Thomas Harriot’s Artis Analyticae Praxis: A first look

(Originally posted at on
September 14, 2012 9:56 AM)

sg07 harriot7

A few months ago, I bought a copy of Seltman and Goulding’s Thomas Harriot’s Artis Analyticae Praxis: An English Translation with Commentary (Springer, 2007) at a BOOKSALE outlet.

Thomas Harriot‘s Artis Analyticae Praxis (The Practice of the Analytic Art) was published in 1631 in Latin, ten years after his death.  (I got the picture on the right from here.)

From Seltman and Goulding’s Introduction (p. 1):

In the algebraic work of Thomas Harriot, it was above all his notation that was revolutionary.  His algebra was the first to be totally expressed in a purely symbolic notation […].

Yet, Harriot is known in general histories of mathematics principally for certain technical innovations in algebra—for the invention of the inequality signs, for equating the terms of a polynomial equation to zero, and for generating such equations from the product of binomial factors, thereby displaying their structure.

I have not read much of Seltman and Goulding’s book, but as a mathematics educator I find Harriot’s work very interesting.  It seems that he was the originator of the decimal digit-by-digit method of obtaining square roots that I was taught in elementary school.

The Artis Analyticae Praxis has two parts; the first has six sections serving as preparatory material for the second part, which is about “the numerical solution of [polynomial] equations by the method of successive approximation” (p. 13).  Harriot builds upon previous work by François Viète, making it “more convenient and practical” (p. 4).

It is quite unfortunate that Seltman and Goulding’s book has numerous typographical errors, many to do with incorrect hyphenation (for example, “The-re” on p. 2, “ha-ve” on p. 12, “tho-se” on p. 20, and so on) and alignment of columns in tables (such as on p. 132).

When I have the time I would like to study this book in more detail.  I feel that it has some exciting insights that can easily be explained by college teachers to their undergraduate students.


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