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: I'm reading Volume II of David Eugene Smith's History of Mathematics. It was published in the early 20th century so 1) volume I is a Project Gutenberg book[0] and there's no reason why some version of volume II shouldn't also be a PG book someday, and 2) it predates the Incompleteness Theorem and the theory of computation. I thought you might enjoy 1925's perspective on the difference engine, from a section on "modern calculating machines".

It was not, however, until the 19th century that any great advance [in modern calculating machines] was made. In 1820 Charles Babbage began the construction of a machine for calculating mathematical tables, and in 1823 the Royal Society secured aid from the British government to enable him to continue his work. Babbage's progress not being satisfactory, this aid was soon withdrawn, but the work continued until 1856, when it was abandoned. From the time when Babbage began to the present, however, the modern calculating machine has been constantly improved, first by Thomas de Colmar (1820), and various types are now in extensive use.

[0] But that book is only 75 pages long, which makes me think that the history was greatly expanded, possibly in the post-public domain era. That would explain why no one ever scanned Volume II.

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