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The tractional construction of differential equations. (La construction tractionnelle des équations différentielles.) (French) Zbl 1195.01002

Collection Sciences dans l’Histoire. Paris: Librairie Scientifique et Technique Albert Blanchard (ISBN 978-2-85367-247-4/pbk). viii, 407 p. (2009).
This is mainly a historical study of mechanical and graphical solutions of differential equations, from the seventeenth century to the present. Much attention is given to the Riccati family.
There is a seventy-page appendix containing the Italian translation of the 1752 Memoir (in Latin) by Vincenzo Riccati (1707–1775), On the Use of Tractional Motion in the Construction of Differential Equations. Riccati was a mathematician and hydraulic engineer, who also made a thorough study of hyperbolic equations. His father, Jacopo, was a broadly educated Venetian scientist and mathematician, for whom the Riccati equation was named. The other chapters of the book are devoted to a variety of topics, primarily involving differential equations and their mechanical solution. There is extensive coverage of the Riccati contributions, ample mention of work on planimeters for calculating planar areas, and a chapter on Ernesto Pascal (1865–1940) and his disciples. A final chapter deals with various work by Czuber, Sobotka, and Kojimbo.
The book ends with an eighteen-page Bibliography.

MSC:

01-02 Research exposition (monographs, survey articles) pertaining to history and biography
34-03 History of ordinary differential equations
65-03 History of numerical analysis
35Q99 Partial differential equations of mathematical physics and other areas of application
65S05 Graphical methods in numerical analysis
01A75 Collected or selected works; reprintings or translations of classics

Biographic References:

Riccati, Vincenzo; Pascal, Ernesto
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