Guidobaldo del Monte∗ Maarten Van Dyck Abstract Guidobaldo del Monte (1545 – 1607) was one of the most prominent Italian mathematicians from the second half of the sixteenth century. He published influential texts on Archimedean mechanics and perspective that contributed substantially to a better understanding of the mathematical foundations of these sciences. He was also one of the most important patrons of the young Galileo. Biography Guidobaldo del Monte (Pesaro, 11 January 1545 – Pesaro, 6 January 1607) was one of the most prominent Italian mathematicians from the second half of the sixteenth century. He was a nobleman from the Duchy of Urbino, and occupied a central position at the courts of the Dukes Guidobaldo II and Francesco II della Rovere for large part of his life, until he fell out of favor in the 1590’s ([7] is a recent source that gathers all available biographical information). He studied at the University of Padua, but he probably received most of his mathematical education from Federico Commandino at court in Urbino. He combined practical work as an architect, designer of instruments, and surveyor of fortifications (see numerous contributions in [3]), with theoretical works on astronomy, perspective and mechanics. In cosmology he appears to have been an orthodox Aristotelian, as judged by his reaction to the supernova of 1604 [4, 8]. Notwithstanding this latter position, he was also one of the most important patrons of the young Galileo. Together with his brother, Cardinal Francesco Maria del Monte (well known for having been a patron of Caravaggio), he helped Galileo secure his first teaching positions at the University of Pisa (in 1589) and Padua ∗ Published in Sgarbi M. (eds) Encyclopedia of Renaissance Philosophy. Springer, Cham. (DOI: 10.1007/978-3-319-02848-4_58-1) 1 (in 1592) [13]. Around this period, Guidobaldo and Galileo also collaborated on an experiment, recorded in Guidobaldo’s notebook, that can be seen to have contained the germs of Galileo’s revolutionary new science of motion by showing that the trajectory of projectiles is approximately parabolic [11]. Innovative and Original Aspects Guidobaldo’s most important books were the Mechanicorum Liber from 1577 (with an Italian translation supervised by Guidobaldo in 1581), the Paraphrasis from 1588, and the Perspectivae Libri Sex from 1600. He also prepared Commandino’s edition of Pappus’ Collectiones Mathematicae for printing in 1588, after the former’s death (see [12]). The Mechanicorum Liber was probably the most influential treatises on mechanics of its time (see [9, 6] for some reflections on its place in the history of mechanics). It carried out in detail an idea taken over from Pappus (and, through Pappus, Heron of Alexandria): to reduce the operation of the so-called simple machines (lever, pulley, axle in a wheel, wedge and screw) to the law of the lever. He gave careful and rigorous treatments of the first three (though the discussion of the axle in a wheel is somewhat hampered by the fact that Guidobaldo had no way of dealing with a bent lever, or equivalently, forces applied in another direction than the weight of bodies), but he had to limit himself to qualitative statements regarding the wedge and screw (a problem aggravated by the fact that he lacked a satisfying treatment of the inclined plane, which played a crucial role in the analysis of both instruments). Importantly, Guidobaldo put the concept of centre of gravity, as defined by Pappus, at the foundation of the science of mechanics. This led him to an extensive discussion on the possibility of what is currently called indifferent equilibrium, which arises when a body is suspended in its centre of gravity: it will remain in any position given to it. This possibility had been denied by earlier authors (such as Jordanus, Tartaglia and Cardano), who were severely criticized for this by Guidobaldo (see [5, 14, 7, 10] for discussion). Partly in reply to some criticisms on his book, he published an extended commentary on Archimedes’ text on the equilibrium of plane figures in his 1588 Paraphrasis. This text was the first printed in-depth analysis of Archimedes’ proof of the law of the lever in modern times (see [16, 15, 7]). Guidobaldo’s texts on mechanics provided an original synthesis of existing ideas and treatments, which actually created what is often 2 referred to as the Archimedean tradition by showing how to conceptually integrate Archimedes’ highly abstract mathematical demonstration of the law of the lever with an analysis of actually operating machines. Guidobaldo’s book on perspective was similarily directed towards foundational issues underlying an established practice. He was the first to give a satisfying and general mathematical treatment of the fundamental principles underlying perspective constructions [1, 2]. The core of his innovation consisted in a rigorous establishment of the concept of a general vanishing point for any set of parallel lines – even if Guidobaldo might not have realized the full generality of his results. Primary Sources • Guidobaldo del Monte. 1577. Mechanicorum liber. Pesaro, apud Hieronymum Concordiam. • Guidobaldo del Monte. 1579. Planisphaeriorum universalium Theorica, Pesaro, apud Hieronymum Concordiam. • Guidobaldo del Monte. 1580. De Ecclesiastici Calendarii restitutione opusculum, Pesaro, apud Hieronymum Concordiam. • Guidobaldo del Monte. 1581. Le Mechaniche dell’illustriss. Sig. Guido Ubaldo de’ Marchesi Del Monte tradotte in volgare dal Sig. Filippo Pigafetta, Venezia, Francesco Franceschi. • Guidobaldo del Monte. 1588. In duos Archimedis Aequeponderantium libros paraphrasis scholijs illustrata, Pesaro, apud Hieronymum Concordiam. • Guidobaldo del Monte. 1600. Perspectivae libri sex, Pesaro, apud Hieronymum Concordiam. • Guidobaldo del Monte. 1609. Problematum astronomicorum libri septem, Venezia, apud Bernardum Iuntam, Io. Baptistam Ciottum. • Guidobaldo del Monte. 1615. De Cochlea libri quatuor, Venezia, apud Evangelistam Deuchinum. 3 References [1] Kirsti Andersen. The Geometry of an Art. The History of the Mathematical Theory of Perspective from Alberti to Monge. Springer, New York, 2007. [2] Kirsti Andersen. Guidobaldo: The Father of the Mathematical Theory of Perspective. In Antonio Becchi, Domenico Bertoloni Meli, and Enrico Gamba, editors, Guidobaldo del Monte (1545–1607). Theory and Practice of the Mathematical Disciplines from Urbino to Europe, pages 145–166. Edition Open Access, Berlin, 2013. [3] Antonio Becchi, Domenico Bertoloni Meli, and Enrico Gamba, editors. Guidobaldo del Monte (1545–1607). Theory and Practice of the Mathematical Disciplines from Urbino to Europe. Edition Open Access, Berlin, 2013. [4] Domenico Bertoloni Meli. Guidobaldo Dal Monte and the Archimedean revival. Nuncius, 7(1):3–34, 1992. [5] Domenico Bertoloni Meli. Thinking with Objects: The Transformation of Mechanics in the Seventeenth Century. Johns Hopkins University Press, 2006. [6] Domenico Bertonloni Meli. Guidobaldo, Galileo, and the History of Mechanics. In Antonio Becchi, Domenico Bertoloni Meli, and Enrico Gamba, editors, Guidobaldo del Monte (1545–1607). Theory and Practice of the Mathematical Disciplines from Urbino to Europe, pages 105–123. Edition Open Access, Berlin, 2013. [7] Martin Frank. Guidobaldo dal Monte’s Mechanics in Context. A Research on the Connections between his Mechanical Work and his Biography and Environment. PhD thesis, Università di Pisa, 2011. [8] Alessandro Giostra. Guidobaldo del Monte e i nuovi corpi celesti. In Antonio Becchi, Domenico Bertoloni Meli, and Enrico Gamba, editors, Guidobaldo del Monte (1545–1607). Theory and Practice of the Mathematical Disciplines from Urbino to Europe, pages 317–338. Edition Open Access, Berlin, 2013. [9] Walter Roy Laird. Guidobaldo del Monte and Renaissance Mechanics. In Antonio Becchi, Domenico Bertoloni Meli, and Enrico Gamba, editors, Guidobaldo del Monte (1545–1607). Theory and Practice of the Mathematical 4 Disciplines from Urbino to Europe, pages 35–51. Edition Open Access, Berlin, 2013. [10] Jürgen Renn and Peter Damerow. The Equilibrium Controversy. Guidobaldo del Monte’s Critical Notes on the Mechanics of Jordanus and Benedetti and their Historical and Conceptual Backgrounds. Edition Open Access, Berlin, 2012. [11] Jürgen Renn, Peter Damerow, and Simone Rieger. Hunting the White Elephant: When and How did Galileo Discover the Law of Fall? Science in Context, 13(3-4):299–419, 2000. [12] Paul Lawrence Rose. The Italian Renaissance of mathematics: studies on humanists and mathematicians from Petrarch to Galileo. Droz, 1976. [13] William R. Shea. Guidobaldo del Monte: Galileo’s Patron, Mentor and Friend. In Antonio Becchi, Domenico Bertoloni Meli, and Enrico Gamba, editors, Guidobaldo del Monte (1545–1607). Theory and Practice of the Mathematical Disciplines from Urbino to Europe, pages 95–104. Edition Open Access, Berlin, 2013. [14] Maarten Van Dyck. Gravitating towards stability: Guidobaldo’s Aristotelian-Archimedean synthesis. History of Science, 44(4):373–407, 2006. [15] Maarten Van Dyck. On the epistemological foundations of the law of the lever. Studies in History and Philosophy of Science Part A, 40(3):315–318, 2009. [16] Maarten Van Dyck. “Argumentandi modus huius scientiae maxime proprius.” Guidobaldo’s mechanics and the question of mathematical principles. In Antonio Becchi, Domenico Bertoloni Meli, and Enrico Gamba, editors, Guidobaldo del Monte (1545-1607). Theory and Practice of the Mathematical Disciplines from Urbino to Europe, pages 9–34. Edition Open Access, Berlin, 2013. 5