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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.

A digital scan is available in the Linda Hall Library Digital Collections. 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 Linda Hall Library makes available all existing digital images from its collection that are in the public domain to be used for any purpose under the terms of a Creative Commons License CC by 4.0. The Library’s preferred credit line for all use is: “Courtesy of The Linda Hall Library of Science, Engineering & Technology.”


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.

Index to Mathematical Treasures

Cynthia J. Huffman (Pittsburg State University), "Mathematical Treasure: Evangelista Torricelli’s Opera Geometrica," Convergence (January 2017)

Mathematical Treasures: The Linda Hall Library