Mathematical Treasure: Evangelista Torricelli’s Opera Geometrica

Cynthia J. Huffman (Pittsburg State University)

The 17th-century Italian mathematician and supporter of Galileo, Evangelista Torricelli, published only one book during his lifetime. The image below is the title page of this 1644 work, Opera Geometria (Linda Hall Library call number QA33.T69 1644).

Title page from Torricelli's 1644 Opera Geometrica.

According to the Dictionary of Scientific Biography, “The volume, Opera Geometria, was divided into three sections: the first dealt with De sphaera et sphaeralibus libri duo; the second contained De motu gravium naturaliter descendentium et proiectorum (the writing submitted to Galileo for his opinion); and the third section consisted of De dimensione parabola. The work, soon known throughout Italy and Europe, had intrinsic value and, through its clear exposition, diffused the geometry of Cavalieri, whose writings were difficult to read.”

This next image is the start of the first section.

Section title page for spherical geometry in Torricelli's Opera Geometrica.

The page below is the start of a section on the squaring of the parabola.

Section header for quadrature of the parabola in Torricelli's Opera Geometrica.

The well-known solid of revolution with infinite surface area yet finite volume, known as Gabriel’s Horn or Torricelli’s Trumpet, made its first appearance in Opera Geometria.

Torricelli's Trumpet in his 1644 Opera Geometrica.

For a portrait of Torricelli, visit the “Evangelista Torricelli’s Academic Lectures” page of Mathematical Treasures.

For more images of Torricelli’s Opera Geometrica, visit the page “Mathematical Treasure: Torricelli’s Geometry” by Frank J. Swetz in Convergence.

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.


Gliozzi, Mario. “Torricelli, Evangelista.” In Dictionary of Scientific Biography, edited by C. C. Gillespie, xiii:433–440. New York: Scribner, 1972.

O'Connor, J. J., and E. F. Robertson. “Evangelista Torricelli.” MacTutor History of Mathematics archive.

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