Subject: Re: [HM] symbol for infinity
From: David Fowler (david.fowler@warwick.ac.uk)
Date: Tue Jan 04 2000 - 06:36:07 EST
There is a photograph of a page of Wallis' _Arithmetica Infinitorum_
(1656) (Wallis' own copy of the book, in fact) on p 13 of my article
'The Binomial Coefficient Function', American Math Monthly 103 (1996)
1-17, which shows an example of his infinity in the top left hand
corner. While some of the symbols on this early typeset page are a
bit messy, this infinity is perfectly formed. His _Opera i_, 1695, is
much more cleanly set throughout, if I remember correctly.
There is also a photograph of a page of Newton's _Annotations out of
Dr. Wallis his Arithmetica Infinitorum_ on p 15. Here Newton is on
the way to finding the binomial theorem for negative powers.
The article opens with some surprising but badly reproduced plates of
graphs associated with the binomial function. These should have been
drawn with some kind of contour and steepest descent lines, but I
couldn't get the machine to do that properly; can anyone manage to do
it, preferably in Mathematica. (In addition the plates were very
badly reproduced by the printer. There are better copies somewhere on
the web, but where?)
The article finishes with a sketch history of the binomial theorem.
David Fowler
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