access to the leading ideas of his time. Desargues’ first publication, and the only one not devoted to geometry and its applications, Un méthode aisée pour apprendre et enseigner a lire et escrire la musique, appeared in Mersenne’s monumental Le Harmonie Universelle (1635-36).

“At approximately this time (1631-36), Desargues began to tutor the young Blaise Pascal (1623-62) in geometry … That Desargues was now actively engaged in geometry is indicated by his 1636 publication of an Example de l'une des manières universelles du S.G.D.L. touchant la pratique de la perspective sans emploier aucun tiers point, de distance ny d'autre nature, qui soit hors du champ de l'ouvrage (Example of one of the Universal Methods of (Desargues) Touching upon the Practice of Perspective without the use of a Vanishing Point, or Point of other Nature, Which is Outside the Picture Space)” (Schneider, p. 12).

“Desargues’s method basically consists in transferring coordinates from the three-dimensional space to the picture plane. In this respect it resembles the procedures introduced by Vaulezard and by Aleaume and Migon for mapping the ground plane into the picture plane. However, Desargues’s method is more general, because it also covers points that do not lie in the ground plane. He characterized the position of a point in the ground plane by listing its distances to the ground line and a line perpendicular to this passing through a given point on the ground line; and he identified a point outside the ground plane by its orthogonal projection upon this plane and the distance between the point and its projection. Rather unusually, he included the possibility that the point lies below the ground plane. To transfer the coordinates to the picture plane, Desargues constructed scales for foreshortening orthogonal, transversal, and vertical lengths” (Andersen, p. 428).

“The publication in 1636 of Jean de Beaugrand’s Geostatice, then of Descartes’s Discours de la méthode in May 1637, gave rise to ardent discussions among the principal French thinkers on the various problems mentioned in the two books: the definition of the center of gravity, the theory of optics, the problem of tangents, the principles of analytic geometry, and so on. Desargues participated very actively in these discussions. Although he made Beaugrand his implacable enemy, his sense of moderation, his concern to eliminate all misunderstandings, and his desire to comprehend problems in their most universal aspect won him the esteem and the respect of Descartes and Mersenne, as well as of Fermat, Roberval, and Étienne Pascal. His letter to Mersenne of 4 April 1638, concerning the discussion of the problem of tangents, illustrates the depth of the insights with which he approached such questions and, at the same time, his inclination to synthesis and the universal. Even though Descartes had prepared for him an introduction to his Géométrie, designed to ‘facilitate his understanding’ of it, Desargues did not follow Descartes in his parallel attempts to algebraize geometry and to create a new system of explaining all the phenomena of the universe. 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).

“The influence of Desargues' thinking on the young Pascal is directly acknowledged in the latter's 1640 publication (at age 16) of an Essay pour les Coniques (Essay on Conics). In this work, which gives what has since become known as Pascal’s Theorem, or the ‘theorem of the mystic hexagram’, as Pascal sometimes called it, we find the following appreciation of Desargues:

‘We shall likewise demonstrate this property of which the original inventor is Mr. Desargues of Lyons who is one of the great minds of this time and versed as well in mathematics, among others that of conics, whose writings on this matter, though small in number, have given ample testimony of his ability to those who had desired to become aware of it, and will not object to allowing, as I believe, the little which I have found on this matter in his writings and which I have attempted to imitate as far as it is possible for me of his method on this subject.

“Interestingly, Descartes at first refused to believe that this paper was by Pascal, insisting that it must be by Desargues himself. The ‘little bit’ which Desargues had by this time published on conics was a very great deal, for in 1639 he brought out his largest known work, the Brouillon project d'une atteinte aux événemens des rencontres du Cone avec un Plan (Rough draft of an attempt at the result of the intersection between a cone and a plane) [only one copy survives]. In this work, Desargues proves, among other things, his celebrated involution theorem. This work caused something of a furor in the Mersenne circle and in fact marks the beginning of a critical attitude toward the work of Desargues which was to trouble him for the rest of his life. One criticism was that Desargues refused to use the traditional language of geometry … Another criticism was that Desargues did not seem to be able to form a clear idea of the kind of reader he was writing for … Today we are perhaps too ready to favor Desargues’ intransigence in these matters, regarding it as a mere foible of genius …

“In 1640, Desargues published two works, one dealing with stone cutting in architecture and the other with the calibration of sundials. The first of these, the Brouillon project d'example d'une manière universelle du S.G.D.L. touchant la pratique du trait à preuves pour la coupe des pierres en l'Architecture ... (Rough draft
of an example of a universal method by (Desargues) touching upon the practice of a previous work concerning stone-cutting in architecture), is of great importance in the history of descriptive geometry. This work of Desargues constitutes the first known attempt at a universal system for finding the true shape of any oblique projection of a solid onto a plane surface. As such, it represents a key step in the development of a
complete method of descriptive geometry which was finally accomplished by Gaspard Monge just after the French Revolution. Desargues' other work of 1640, the Manière
universelle de poser le style aux rayons du soleil en quel conque endroit possible, avec la règle, le compas, l'esguerre et le plomb (Universal method for situating the gnomon to the rays of the sun in any possible locality, using the rule, the compass, the square and the plumbline), apparently has not survived. Its content was probably similar to Bosse’s 1643 explanation of this method …

“We turn now to the attacks which Desargues brought upon himself as a result of publishing his views on a method of perspective which seemed to him to both plagiarize and misrepresent his own ideas. In examining these developments, two points should be kept in view. First, unlike Mersenne, who knew how to be politic in matters of published criticism, Desargues is grossly impolitic. Desargues attacks the person and grants his enemy no chance of suing for peace. Thus he receives from his opponent only what his harsh terms will allow for: a personal and vindictive counterattack. Second, ours is perhaps not a time in which it is particularly easy to appreciate either the love of scandal or the cut-throat tactics which often prevailed in the popular press of 17th century Paris.

“In 1642, the house of Melchior Tavernier and Francois l’Anglois brought out an anonymous publication on perspective called La Perspective pratique nécessaire à tous paintres, sculpteurs, graveurs, architects, orphevres, bordeurs, et autres se servans du dessine (The practical perspective necessary to all painters, sculptors, engravers, architects, goldsmiths, embroiderers, and other designers). In this work, which was actually by Jean Dubreuil (1602-70), Desargues thought his ideas had been both plagiarized and corrupted. In actual fact, Dubreuil did credit Desargues in the preface, but what seems to have particularly irritated Desargues was that in addition to violating his rights to publication, the book credited him with a perspective method which was full of errors. Taton suggests that the motive for this publication may have been rivalry between the house of Tavernier and Bosse/Desargues’ publisher Des Hayes who was about to release Bosse’s explanation of Desargues’ perspective method. In any event, Desargues’ response was to print two broadsides in placard form and post them in the streets of Paris. One of these he called Erreur incroyable … (Incredible error …), and the other Faute et faussetes énormes … (Enormous faults and duplicities …). While no copies of these placards are known, Poudra was able to identify a few quotations from them in other publications relating to the dispute. Of these, one will serve to illustrate what the titles already suggest of Desargues' tone and frame of mind in this matter. It also suggests that the real basis for the intensity of Desargues' reaction may have been a certain duplicity on Dubreuil’s part. Having at some previous time negatively criticized the method, Dubreuil nonetheless used it to his own advantage in this book. Desargues' references in the passage to ‘five years’ agrees roughly with the 1636 publication of his perspective method:

‘Even though for five years he (Dubreuil) has had the desire to be able to convince by his way of talking that this universal method which he attributes to himself is good for nothing, it is nevertheless the case that in this book on perspective practice there appears a figure (illustrating Desargues' method) which he calls his own, falsified though it is by the shabby claws of envy.’

“First, Dubreuil himself replied in a pamphlet also published by Tavernier and l’Anglois [Diverses méthodes universelles …]. In this, Debreuil stated that he had been wrong to claim that the perspective method was Desargues' invention, because it had already appeared in a work by Vauzelard [Abrégé ou raccourcy de la perspective par l’imitation, 1631] and in another by Aleaume written in 1628 [La perspective spéculative et pratique... de l’invention de feu Jacques Aleaume ... mise au jour par Estienne Migon, 1643]. To add further fuel to fire, he declared that all of Desargues’ works were, for all practical purposes, completely without value. One can easily imagine Desargues’ state of mind upon seeing this in print. Now he was being accused of plagiarism, with a dose of incompetence added for good measure. Desargues responded in April, 1642 with a 15-page pamphlet giving detailed explanations of the errors in Dubreuil’s text [Six erreurs …]. Continuing to fan the flames from his side of the fire, Desargues referred to Dubreuil as a ‘maladroit copyist’ in his pamphlet.

“From this point, the publishers Tavernier and l’Anglois took a more open and active part in the dispute. They began to collect all of the negative criticism they could find on the work of Desargues and proceeded to publish it in a series of broadsides bearing the title: Advis charitables sur les diverses oeuvres et feuilles volantes du Sieur Girard Desargues, publiées sous les titres … (Charitable advice regarding the diverse works and loose sheets of Mr. Girard Desargues of Lyons, published under the titles …)” (Schneider, pp. 12-25).

Poudra attributes the Advis charitables, which is anything but charitable, either to Dubreuil or, more likely, to the publisher Melchior Tavernier – an attempt to increase his business by fanning the flames of the dispute. It incorporates the following four works:

Response à un amy, contenant un examen d’un brouillon project, donné … par le Sieur Desargues, sur le fait particulierement d’un exemple qu’il propose d’une manière universelle touchant la pratique du trait à preuve, pour la coupe des pierres en l’Architecture.

This is an examination of the works of Desargues consisting of three articles, on perspective, gnomonics, and architecture, respectively: Examen léger de la pratique de perspective du sieur Desargues; Examen léger de la pratique de faire des quadrans du sieur Desargues; and Examen de la pratique du traict des voultes du sieur Desargues. Although announced as ‘light criticisms’, they are actually bitter and violent attacks on Desargues, who is accused of having copied the work of Aleaume or Valuezard.

Lettre de Monsieur de Beaugrand … sur le suject des feuilles intitulés: Brouillon Project d’une attainte aux événements des rencontres du Cone avec un plan … par le S. G. D. L.

A violent attack by Beaugrand on the Brouillon Projet on conics.

Examen de la manière de faire des quadrants, enseignée à la fin du Brouillon Projet de la coupe des pierres &c., par G. D. L.

A criticism of Desargues’ lost work on gnomonics.

Extraict d’une letter de Mr R. touchant les erreurs pretendus dans le livre de La Perspective Pratique.

This is a point-by-point rebuttal, presumably by Dubreuil, of the corrections made by Desargues in Six erreurs.

In general, the criticisms of the Charitable Advice are of following kinds: Desargues had no skill in any of the arts in which he pretends to give instruction; he writes in an obscure and convoluted style which cannot be understood by the common workers he proposes to instruct; he makes pretentious and unsupported claims for the universality of his methods; he has frequently taken his methods from other sources which he does not credit; he vainly wishes to be counted among the learned but has no educational credentials which would entitle him to such respect; since the arts and sciences are no easy things to master, Desargues could not have so quickly devised universal methods for practices in which he has no skill; he will not be guided either by nature or by the methods of exposition and analysis perfected by the great scholars of earlier times; though he pretends to give methods for craftsmen, he insists that they must be judged, not by the craftsmen themselves, but by scholars and geometers who have no
practical experience in such matters; and his methods are only ideas and, as such, are not adapted to the exigencies of practice.

“Desargues' response to the Charitable Advice appeared in two forms. The first was a placard published December 16, 1642 with the title: Reponses à causes & moyens d'opposition (Responses to the motives and methods of opposition). Except for a brief passage quoted in a later criticism, this work has been lost. At this time, Bosse was also preparing his explanations of Desargues’ stereotomy and sundial method for publication in 1643. Into these the two authors now inserted several items by way of response to the criticism. The most interesting and informative of these are Desargues’ Reconnaissances in which he acknowledges that he is the author of the idea which Bosse presents …

“Desargues thought of his papers as sketches giving only the kernel of an idea and in such a way that a scholar might understand it. For Desargues, then, a ‘brouillon’ is a synopsis or abstract which on many points merely provides an outline of what would have to be said by way of explanation in the more extended work for which it provides the sketch. In the last analysis, it would appear that Desargues was writing for a person very like himself – a self-tutored savant with a somewhat utopian conception of the relation between theory and practice. It is probable that Desargues intended his own papers to circulate only among those few friends and scholars who
were interested in his ideas. He printed his papers only in small quantities and this, in part, accounts for the virtual disappearance of original copies. There is no indication that Desargues himself ever intended to write the books which would give the polished and detailed accounts of his ideas alluded to in the quoted passage, and, were it not for Bosse’s efforts, we would today know even less of his ideas” (Schneider, pp. 27-32).

Dubreuil “was an enthusiastic perspectivist who wanted to inform practitioners about the discipline without burdening them with theory. He admitted to having been inspired by many others, referring to ‘all my private Thefts’ and mentioning some of the authors who had influenced the field of the practice of perspective: Vredeman de Vries, Serlio, Barbaro, Vignola, Sirigatti, Accolti, and Marolois. In choosing his style Dubreuil took over Vredeman de Vries’s idea of including a large number of diagrams and letting the text comment on them. He favoured the distance point construction, but also described other ways of obtaining perspective images, including Desargues’s method. In his first book Dubreuil primarily dealt with compositions dominated by the three main directions: orthogonals, transversals and verticals. In 1647 he published a continuation of his perspective work devoting it to objects that are limited by oblique planes, and in particular to perspective images of polyhedra. Finally, in 1649 he added a third part, in which he took up the question of how to make perspective constructions when the picture plane is not vertical or not flat, but for instance a floor, a ceiling, an oblique plane, or a vault. Furthermore, in this third and last volume he also treated all sorts of anamorphoses” (Andersen, p. 448).

We do not know how many copies of Six erreurs were printed. However, it is known that 50 copies were printed, both of Desargues’ 1636 work on perspective and of his 1639 work on conics. It seems unlikely that the print run of Six erreurs would be any larger.

De Vitry 233 (this copy – the presence of the Six erreurs in the first volume was noted in the auction catalogue but its rarity and authorship were not). Andersen, The Geometry of an Art, 2007. Poudra, Oeuvres de Desargues, t. II, 1864. Schneider, Girard Desargues, the architectural and perspective geometry: a study in the rationalization of figure, Doctoral Dissertation, University of Virginia, 1983. Taton, L’oeuvre mathématique de Desargues, 1951. Skinner, ‘Thomas Hobbes and His Disciples in France and England,’ Comparative Studies in Society and History 8 (1966), pp. 153-167. For Du Verdus, see Hobbes, Correspondence, Vol. 2, pp. 903-913.

Four works bound in three vols., 4to (255 x 175mm). [Six erreurs:] pp. [ii, title], [6, numbered 1-3 on rectos only], 4 [second title], 5-7 (numbered on versos only), with three engraved plates (the first two printed on rectos of text leaves); 8 leaves, unsigned. [Perspective pratique, vol. I:] pp. [xxiii], 150, including engraved and letterpress titles, with 150 full-page engraved plates. [Diverses méthodes universelles:] pp. [xv], 10, with 10 full-page engraved plates. [Advis charitables:] pp. [iv], [Response:] pp. 14, [2, blank], [Lettre:] pp. 10, [2, blank], [Examen:] pp. 17, [Extraict:] pp. [iv] (the Lettre and Examen each lack the engraved plate, as almost always). [Perspective pratique, vol. II:] pp. [xxv], 123, [11], including engraved and letterpress titles, with 123 full-page engraved plates. [Perspective pratique, vol. III:] pp. [xli], 50, [7], 51-63, [5], 64-91, [7], 92-107, [7], 109-124, [9], 125-156, [5], 157-165, [14], including engraved and letterpress titles, with 166 engraved plates (2 folding) (ink stamp ‘C Calonne / Bethune / 1827’ on titles of the three volumes of Dubreuil’s La perspective pratique, but not on the other works). Uniform contemporary speckled calf, spines gilt in compartments with red and black lettering-pieces (a little rubbed).

Item #5918

Price: $45,000.00