The graphical integration of ordinary differential equations
The development of the graphic integration of ordinary differential equations is considered here as a ``little known phenomenon''. The article presents techniques and instruments used for the graphic integration and looks for their historic origins by going back to the beginning of calculus. In Sect. 1 the polygonal methods are described from Descartes (1639), Newton (1679). Leibniz (1694) a.o. to perfections in 20th century. In Sect. 2 the methods of radius of curvature are described from Poncelet (1827--1830) to Meissner (1913). Sect. 3 is devoted to the use of tractional motion for the conception of integraphs: Leibniz (1693), Bernoulli (1694), Perks (1706), Poleni (1728), the integraphs B. Abdank-Abakanowicz (1886), L.-F. Jacob (1707), E. Pascal (1910). In Sect. 4 the reduction to graphic quadratures is described: Montucla (1802), the planimeters by Hermann (1814), Amsler (1854), successive approximations by Thomson (1876), Runge (1907), Kholodovsky (1929). The text is illustrated by 28 figures, the extensive references are added.
scientific article; zbMATH DE number 2037203
scientific article