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On two occasions I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.
Loci: Convergence
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Mathematical Treasures
Leonhard Euler's Integral Calculus
The title page of Leonard Euler’s Integral Calculus, vol. 1 (1768). The complete work in three volumes appeared in the interval 1768 – 1770. This was the first complete textbook published on the integral calculus. The entire Integral Calculus is available at the Euler Archive.
Euler’s discussion on page 121 of volume 1 of his Integral Calculus concerning the integration of logarithmic and exponential functions. Note that Euler used lx to represent what we write as ln(x).
An excerpt, pp. 182–183, from volume 2 of Euler’s Integral Calculus, demonstrating a series solution for a differential equation.