> A few months ago, as part of the thread "Early Mathematics", we
> discussed the history of base 5 versus base 10. Now it seems that
> we're into base 20.
There's also base 4. The following is from a beautiful book by Sturmius. My
copy was published in London in 1700. I don't know when Sturmius first wrote
it, but he was at Altdorf, and this is a translation (translated by J.R., A.M.
and R.S.S. I wonder who they were?), so surely it was written before 1700.
The title page includes the following:
Mathesis Enucleata:
Or, the
Elements
Of the
Mathematicks
By J. Christ. Sturmius
[...]
1700
Page 4 includes:
"Here I cannot omit, on this occasion, what the forementioned Wiegelius has
hinted about another way of Numeration, and which Dr. Wallis mentions, Oper.
Mathemat. Part I p. 25 & 66, shewing there a way (and illustrating it by
Examples) of Numeration, and of Expressing the Figures; which proceeds thus;
whereas now adays in numbering we ascend from unity or 1 to ten (the reason
whereof; after which Aristotle makes a prolix Inquiry, Probl. 3 Sect. 15 was
taken without doubt from the denary Number of our Fingers) if from unity we
proceed only to four, (which Aristotle in the same place tells us some of
the Thracians used to do of old,) and thence returning back again to Unity,
we should proceed again after the same way; we might after that way obtain
a vastly more simple and easie Arithmetick, than we have now adays."
The book includes a nearly complete mathematical education appropriate
for about 1600, including Cavalieri's method of indivisibles, Descartes'
analysis of species, and a good deal of geometry. The curious gem about base
four arithmetic, though, was quite a surprise.
I've never seen or heard elsewhere what Sturmius attributes to Wallis
about base four arithmetic, though.
*************************************************************************
* Ed Sandifer * sandifer@wcsu.ctstateu.edu *
* Professor of Mathematics * *
* Western Connecticut State University* www.wcsu.ctstateu.edu/~SANDIFER/*
* Danbury, CT 06810 * *
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