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Mathematical Treasure: Military Fortifications

Frank J. Swetz (Pennsylvania State University)

With the rise of more powerful artillery in Europe came the demand for better, stronger fortifications. Military engineers found a new area of applied geometry, the design of fortifications. Buonaiuto Lorini (ca. 1537-1611) was a Florentine nobleman and military engineer/architect. He spent much of his career in the service of the Venetian Republic. His major written work was the five-volume (later to be extended to six volumes) Delle Fortificationi (1592). This work went through several editions and translations to become a major reference on the subject of military construction. An image of the first text page for the 1597 edition is shown below.

A portrait of the proud author faces the page above.

The first few pages of the book are devoted to reviewing basic geometric concepts.

On page 13 is a diagram for a typical fort of this period. The drawing is to scale with the measurements given in bracci, plural for braccio, an Italian measure equal to the length of a man’s arm, or 66-68 cm.

On pages 30-31, the profile of a military situation is given where an attacking, entrenched force, is moving towards and firing at a fortified structure. Note the use of a grid screen to illustrate elevation. Is this a graph? Does the “graph” represent the situation depicted below it?

The images above are presented courtesy of the History of Science Collections, University of Oklahoma Libraries.

Index to Mathematical Treasures


Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: Military Fortifications," Convergence (May 2019)