Mathematical Treasure: Compendium of Mathematics

Bartholomäus Keckermann (ca. 1572–1609) was a German humanist and author who was interested in 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. He wrote numerous short works on a variety of subjects—such as logic, theology, and philosophy—but most were published posthumously. Thus, in 1617 his writings on mathematics were collected into a Systematic Compendium of all of Mathematics: that is, Geometry, Optics, Astronomy and Geography, for the use of students. The title page of the 1661 edition of this work is shown above.

Keckermann was known for his “analytic approach” to examining knowledge. Shown above is 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. Such diagrams were frequently provided by 17th-century authors, who were working out their thoughts on ideas such as the relationship between pure and applied mathematics or the proper order for teaching mathematical subjects, and they persisted until late in the 19th century, as in the textbooks compiled by the American, Charles Davies.

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.

Index to Mathematical Treasures