The arts of war, such as artillery, fortification and military surveying, probably represent the sphere of activity where Renaissance geometers most commonly asserted the practical relevance of their discipline. Despite this, historians of mathematics and of instruments have neglected this area of practical geometry, preferring to study navigation, for example, or astronomy, optics and perspective.
Yet many mathematical authors of the sixteenth and seventeenth centuries sought to impress their readers by illustrating instruments in use at critical moments of conflict, perhaps even in the thick of battle. The Museum of the History of Science has one of the finest collections of early artillery instruments and its books provide ample illustrations of the alleged advantage they offered in battle. In addition, more universal mathematical instruments often have relevant scales and claimed to include warfare among their many applications.
The illustration above, from a book published in 1648 but dealing with an instrument designed in the late sixteenth century, shows one of the applications of the triangulation instrument of Joost Bürgi. An infantry batallion has been landed by ship and advances on an inadequately defended fortification. An extensive estuary seems to prevent a more direct engagement by the hapless onlookers. Bürgi’s instrument, however, permits a rapid triangulation from a measured baseline, a measurement of the range of the attackers and an accurate bombardment – even on a moving target. Really? One area the exhibition has to address is the use of what today would be called ‘hype’ in the selling of practical mathematics and its instrumentation.
The illustration reminds us of two other aspects of the geometry of war – the geometrical design of fortifications and the problems of ballistics. A further relevant topic it does not introduce is the purported military significance of what turned out to be one of the most important innovations in scientific instruments – the invention of the telescope.
The exhibition will open in the Museum on the 20th of February 1996 and will run until the 25th of May.