Girard Desargues

architect engineer mathematician scientist

February 21, 1591 (age 69)

Lyon, France

The first evidence of Girard scientific activity places him in Paris on September 9, 1626, when, with another Lyonnais, François Villette, he proposed to the municipality that it construct powerful machines to raise the water of the Seine, in order to be able to distribute it in the city. Adrien Baillet, the biographer of Descartes, declares that Desargues participated as an engineer at the siege of La Rochelle in 1628 and that he there made the acquaintance of Descartes, but there is no evidence to confirm this assertion. According to the engraver Abraham Bosse, a fervent disciple of Desargues, the latter obtained a royal license for the publication of several writings in 1630. It was about this time that Desargues, living in Paris, seems to have become friendly with several of the leading mathematicians there: Mersenne, Gassendi, Mydorge, and perhaps Roberval. Although it is not certain that he attended the meetings at Théophraste Renaudot’s Bureau d’Adresses in 1629, Mersenne cites him, in 1635, as one of those who regularly attended the meetings of his Académie Parisienne. In 1636 Desargues published two works: “Une méthode aisée pour apprendre et enseigner à lire et escrire la musique,” included in Mersenne’s Harmonie universelle, and a twelve-page booklet with one double plate that was devoted to the presentation of his “universal method” of perspective. The latter publication bore a signature that reappeared on several of Desargues’ important works: S.G.D.L. (Sieur Girard Desargues Lyonnais). 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’ ability. The publication in 1636 of Jean de Beaugrand’s Geostatice, then of Descartes’ 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. In July 1639 Beaugrand criticized Desargues’ work, asserting that certain of his demonstrations can be drawn much more directly from Apollonius. Irritated that Desargues, in an appendix to his study of conic sections, had discussed the principles of mechanics and had criticized Beaugrand’s conception of geostatics, Beaugrand wrote in July 1640, a few months before his death, another violent pamphlet against the Brouillon project. In August 1640, Desargues published, again under the general title Brouillon project, an essay on techniques of stonecutting and on gnomonics. While refining certain points of his method of perspective presented in 1636, he gives an example of a new graphical method whose use he recommends in stonecutting and furnishes several principles that will simplify construction of sundials. He cites the names of a few artists and artisans who have already adopted the graphical methods he advocates: in particular the painter Laurent de La Hire and the engraver Abraham Bosse. 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 all those who were attached to the old methods and felt they were being injured by his preference for theory rather than practice. At the end of 1640 Desargues published a brief commentary on the principles of gnomonics presented in his Brouillon project; 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.” At the beginning of 1641 Desargues had Mersenne propose to his mathematical correspondents that they determine circular sections on cones having a conic for a base and any vertex. He himself had a general solution obtained solely by the methods of pure geometry, a solution that is known to us through Mersenne’s comments. Roberval, Descartes, and Pascal were interested in the problem, which Desargues generalized in his investigation of the plane sections of cones satisfying the above conditions. References in publications of the period seem to indicate that around 1641 Desargues published a second essay on conic sections, cited sometimes under the title of Leçons de ténèbres. But since no copy of this work has been found, one may suppose that there may be some confusion here with another work, either the Brouillon project of 1639 or with a preliminary edition of certain manuscripts on perspective that were later included in Bosse’s Manière universelle de Mr Desargues pour pratiquer la perspective. Desargues strove to spread the use of his graphical methods among practitioners and succeeded in having them experiment with his stonecutting diagrams without encountering very strong resistance. At the beginning of 1642, however, the anonymous publication of the first volume of La perspective pratique (written by Jean Dubreuil) gave rise to bitter polemics. Finding that his own method of perspective was both copied and distorted in this book, Desargues had two placards posted in Paris in which he accused the author and the publishers of this treatise of plagiarism and obtuseness. The publishers asserted that they had drawn his so-called “universal” method from a work by Vaulezard and from a manuscript treatise of Jacques Aleaume (1562-1627) that was to be brought out by E. Migon. Desargues having replied with a new attack, Tavernier and l'Anglois, Dubreuil’s publishers, brought out in 1642 a collection of anonymous pamphlets against Desargues’ various writings on perspective, stonecutting, and gnomonics, to which they added the Lettre de M. de Beaugrand of August 1640, which was directed against his projective study of conics. Desargues, greatly affected by these attacks, which concerned the body of his work and put his competence and his honesty in question, entrusted to his most fervent disciple, the engraver Abraham Bosse, the task of spreading his methods and of defending his work. In 1643 Bosse devoted two treatises to presenting Desargues’ methods in stonecutting and in gnomonics: La pratique du trait à preuves de Mr Desargues, Lyonnois, pour la coupe des pierres en l’architecture, and La manière universelle de Mr Desargues, Lyonnois, pour poser l’essieu et placer les heures et autres choses aux cadrans au soleil. Preceded by an “Acknowledgment” in which Desargues states he has given Bosse the responsibility for the spread of his methods, these works are clearly addressed to a less informed audience than the brief essays that Desargues had published on the same subjects. In 1644, however, new attacks were launched against Desargues’ work. They originated with a stonecutter, J. Curabelle, who violently criticized his writings on stonecutting, perspective, and gnomonics, as well as the two treatises Bosse published in 1643, claiming to find nothing in them but mediocrity, errors, plagiarism, and information of no practical interest. A very harsh polemic began between the two men, and Desargues published the pamphlet Récit au vray de ce qui a esté la cause de faire cet escrit, which contains a number of previously unpublished details on his life and work. He also attempted to sue Curabelle, but the latter seems to have succeeded in evading this action. After 1644 evidence of his scientific and polemic activity becomes much rarer. Besides the “Acknowledgment” and the geometric elaborations inserted in Bosse’s 1648 treatise on perspective, Descartes’ correspondence alludes to an experiment made by Desargues, toward the end of 1647, in the context of the debates and investigations then being conducted by the Paris physicists on the nature of the barometric space. 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. In Paris the authors of the period attribute to Desargues, besides a few houses and mansions, several staircases whose complex structure and spectacular character attest to the exactitude and efficacy of his graphical stonecutting procedures. It also seems that he collaborated, for the realization of certain effects of architectural perspective, with the famous painter Philippe de Champaigne. In the region of Lyons, Desargues’ architectural creations were likewise quite numerous; he participated in the planning of several private and public buildings and of rooms whose architecture was particularly delicate. It is necessary to mention the private instruction he gave at Paris in order to reveal his different graphical procedures. Even before 1640 he had several disciples at Paris, as well as at Lyons, where, Moreri states, he was “of great assistance to the workmen to whom he communicated his diagrams and his knowledge, with no motive other than being useful.” In 1660 Desargues was again active in the intellectual life of Paris, attending meetings at Mont-mor’s Academy, such as one on November 9, 1660, at which Huygens heard him present a report on the problem of the existence of the geometric point and sharply discuss the matter with someone who contradicted him. This is the last trace of his activity; the reading of his will at Lyons on October 8, 1661 revealed only that he had died several days before, without stating the date or place of his death, concerning which no document has yet been found.

Girard Desargues Edit Profile

also known as Sieur Girard Desargues Lyonnais

architect engineer mathematician scientist

Background

Girard Desargues was born on February 21, 1591, in Lyon, France. He was one of the nine children of Girard Desargues, collector of the tithes on ecclesiastical revenues in the diocese of Lyons, and of Jeanne Croppet. His family had been very rich for several generations and had supplied lawyers and judges to the Parlement in Paris as well as to that in Lyon.

Education

Desargues seems to have studied at Lyon.

Career

The first evidence of Girard scientific activity places him in Paris on September 9, 1626, when, with another Lyonnais, François Villette, he proposed to the municipality that it construct powerful machines to raise the water of the Seine, in order to be able to distribute it in the city. Adrien Baillet, the biographer of Descartes, declares that Desargues participated as an engineer at the siege of La Rochelle in 1628 and that he there made the acquaintance of Descartes, but there is no evidence to confirm this assertion. According to the engraver Abraham Bosse, a fervent disciple of Desargues, the latter obtained a royal license for the publication of several writings in 1630.

It was about this time that Desargues, living in Paris, seems to have become friendly with several of the leading mathematicians there: Mersenne, Gassendi, Mydorge, and perhaps Roberval. Although it is not certain that he attended the meetings at Théophraste Renaudot’s Bureau d’Adresses in 1629, Mersenne cites him, in 1635, as one of those who regularly attended the meetings of his Académie Parisienne.

In 1636 Desargues published two works: “Une méthode aisée pour apprendre et enseigner à lire et escrire la musique,” included in Mersenne’s Harmonie universelle, and a twelve-page booklet with one double plate that was devoted to the presentation of his “universal method” of perspective. The latter publication bore a signature that reappeared on several of Desargues’ important works: S.G.D.L. (Sieur Girard Desargues Lyonnais).

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’ ability.

The publication in 1636 of Jean de Beaugrand’s Geostatice, then of Descartes’ 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.

In July 1639 Beaugrand criticized Desargues’ work, asserting that certain of his demonstrations can be drawn much more directly from Apollonius. Irritated that Desargues, in an appendix to his study of conic sections, had discussed the principles of mechanics and had criticized Beaugrand’s conception of geostatics, Beaugrand wrote in July 1640, a few months before his death, another violent pamphlet against the Brouillon project.

In August 1640, Desargues published, again under the general title Brouillon project, an essay on techniques of stonecutting and on gnomonics. While refining certain points of his method of perspective presented in 1636, he gives an example of a new graphical method whose use he recommends in stonecutting and furnishes several principles that will simplify construction of sundials. He cites the names of a few artists and artisans who have already adopted the graphical methods he advocates: in particular the painter Laurent de La Hire and the engraver Abraham Bosse. 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 all those who were attached to the old methods and felt they were being injured by his preference for theory rather than practice.

At the end of 1640 Desargues published a brief commentary on the principles of gnomonics presented in his Brouillon project; 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.”

At the beginning of 1641 Desargues had Mersenne propose to his mathematical correspondents that they determine circular sections on cones having a conic for a base and any vertex. He himself had a general solution obtained solely by the methods of pure geometry, a solution that is known to us through Mersenne’s comments. Roberval, Descartes, and Pascal were interested in the problem, which Desargues generalized in his investigation of the plane sections of cones satisfying the above conditions. References in publications of the period seem to indicate that around 1641 Desargues published a second essay on conic sections, cited sometimes under the title of Leçons de ténèbres. But since no copy of this work has been found, one may suppose that there may be some confusion here with another work, either the Brouillon project of 1639 or with a preliminary edition of certain manuscripts on perspective that were later included in Bosse’s Manière universelle de Mr Desargues pour pratiquer la perspective.

Desargues strove to spread the use of his graphical methods among practitioners and succeeded in having them experiment with his stonecutting diagrams without encountering very strong resistance. At the beginning of 1642, however, the anonymous publication of the first volume of La perspective pratique (written by Jean Dubreuil) gave rise to bitter polemics. Finding that his own method of perspective was both copied and distorted in this book, Desargues had two placards posted in Paris in which he accused the author and the publishers of this treatise of plagiarism and obtuseness. The publishers asserted that they had drawn his so-called “universal” method from a work by Vaulezard and from a manuscript treatise of Jacques Aleaume (1562-1627) that was to be brought out by E. Migon. Desargues having replied with a new attack, Tavernier and l'Anglois, Dubreuil’s publishers, brought out in 1642 a collection of anonymous pamphlets against Desargues’ various writings on perspective, stonecutting, and gnomonics, to which they added the Lettre de M. de Beaugrand of August 1640, which was directed against his projective study of conics.

Desargues, greatly affected by these attacks, which concerned the body of his work and put his competence and his honesty in question, entrusted to his most fervent disciple, the engraver Abraham Bosse, the task of spreading his methods and of defending his work. In 1643 Bosse devoted two treatises to presenting Desargues’ methods in stonecutting and in gnomonics: La pratique du trait à preuves de Mr Desargues, Lyonnois, pour la coupe des pierres en l’architecture, and La manière universelle de Mr Desargues, Lyonnois, pour poser l’essieu et placer les heures et autres choses aux cadrans au soleil. Preceded by an “Acknowledgment” in which Desargues states he has given Bosse the responsibility for the spread of his methods, these works are clearly addressed to a less informed audience than the brief essays that Desargues had published on the same subjects.

In 1644, however, new attacks were launched against Desargues’ work. They originated with a stonecutter, J. Curabelle, who violently criticized his writings on stonecutting, perspective, and gnomonics, as well as the two treatises Bosse published in 1643, claiming to find nothing in them but mediocrity, errors, plagiarism, and information of no practical interest. A very harsh polemic began between the two men, and Desargues published the pamphlet Récit au vray de ce qui a esté la cause de faire cet escrit, which contains a number of previously unpublished details on his life and work. He also attempted to sue Curabelle, but the latter seems to have succeeded in evading this action.

After 1644 evidence of his scientific and polemic activity becomes much rarer. Besides the “Acknowledgment” and the geometric elaborations inserted in Bosse’s 1648 treatise on perspective, Descartes’ correspondence alludes to an experiment made by Desargues, toward the end of 1647, in the context of the debates and investigations then being conducted by the Paris physicists on the nature of the barometric space. 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.

In Paris the authors of the period attribute to Desargues, besides a few houses and mansions, several staircases whose complex structure and spectacular character attest to the exactitude and efficacy of his graphical stonecutting procedures. It also seems that he collaborated, for the realization of certain effects of architectural perspective, with the famous painter Philippe de Champaigne. In the region of Lyons, Desargues’ architectural creations were likewise quite numerous; he participated in the planning of several private and public buildings and of rooms whose architecture was particularly delicate.

It is necessary to mention the private instruction he gave at Paris in order to reveal his different graphical procedures. Even before 1640 he had several disciples at Paris, as well as at Lyons, where, Moreri states, he was “of great assistance to the workmen to whom he communicated his diagrams and his knowledge, with no motive other than being useful.”

In 1660 Desargues was again active in the intellectual life of Paris, attending meetings at Mont-mor’s Academy, such as one on November 9, 1660, at which Huygens heard him present a report on the problem of the existence of the geometric point and sharply discuss the matter with someone who contradicted him. This is the last trace of his activity; the reading of his will at Lyons on October 8, 1661 revealed only that he had died several days before, without stating the date or place of his death, concerning which no document has yet been found.

Achievements

Girard Desargues went down in history as one of the most prominent mathematicians of the 17th century. In his geometrical work he introduced the principal concepts of projective geometry: the consideration of points and straight lines to infinity, studies of poles and polars, the introduction of projective transformations, the general definition of focuses, the unitary study of conics, and other concepts.

Desargues' theorem, the Desargues graph, and the crater Desargues on the Moon are named in his honour.

Works

Oeuvres De Desargues Oeuvres De Desargues

The Geometrical Work of Girard Desargues The Geometrical Work of Girard Desargues

book
- The Geometrical Work of Girard Desargues
  (This is an English translation of Desargues' Rough Draft ...)
  1986
- Oeuvres De Desargues 1864

Views

Desargues’ 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.

Although he praised the unitary conception that inspired Desargues, Descartes doubted that the use of geometry alone could yield results as good as those that a recourse to algebra would provide. The rapid success of the Cartesian method of applying algebra to geometry was certainly one of the basic reasons for the poor diffusion of Desargues’ ideas.

Quotations: "I freely confess that I never had taste for study or research either in physics or geometry except in so far as they could serve as a means of arriving at some sort of knowledge of the proximate causes... for the good and convenience of life, in maintaining health, in the practice of some art,... having observed that a good part of the arts is based on geometry, among others that cutting of stone in architecture, that of sundials, that of perspective in particular."

Personality

Desargues was a geometer of profoundly original ideas, sustained at the same time by a sense of spatial reality, by a much more precise knowledge of the great classic works than he admitted, and by an exceptional familiarity with the whole range of contemporary techniques.

Although Desargues made Jean 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.

Quotes from others about the person

"Desargues the architect was doubtless influenced by what in his day was surrealism. In any event, he composed more like an artist than a geometer, inventing the most outrageous technical jargon in mathematics for the enlightenment of himself and the mystification of his disciples. Fortunately Desarguesian has long been a dead language." - Eric Temple Bell

"After his own fashion, Desargues discussed cross ratio; poles and polars; Kepler's principle (1604) of continuity, in which a straight line is closed at infinity and parallels meet there; involutons; assymptotes at tangents at infinity; his famous theorem on triangles in perspective; and some of the projective properties of quadrilaterals inscribed in conics. Descartes greatly admired Desargue's invention, but happily for the future of geometry did not hesitate on that account to advocate for his own." - Eric Temple Bell

"Pascal made grateful acknowlegement to Desargues for his skill in projective geometry." - Eric Temple Bell

"Blaise Pascal... was one of the very few contemporaries who appreciated the worth of Desargues. He says in his Essais pour les coniques, 'I wish to acknowledge that I owe the little that I have discovered on this subject to his writings.' " - Florian Cajori

"We owe to Desargues the theory of involution and of transversals; also the beautiful conception that the two extremities of a straight line may be considered as meeting at infinity, and that parallels differ from other pairs of lines only in having their points of intersection at infinity. He re-invented the epicycloid and showed its application to the construction of gear teeth, a subject elaborated more fully later by La Hire." - Florian Cajori

"Pascal greatly admired Desargues' results... Pascal's and Desargues writings contained some of the fundamental ideas of modern synthetic geometry." - Florian Cajori

"One of the first important steps to be taken in modern times... was due to Desargues. In a work published in 1639 Desargues set forth the foundation of the theory of four harmonic points, not as done today but based on the fact that the product of the distances of two conjugate points from the center is constant. He also treated the theory of poles and polars, although not using these terms." - David Eugene Smith

"The famous geometer Desargues worked on the lines of Kepler and is now commonly credited with the authorship of some of the ideas of his predecessor. ...the oneness of opposite infinities followed simply and logically from a first principle of Desargues, that every two straight lines, including parallels, have or are to be regarded as having one common point and one only. A writer of his insight must have come to this conclusion, even if the paradox had not been held by Kepler, Briggs, and we know not how many others, before Desargues wrote. ...Desargues must have learned directly or indirectly from the work in which Kepler propounded his new theory of these points, first called by him the Foci (foyers), including the modern doctrine of real points at infinity." - Charles Taylor

Connections

It is unknown whether Desargues was married and had any children or not.

Father:: Girard Desargues
Mother:: Jeanne Croppet
colleague:: Abraham Bosse
colleague:: René Descartes
colleague:: Marin Mersenne
colleague:: Pierre Gassendi
colleague:: Claude Mydorge

Main Photo