For a very long time i've searched in the internet what was the actual integrating device which Leibniz designed in 1693. Yesterday i found the answer - the instrument which Leibniz deviced is the earliest example of an "integraph" - a mechanical quadrature device for plotting the integral value of a continous function. But i didn't succeed in understanding the way it works. I'm the editor which yesterday added the information in wikipedia about Leibniz's integraph, so i don't need the wiki references. Also i dont need the wiki article "integraph",since i tried to read it and i didnt understand that article.

So my question asks for a detailed explanation of the mechanism of Leinbiz's integraph. I'll also be glad to find out what was the influence of Leibniz's device in the 18th century, but that is not the main question.


Leibniz did indeed describe a mechanism for tracing the solution to any differential equation of the form dy/dx=f(x) using tractional motion. For a detailed explanation, see Viktor Blåsjö, The myth of Leibniz’s proof of the fundamental theorem of calculus, Nieuw Archief voor Wiskunde, ser. 5, 16(1), 2015, 46–50, especially Figure 6, available for free here: http://www.nieuwarchief.nl/serie5/pdf/naw5-2015-16-1-046.pdf

Leibniz's mechanism was intended to make a theoretical point. It is useless in practice. The influence of Leibniz's device in the 18th century was, I believe, negligible, although others continued making tractional integraphs (see Dominique Tournès, La construction tractionnelle des équations différentielles, Paris: Blanchard, 2009).

  • $\begingroup$ Thanks for the link. it really looks like the best source possible for rreading about Leibniz's integraph. $\endgroup$ – user2554 Jul 11 '17 at 10:32

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