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Mathematical Treasure: Stefano degli Angeli’s De superficie vngulae and Problemata geometrica sexaginta

Author(s): 
Frank J. Swetz (The Pennsylvania State University)

Stephano degli Angelis (1623-–1697) was an Italian mathematician, philosopher and Catholic priest. A student of Cavalieri, he promoted the concept of indivisibles. In 1661, he published De Superficie Ungulae, which consisted of two geometrical treatises, one on the measurement of angles in geometrical solids and one on the quadrature of ellipses, parabolas, and hyperbolas. He thus contributed to the analysis of the properties of conic sections.

The title page of Stephano degli Angelis’s 1661 De superficie vngulae, et de quartis liliorum parabolicorum & cycloidalium tractatus duo geometrici.

Several plates of illustrations are included for reference.

First plate from Stephano degli Angelis’s 1661 De superficie vngulae, et de quartis liliorum parabolicorum & cycloidalium tractatus duo geometrici.

Another plate from Stephano degli Angelis’s 1661 De superficie vngulae, et de quartis liliorum parabolicorum & cycloidalium tractatus duo geometrici.

A sample pages of the text:

Beginning of Treatise 2 in Stefano degli Angeli's De superficie vngulae, et de quartis liliorum parabolicorum & cycloidalium tractatus duo geometrici.

In 1658, degli Angelis published a collection of problems in geometry with the title Problemata geometrica sexaginta.

  Title page from Stefano degli Angelis's 1658 Problemata geometrica sexaginta.

Examples of the content in the examination of geometry problems:

First page from Stefano degli Angelis's 1658 Problemata geometrica sexaginta.

Page 2 from Stefano degli Angelis's 1658 Problemata geometrica sexaginta.

Page 201 from Stefano degli Angelis's 1658 Problemata geometrica sexaginta.

Page 202 from Stefano degli Angelis's 1658 Problemata geometrica sexaginta.

A full digitization of De superficie vngulae is available from Museo Galileo. A full digitization of Problemata geometrica sexaginta is available at the Biblioteca Europea di Informazione e Cultura (BEIC).

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Stefano degli Angeli’s De superficie vngulae and Problemata geometrica sexaginta," Convergence (February 2023)