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Mathematical Treasure: Oronce Fine's Protomathesis

Frank J. Swetz (The Pennsylvania State University)

Oronce Fine (1494-1555) was a French mathematician and cartographer. In his Protomathesis, published in 1532, Fine presented a compendium of mathematics consisting of writings on arithmetic, geometry, trigonometry, astronomy, and instrument-making.

Title page: Protomathesis

Title page of the copy of Oronce Fine's 1532 Protomathesis held by the Linderman Library of Lehigh University in Bethlehem, Pennsylvania

Frontispiece: Fine's Protomathesis

The frontispiece plate shows a scholar in discussion with the muse Uranus, patron of knowledge, before a model of the universe. It is thought that Fine depicted himself as the scholar.

Measuring depths in Fine's Protomathesis

Fine presented examples showing the use of a quadrant in determining the inaccessible depth of a well, cistern, and ravine, respectively.

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in “Mathematical Treasures.” In particular, MAA Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.

Convergence also has on display as another "mathematical treasure," from the Columbia University Library Rare Book and Manuscript Collection, two additional pages from the geometry section of Fine's Protomathesis.


Swetz, Frank J., "Mathematical Treasure: Oronce Fine's Protomathesis," Loci (March 2013), DOI: 10.4169/loci003958

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Oronce Fine's [em]Protomathesis[/em]," Loci (April 2013), DOI:10.4169/loci003958