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Mathematical Treasure: Compendium of Mathematics

Frank J. Swetz (Pennsylvania State University)

Bartholomäus Keckermann (ca. 1572-1609) was a German humanist and prolific author who wrote on the emerging sciences of his time. In 1558, a Gymnasium was established in Danzig, in the Royal State of Prussia. In actuality, the school, as an institution of higher education, functioned more like a university than a secondary school. From 1602 to 1609, Keckermann served as its rector. In 1617, he wrote his Systematic Compendium of all of Mathematics: that is, Geometry, Optics, Astronomy and Geography, for the use of his students. The title page of the 1661 edition of this work is shown above.

Keckermann was known for his “analytic approach” to examining knowledge. Here in the Prolegomena to his Compendium, he provided the reader with a systematic outline of his conception of the various branches of mathematics and their relationships to each other.

Here on page 278, within the section on astronomy, is a plate of illustrations depicting the nested circular universe and attempting, through the use of diagrams, to explain the nocturnal cycles of the revolving planets.

The images above are provided courtesy of Archives and Special Collections, Dickinson College, Carlisle, Pennsylvania.

Mathematical Treasures Index

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: Compendium of Mathematics," Convergence (August 2015)