Abstract
In 1672, describing his arithmetic machine Leibniz wrote that such a machine suitably arranged could easily, promptly, and with sure result accomplish any addition and subtraction (like Pascal’s calculating box) but also any multiplication, division and extraction of square roots. In short, Leibniz said, the entire arithmetic could be subjected to that machinery. As for the practical interest of the machine, he said (Leibniz 1672) that:
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it will be desirable to all who are engaged in computations which, it is well known, are the managers of financial affairs, the administrators of others estates, merchants, surveyors, geographers, navigators, astronomers, and any of the crafts that use mathematics.
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References
Carnot, L. (1797): Réflexions sur la métaphysique du calcul infinitesimal (Paris) 4th edition 1860, reprinted by Albert Blanchard, 1970
Lebesgue, H. (1950): Leçons sur les constructions géométriques ( Gauthier- Villars, Paris )
Leibniz, G.I. (1672): “Machina Arithmetica in qua non Additio tantum Sub-stractio…” translated by Mark Kormes in A Source Book in Mathematics ed. by D.E. Smith ( McGraw-Hill, New York, 1926 ), pp. 173–181
Leibniz, G.W. (1684): “Nova Methodus pro Maximis et Minimis, etc.” translated by D. J. Struik in A Source Book in Mathematics 1200–1800 ( Harvard University Press, Cambridge MA, 1969 ), pp. 272–280
Lovelace, A. (1843): “Notes by the Translator” to L.F. Menabrea in “Sketch of the Analytical Engine Invented by Charles Babbage” in Taylor’s Scientific Memoirs, III
Pappus, (ca. 320): “Mathematical collection” IV translated by I. Thomas in Selections Illustrating the History of Greek Mathematics I ( Heinemann, London, 1939 ), pp. 337–347
Vuillemin, J. (1961): Mathématiques et Métaphysique chez Descartes (Presses Universitaires de France, Paris), 2nd ed., 1987
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© 1993 Springer-Verlag Berlin Heidelberg
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Henry, P. (1993). Mathematical Machines. In: Haken, H., Karlqvist, A., Svedin, U. (eds) The Machine as Metaphor and Tool. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77711-0_7
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DOI: https://doi.org/10.1007/978-3-642-77711-0_7
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