The following image is the title page of volume 1 of Maria Gaetana Agnesi’s *Instituzioni Analitiche ad uso della gioventù italiana (Foundations of Analysis for the Use of Italian Youth)*, published in 1748 in Italian in Milan, and a two-volume work on algebra and calculus. The book was written as a teaching text and received high praise from a committee of the Académie des Sciences in Paris for uniformly synthesizing and clarifying the work of others on calculus. According to the *Dictionary of Scientific Biography*, “this book won immediate acclaim in academic circles all over Europe and brought recognition as a mathematician to Agnesi.”

The work was translated into English by Rev. John Colson (who learned Italian just so he could translate *Analytical Institutions*) and published in 1801. Here is the title page of the English translation of Volume 1 and the start of a preface by the editor.

Today many people know of Agnesi due to a mistranslation of the name of a cubic curve she discusses in *Analytical Institutions*.

While Agnesi called this curve *la Versiera*, Colson translated it as *the Witch* and the curve became known commonly as *the Witch of Agnesi*. The first two images below are from the original Italian edition, followed by two images from the English translation.

Since the Linda Hall Library collections include both the original Italian version and the English translation, readers are able to take a look at the volumes side by side. In doing so, it is interesting to note that in the original Italian version, Agnesi uses the notation and terminology of Leibniz, while in the English translation, Colson uses Newton’s notation and terminology. For an example, see the images below from Section 28 of Volume 2.

The picture below from page 16 of volume 1 in Italian shows examples of polynomial multiplication.

Negative exponents are explained on page 56 and rational exponents on page 57.

For more images of Maria Agnesi’s *Analytical Institutions*, in both Italian and English, visit the page Mathematical Treasures - Maria Agnesi's Analytical Institutions, by Frank J. Swetz and Victor J. Katz, in *Convergence.*

Complete digital scans of the English translation of *Analytical Institutions*, Volume 1 and Volume 2, are available in the Linda Hall Library Digital Collections. The call number for the original Italian version of Agnesi’s *Analytical Institutions* is QA35.A315 1748, while the English translation is QA35.A3 1801.

*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.*

### References

Kramer, Edna. “Agnesi, Maria Gaetana.” In *Dictionary of Scientific Biography*, edited by C. C. Gillespie, *i*:75–77. New York: Scribner, 1972.

O'Connor, J. J., and E. F. Robertson. “Maria Gaëtana Agnesi.” *MacTutor History of Mathematics archive.* http://www-history.mcs.st-and.ac.uk/Biographies/Agnesi.html.

Swetz, Frank J., and Victor J. Katz. “Mathematical Treasures - Maria Agnesi's Analytical Institutions.” *Convergence* (January 2011). http://www.maa.org/press/periodicals/convergence/mathematical-treasures-maria-agnesis-analytical-institutions.

“Witch of Agnesi.” *Wikipedia*. https://en.wikipedia.org/wiki/Witch_of_Agnesi.

Index to Mathematical Treasures