History
According to the book by Frank Smithies (Cauchy and the Creation of Complex Function Theory, Cambridge University Press, 1997, p.177), Augustin Louis Cauchy presented a theorem similar to the above on 27 November 1831, during his self-imposed exile in Turin (then capital of the Kingdom of Piedmont-Sardinia) away from France. However, according to this book, only zeroes were mentioned, not poles. This theorem by Cauchy was only published many years later in 1974 in a hand-written form and so is quite difficult to read. Cauchy published a paper with a discussion on both zeroes and poles in 1855, two years before his death.
Read more about this topic: Argument Principle
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