- Email: [email protected]
Desargues en son temps
312
REVIEWS
HMAT 28
Cohn, P. M. 1981. Universal Algebra. Dordrecht: Kluwer Academic. Dieudonn´e, J. 1970. The work of Nicolas Bourbaki. Amer. Math. Monthly 77, 134–145. Edwards, H. M. 1992. Mathematical ideas, ideals, and ideology. Math. Intelligencer 14(2), 6–19. Gr¨atzer, G. 1968. Universal Algebra. Princeton, NJ: Van Nostrand. Mac Lane, S. 1981. History of abstract algebra. In American Mathematical Heritage: Algebra and Applied Mathematics, J. D. Tarwater, J. T. White, and J. D. Miller, Eds., pp. 3–35. Lubbock: Texas Tech Press. Sono, M. 1917/1918. On congruences, I–IV. Mem. Coll. Sci. Kyoto 2, 203–226/3, 113–149, 189–197, 223–349. Van der Waerden, B. L. 1966. Die Algebra seit Galois. Jahresber. Deutsch. Math. Verein. 68, 155–165. Wedderburn, J. H. M. 1907. On hypercomplex numbers. Proc. London Math. Soc. 6, 77–118. Weyl, H. 1981. Memorial address. In Emmy Noether, 1882–1935, A. Dick, Ed., pp. 112–152. Basel: Birkh¨auser. Wussing H., 1984. The Genesis of the Abstract Group Concept. Cambridge, MA: MIT Press. [Translated from the German by A. Shenitzer] doi:10.1006/hmat.2001.2324
Desargues en son temps. Edited by Jean Dhombres and Jo¨el Sakarovitch. Paris (Blanchard). 1994. 483 pp. Reviewed by Alessandra Fiocca University of Ferrara, Department of Mathematics, via Machiavelli 35, 44100 Ferrara, Italy
Studies on Girard Desargues have enjoyed a revival in the middle of the 20th century, thanks to the important research by Ren´e Taton [Taton 1951]. Studies on isolated aspects of Desargues’ work, particularly on perspective and conic theory, appeared in the eighties and particularly in the nineties in connection with the projected edition of Desargues’ complete works by Jean-Pierre Le Goff, Ren´e Taton, and Jean Dhombres. The book under review, Desargues en son temps, is connected with this project, and its main characteristic is to propose a global study of Desargues informed by the latest discoveries, while the collaboration between historians of art, architecture, technology, mathematics, perspective, gnomonics, and philosophy provides it with a wide spectrum of contributions. It contains 29 articles in three languages, organized into four main sections. The first section situates Girard Desargues in his time, both socially and scientifically. It opens with a remarkable chapter by Damish that presents Desargues as a point of connection between art and science and studies the concrete relationships he established with the artists of his epoch, painters, carvers, architects, or stone-cutters. Taton then sketches out a picture of Parisian scientific and cultural life, pointing out the contradictions in Desargues’ character, whose intellectual qualities were recognized by the most important mathematicians of his epoch, but who was strongly opposed when he tried to establish graphic techniques on theoretical bases. Two contributions, by Mesnard and Knobloch, examine more specifically Desargues’ interesting and varied influence on Blaise Pascal and on Marin Mersenne, respectively. The contributions by Dhombres and Maltese focus on the decisive role of the study of conic sections in the first third of the 17th century, as a phase of transition from the algebra of proportions to analytic geometry and the function concept. The section
HMAT 28
REVIEWS
313
closes with new biographical data, found by Picolet, in particular concerning the financial circumstance of Desargues’ family. The second part of the collection is devoted to perspective and geometry. It contains in-depth analyses of Desargues’ innovations in these fields and of their reception (Le Goff), of his conception and uses of infinity (Field)—close to those of the practical tradition and commonsense-cum-Aristotelian philosophy—of his epistemological and didactic thought (Bessot), in particular the conviction that the correctness of the techniques of artisans comes from theoretically based truths. The section also discusses Desargues’ sources for perspective (Laurent) and contemporary related works. Pinault studies the pictorial cycle which Laurent de la Hyre carried out for the Parisian Church of Saint Etiennedu-Mont, emphasizing how studies in perspective impregnated the work of the artist. Flacon discusses the work of Abraham Bosse, friend of Desargues, professor of perspective at the Parisian Acad´emie Royale de Peinture et Sculpture and the strongest supporter of Desargues’ ideas about perspective, explaining in particular the terms of the controversy originating in Bosse’s idea that the artist has to draw according to rules of perspective. Fiorani studies both shadow projection and aerial perspective in Desargues’ and Bosse’s work, discussing the relationships among Leonardo, Desargues, and Bosse through a study of the origin and meaning of a drawing on shadow projection sent by Poussin to Paris and of what Desargues and Bosse called “la Regle du fort et faible.” Three chapters discuss the more indirect influence of Desargues and his reinterpretation by different authors: Leibniz (Echeverria), Spanish authors (Navarro de Zuvillaga) (while in perspective, Thomas Vincente Tosca’s work (1713) was influenced by Desargues through Deschales, and Benito Bails’ work (1779) through Fr´ezier and La Hire, no reference to Desargues was found in gnomonics, which had a stronger autochtonous tradition), and last, but not least, the geometers of the 19th century such as Michel Chasles (Bkouche). The third section concerns gnomonics, stereotomy, and architecture. It contains various detailed reconstructions of Desargues’ contributions to these topics, for instance on sundials (Oudet, Sinisgalli, and Vastola), on stonecutting (Sakarovitch), and on the water raising machine (Picon). It also explores Desargues’ complicated relations to his contemporaries, in particular his polemics with Curabelle, and restores the contexts of these relations. Saint Aubin analyzes the great number of treatises devoted to stonecutting and the large number of architectural buildings with stairs on freestone vaults during the 17th century as a reaction by a guild fearing for its prerogative and attempting to prove its practical ability. BottineauFuchs shows how the activity of Bosse as a promotor of Desargues’ ideas was inserted into a preexistent personal production, while Le Mo¨el’s contribution provides new information on Curabelle and the evolution of an architect’s trade between the reign of Louis XIII and that of Louis XIV. A comparison of Desargues with the Italian architect Guarino Guarini of Modena (Docci, Migliari, and Bianchini) who was also attached to the unity of theory and praxis ends this section. The last three contributions concern the historical setting of Lyon, Desargues’ original home, at his time; Cottin shows the difference in origin and disposition of those who carried out the traditional functions of an architect between the 16th and 17th centuries, in particular how subsidiary sciences became necessary to architecture. Cuer discusses the milieu of the legal professions in Lyon in Desargues’ epoch, a milieu to which Desargues was closely connected through his father, a royal notary. Chabout provides new elements concerning
314
REVIEWS
HMAT 28
Desargues’ presence and activity in the district of Lyon, the results of one and a half years of research into the “Archives Municipales de Lyon” and the “Archives D´epartmentales du Rhˆone.” A final essay (Taton) summarizes the discovery and the various editions of Desargues’ scientific, technical, and polemical works. The volume closes with a general bibliography. Desargues en son temps thus offers a broad outline of the historical research connected with Desargues’ intellectual figure, so that the volume will be welcomed by a wide audience. For those interested in understanding the difficult connections between deductive reasoning and cleverness in the sphere of practice in several contexts, Desargues en son temps is absolutely essential reading. REFERENCES Taton, R. 1951. L’oeuvre math´ematique de Girard Desargues. Paris: P.U.F.; reprinted with a postface Lyon: IEE/ Paris: Vrin, 1988. doi:10.1006/hmat.2001.2325
REVIEWS
HMAT 28
Cohn, P. M. 1981. Universal Algebra. Dordrecht: Kluwer Academic. Dieudonn´e, J. 1970. The work of Nicolas Bourbaki. Amer. Math. Monthly 77, 134–145. Edwards, H. M. 1992. Mathematical ideas, ideals, and ideology. Math. Intelligencer 14(2), 6–19. Gr¨atzer, G. 1968. Universal Algebra. Princeton, NJ: Van Nostrand. Mac Lane, S. 1981. History of abstract algebra. In American Mathematical Heritage: Algebra and Applied Mathematics, J. D. Tarwater, J. T. White, and J. D. Miller, Eds., pp. 3–35. Lubbock: Texas Tech Press. Sono, M. 1917/1918. On congruences, I–IV. Mem. Coll. Sci. Kyoto 2, 203–226/3, 113–149, 189–197, 223–349. Van der Waerden, B. L. 1966. Die Algebra seit Galois. Jahresber. Deutsch. Math. Verein. 68, 155–165. Wedderburn, J. H. M. 1907. On hypercomplex numbers. Proc. London Math. Soc. 6, 77–118. Weyl, H. 1981. Memorial address. In Emmy Noether, 1882–1935, A. Dick, Ed., pp. 112–152. Basel: Birkh¨auser. Wussing H., 1984. The Genesis of the Abstract Group Concept. Cambridge, MA: MIT Press. [Translated from the German by A. Shenitzer] doi:10.1006/hmat.2001.2324
Desargues en son temps. Edited by Jean Dhombres and Jo¨el Sakarovitch. Paris (Blanchard). 1994. 483 pp. Reviewed by Alessandra Fiocca University of Ferrara, Department of Mathematics, via Machiavelli 35, 44100 Ferrara, Italy
Studies on Girard Desargues have enjoyed a revival in the middle of the 20th century, thanks to the important research by Ren´e Taton [Taton 1951]. Studies on isolated aspects of Desargues’ work, particularly on perspective and conic theory, appeared in the eighties and particularly in the nineties in connection with the projected edition of Desargues’ complete works by Jean-Pierre Le Goff, Ren´e Taton, and Jean Dhombres. The book under review, Desargues en son temps, is connected with this project, and its main characteristic is to propose a global study of Desargues informed by the latest discoveries, while the collaboration between historians of art, architecture, technology, mathematics, perspective, gnomonics, and philosophy provides it with a wide spectrum of contributions. It contains 29 articles in three languages, organized into four main sections. The first section situates Girard Desargues in his time, both socially and scientifically. It opens with a remarkable chapter by Damish that presents Desargues as a point of connection between art and science and studies the concrete relationships he established with the artists of his epoch, painters, carvers, architects, or stone-cutters. Taton then sketches out a picture of Parisian scientific and cultural life, pointing out the contradictions in Desargues’ character, whose intellectual qualities were recognized by the most important mathematicians of his epoch, but who was strongly opposed when he tried to establish graphic techniques on theoretical bases. Two contributions, by Mesnard and Knobloch, examine more specifically Desargues’ interesting and varied influence on Blaise Pascal and on Marin Mersenne, respectively. The contributions by Dhombres and Maltese focus on the decisive role of the study of conic sections in the first third of the 17th century, as a phase of transition from the algebra of proportions to analytic geometry and the function concept. The section
HMAT 28
REVIEWS
313
closes with new biographical data, found by Picolet, in particular concerning the financial circumstance of Desargues’ family. The second part of the collection is devoted to perspective and geometry. It contains in-depth analyses of Desargues’ innovations in these fields and of their reception (Le Goff), of his conception and uses of infinity (Field)—close to those of the practical tradition and commonsense-cum-Aristotelian philosophy—of his epistemological and didactic thought (Bessot), in particular the conviction that the correctness of the techniques of artisans comes from theoretically based truths. The section also discusses Desargues’ sources for perspective (Laurent) and contemporary related works. Pinault studies the pictorial cycle which Laurent de la Hyre carried out for the Parisian Church of Saint Etiennedu-Mont, emphasizing how studies in perspective impregnated the work of the artist. Flacon discusses the work of Abraham Bosse, friend of Desargues, professor of perspective at the Parisian Acad´emie Royale de Peinture et Sculpture and the strongest supporter of Desargues’ ideas about perspective, explaining in particular the terms of the controversy originating in Bosse’s idea that the artist has to draw according to rules of perspective. Fiorani studies both shadow projection and aerial perspective in Desargues’ and Bosse’s work, discussing the relationships among Leonardo, Desargues, and Bosse through a study of the origin and meaning of a drawing on shadow projection sent by Poussin to Paris and of what Desargues and Bosse called “la Regle du fort et faible.” Three chapters discuss the more indirect influence of Desargues and his reinterpretation by different authors: Leibniz (Echeverria), Spanish authors (Navarro de Zuvillaga) (while in perspective, Thomas Vincente Tosca’s work (1713) was influenced by Desargues through Deschales, and Benito Bails’ work (1779) through Fr´ezier and La Hire, no reference to Desargues was found in gnomonics, which had a stronger autochtonous tradition), and last, but not least, the geometers of the 19th century such as Michel Chasles (Bkouche). The third section concerns gnomonics, stereotomy, and architecture. It contains various detailed reconstructions of Desargues’ contributions to these topics, for instance on sundials (Oudet, Sinisgalli, and Vastola), on stonecutting (Sakarovitch), and on the water raising machine (Picon). It also explores Desargues’ complicated relations to his contemporaries, in particular his polemics with Curabelle, and restores the contexts of these relations. Saint Aubin analyzes the great number of treatises devoted to stonecutting and the large number of architectural buildings with stairs on freestone vaults during the 17th century as a reaction by a guild fearing for its prerogative and attempting to prove its practical ability. BottineauFuchs shows how the activity of Bosse as a promotor of Desargues’ ideas was inserted into a preexistent personal production, while Le Mo¨el’s contribution provides new information on Curabelle and the evolution of an architect’s trade between the reign of Louis XIII and that of Louis XIV. A comparison of Desargues with the Italian architect Guarino Guarini of Modena (Docci, Migliari, and Bianchini) who was also attached to the unity of theory and praxis ends this section. The last three contributions concern the historical setting of Lyon, Desargues’ original home, at his time; Cottin shows the difference in origin and disposition of those who carried out the traditional functions of an architect between the 16th and 17th centuries, in particular how subsidiary sciences became necessary to architecture. Cuer discusses the milieu of the legal professions in Lyon in Desargues’ epoch, a milieu to which Desargues was closely connected through his father, a royal notary. Chabout provides new elements concerning
314
REVIEWS
HMAT 28
Desargues’ presence and activity in the district of Lyon, the results of one and a half years of research into the “Archives Municipales de Lyon” and the “Archives D´epartmentales du Rhˆone.” A final essay (Taton) summarizes the discovery and the various editions of Desargues’ scientific, technical, and polemical works. The volume closes with a general bibliography. Desargues en son temps thus offers a broad outline of the historical research connected with Desargues’ intellectual figure, so that the volume will be welcomed by a wide audience. For those interested in understanding the difficult connections between deductive reasoning and cleverness in the sphere of practice in several contexts, Desargues en son temps is absolutely essential reading. REFERENCES Taton, R. 1951. L’oeuvre math´ematique de Girard Desargues. Paris: P.U.F.; reprinted with a postface Lyon: IEE/ Paris: Vrin, 1988. doi:10.1006/hmat.2001.2325