Written by Thomas Harriot, *Artis Analyticae Praxis* (*Practice of the Art of Analysis*) was published in 1631, ten years after Harriot’s death. According to Katz and Parshall, “a convert to Viète’s ideas, the Englishman [Harriot] extended them by making algebraic arguments even more symbolic. ... Harriot’s notational innovations made Viète’s ideas an even more useful tool for manipulating and solving equations. [Then] Fermat … fashioned these ideas into a tool for dealing algebraically with curves in the plane.” (Katz & Parshall, pp. 249, 252) Below is the title page of *Artis Analyticae Praxis*.

Next are images of three pages with examples of arithmetic operations using variables.

The image below shows the derivation of the quadratic equation \( a^2 – ba + ca = bc \) from expanding \( (a – b)(a + c) = 0 \).

The image below shows reducing the trinomial \( a^3 – 3ba^2 + 3b^2a = b^3 + c^3 \) to the binomial \( a^3 – 3bca = b^3 + c^3 \).

Images from another copy of the 1631 edition of *Artis Analyticae Praxis* can also be found in *Convergence*.

English translations of Harriot’s *Artis Analyticae Praxis* are available on the web and in print.

A complete digital scan of *Artis Analyticae Praxis* is available in the Linda Hall Library Digital Collections. The call number is QA33.H37 1631.

*Images in this article are courtesy of the Linda Hall Library of Science, Engineering & Technology and used with permission. The images may be downloaded and used for the purposes of research, teaching, and private study, provided the Linda Hall Library of Science, Engineering & Technology is credited as the source. For other uses, check out the LHL **Image Rights and Reproductions** policy.*

### Reference

Katz, Victor J., and Karen Hunger Parshall. *Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century. *Princeton: Princeton University Press, 2014.

Index to Mathematical Treasures