Science Teaching in Early Modern Europe

Teaching Euclid in a practical context: Linear perspective and practical Geometry

In 1573 Egnazio Danti published the first Italian translation of Euclid’s Optics, lamenting a severe decline in interest in this discipline “among men of science”. According to the Medicean cosmographer, the situation was so critical that, in order to learn the principles of “prospettiva” (i.e., optics), “we may no longer go the Philosopher’s schools to learn it, since it has been banished from them, but the little which remains to us is limited to some practical aspects learned from the mechanical artificers”. After the great Medieval season of optical studies conducted by philosophers from the Universities of Oxford and Paris the science of vision returned, in effect, to occupy the minds of scientists only at the beginning of the 17^th century, with the work of Kepler and the dissemination of Galileo’s telescope. In the intermediate period, geometric optics progressed mainly through its practical applications, especially through “that part of perspective which pertains to painting”, termed “prospectiva pingendi” by Piero della Francesca, and through the spread of methods and instruments for measuring by sight. The “mechanical artificers” mentioned by Danti were architects, painters or surveyors whose mathematical training constitutes the subject dealt with in this article. A determinant role in the teaching of the Euclidean principles (Elements and Optics) – presumably also for perfecting the rules of pictorial perspective – was played first by the abacus masters, then by the mathematicians linked to the artists’ workshops (Luca Pacioli, Ostilio Ricci), and lastly by the “readers” of Euclid in the new academic institutions of the 16th century.