Home arrow Events arrow Anno 2009 arrow Galilean Seminar CFV 2009
Date Display
Monday, 17 June 2024
Main Menu
Education research
News Feed
WEB Link
Credits Link
Last News
Correlated Article
History papers
Quantum Physics
Scientific Instruments
General Bibliography
Last twenty
Galilean Seminar CFV 2009 Print E-mail

Galileo Galilei.

On "Trattato di Fortificazione" and Mechanical Science in The Renaissance

Raffaele Pisano - Research Colloquy

Trattato di Fortificazione

First  page of a Trattato di fortificazione, sec. XVII  (BNCF, Ms. Gal. 31, c. 4r).
© Biblioteca Nazionale Centrale di Firenze
Centre François Viète - Épistémologie, Histoire Des Sciences Et Des Techniques
24 November 2009, Salle des séminaires, 17h-19h 
Univesité de Nantes, France 
Faculté des Sciences et des Techniques
2 rue de la Houssinière - BP 92208 - 44322 NANTES Cedex 3 


 "A brief introduction to Galilei’ Trattato di Fortificatione" (© Raffaele Pisano)

   In order to catch crucial aspects (e.g. bastion defence systems, enfilade and flank guns, drawbridge) of the Renaissance fortification plans of a primeval mechanical science, different from the medieval machines, I shall present an historical analyse of Trattato di Fortificazione (1592-93) by Galilei. Two essays on the military fortifications he wrote in different moments: Breve instruzione all’architettura militare and Trattato di Fortificazione.  Precisely, Breve instruzione all’architettura militare is a collection of his first lessons (around halves the XVI sec.) at Univerità degli Artisti; the second is a collection of by his private lessons during a part of his stay in Padova (1592-93). They are probably teaching speeches collected by his pupils and on indications of Galilei. In fact, it was usual that scholars and famous researchers were in demand as private lecturers for some particular matters. On the other hand
[…] il vivere della cattedra solamente era quasi impossibile e delle lettioni private bisognava farsi pagare […]” (Sagredo in “Lettera del 1° sett. 1599”: Galilei G.  1890-1909. Opere, Vol. X, p. 77, op. cit.).
   Recent works investigated on Galilei’ teaching activities in Padova and arsenal underlining two main activities at Galileo’s home: the workshop and the private lessons - were absorbing a great amount of his time, not to speak of the general administration of the household. Therefore, it is possible to claim that Galilei wrote these Iuvenilia manuscripts belong to his immature scientific age. However, these works contain already the characteristic signature of his way of driving for problem in the process of scientific knowledge; even if, as mentioned above, they are considered a teaching activity, whose the objectives were also pedagogic. The absence of the use of advanced calculus is important to remark: he did not use decimal fractions even if Simon Stevin (1548-1620) in 1585 already introduced them in Europe. No doubt, he had a knowledge of it (being a lecturer of mathematics in Pisa), though it he was tied up to the use of the relationships and the proportionalities both physical magnitudes and mathematical ones. He also introduced applications on Elements exposed in Book V. Galilei’ attitude for Euclidean geometry emerges since his private teachings in Firenze-Siena (1585-1589) or from the public ones (1589-1592) in Pisa, as professor of mathematics where he was lecturer of Tolomeo’ (100-178 ca. a.C.) Astronomy and the Euclid’ (fl. 300 b.C.) Geometry. None of the two mentioned Galilean manuscripts on fortifications is autograph, and since the second of them, as a matter of fact, is a theoretical advancement of the first one, it is possible to claim that Breve instruzione all’architettura militare is antecedent (even if fl. 1592-94) to Trattato di Fortificazione. Banfi and Geymonat works (1908-1991), relatively to the military Galilean studies, focused on Operazioni del Compasso geometrico e militare (1606). On my hand, I will try to mostly underline both the more remarkable scientific aspects on the study of the fortifications, and foundational elements of mechanical science. The two manuscripts, although unusual in their conception (at least the second one) are finite works. Of course, they need some remarks. E.g, the discourse on the trajectories of the bullets derived from a not yet definitive reasoning, not to mention sketches by Galilei showing rectilinear directions of the trajectories. This aspect suggests that the parabolic theory had not still a modern characteristic; but they contributed to propose a brevet (1594) of una macchina da alzare acqua.

     Galilei focused on the war events countersigned by the typology of the sito. By means of this Trattato he erroneously dealt with non-violent motion by rectilinear trajectory: e.g., downward the natural motions are represented with rectilinear trajectories. It is possible to claim that his wrong interpretation by analogy with the natural and violent motions (in this part of his life) still recalls some medieval assumptions. It is still ambiguous whether in the Trattato di Fortificatione - in front of a bullet moving by non-rectilinear trajectory - he did not rise enough doubts on the matter. Moreover, with regards to fortifications, it seems that Galilei presents a graphical scale - which Tartaglia had already proposed in his Quesiti et Inventioni diverse (1546; 1554) - but the Pisano did not quote him; but a graphical scale by Galilei is not included in his Trattato. In details, one can only see a disegn by a graphical scale (Opere, Vol. II, p. 123) that does not belong to Galilei. Besides, the other figures were drawn by means of a scale factor not corresponding to the Galilean figures.

   Leonardo works are an important (and partially correct) attempt to formulate a general theoretical organization involving a greater formalization (compared to predecessors) able to clear up and preview e.g., the deformability of bodies in mechanics and architecture. Tartaglia first proposed an important criticism to Aristotle’s law lever and gave an important contribution to Jordanus de Nemore’ (13th century). Unlike Leonardo da Vinci, just interested in the deformability of beams, Galilei studied the resistance and then the break of the body, especially cantilevers. He proposed a synthesis of well-built Aristotelian and Archimedean approaches not managing to bring out their contradictions. The theory upon the resistance was (essentially) founded on two basic (theoretical-practical) assumptions 1) A geometrical assumption that permitted to study the breaking mechanism. 2) A mechanical assumption that concerned the ways of breakage of bodies, involving also the physical nature of matter.

   In this seminar I shall present Galileo Galilei’ (1564-1642) Trattato di Fortificazione (1592-93) which seems that has not been enough inquired such as happened for his mechanics.  I also deal with cases-study in mechanics: Leonardo, Tartaglia and Galilei. I shall also include notes on larger scientific debate at that time during the Renaissance. Here in the following, I shall briefly remark the outline of the problem both Trattato di Fortificazione and mechanics.


Aristotele 2000, Problemi meccanici, by Bottecchia M.E. Dehò, Cosenza: Rubbettino Editore.
E.J.Brown, 1967-68, The scientia de ponderibus in the later middle ages, Ph.D Thesis, Madison: University of Winscosin, Main advisor: Clagett M., printed by UMI ProQuest C
G.Galileo, 1890-1909, Opere di Galileo Galilei, ed. Naz. by A. Favaro. Ivi., Breve instruzione all’architettura militare, Vol. II, 15-75; Trattato di Fortificazione, Vol. II, 77-146, Barbera (ed.), Firenze
M.P.Vitruvio, 1990. De Architectura Libri. Testo latino a fronte, a cura di Migotto L., Pordenone: Studio Tesi (ed.).
N.Tartaglia, 1554. Quesiti et inventioni diverse de Nicolo Tartaglia brisciano, Brescia.
N.Tartaglia, 1565. Iordani Opvscvlvm de Ponderositate, Nicolai Tartaleae Stvdio ..., Venetiis.
N.Tartaglia,1537. La noua scientia de Nicolo Tartaglia: con una gionta al terzo libro, per Stephano Da Sabio, Venetia.
S.Stevin, 1605-08. Hypomnemata Mathematica, ex officina Ioannis Patii, Lvgodini Batavorvm.


A. Pellicanò 2001. Del periodo giovanile di Galileo Galilei. Il trattato di fortificazione, Gangemi (ed.),Roma.
B.S.Hall, 1997. Weapons & Warfare in Renaissance Europe, Baltimore: John’s Hopkins University Press.
D.Capecchi 2003. Storia della scienze delle costruzione, Bari: Progedit.
D.Capecchi, R.Pisano, 2007, “Torricelli e la teoria dei baricentri come fondamento della statica”, Physis, Vol. XLIV, 1-29.
D.Capecchi, R.Pisano, 2008, “La meccanica in Italia nei primi anni del Cinquecento. Il contributo di Niccolò Tartaglia”, XXV  Congr.  SISFA, C17.1-C17.6.
D.Capecchi, R.Pisano, 2007, Il principio di Torricelli prima di Torricelli”, Proceedings of XXIV Congresso Nazionale di Storia della Fisica e dell’Astronomia, Napoli Avellino, 107-112
D.Capecchi, R.Pisano, 2009 “Il ruolo della scienza nella trasformazione delle cinta murarie fortificate del Cinquecento”, in Atti SISFA 2006, in press
E. Festa. Galileo Galilei. La lotta per la scienza, Laterza, Bari.
I.Hogg, 1982. Storia delle Fortificazione, Novara:  Istituto Geografico De Agostini.
J. Renn, M. Valleriani 2001. “Galileo and the Challenge of the arsenal”, Nuncius, XVI, (2), 481-503.
J. Renn, J. Buttner, P. Damerow, M. Schemmel, M. Valleriani. 2002. “Galileo and shared knowledge of his time”, Max Planck Institute for the history of science, berlin, pre-print 228.
M. Clagett, E.A, Moody, 1952, Medieval science of weights, Madison: University of Wisconsin Press
P.-M.Duhem,1905-06. Les origines de la Statique, Tome I-II, Paris: Hermann (ed.).press.
R.Pisano, 2007. “Brief history of centre of gravity theory. Epistemological notes” in Procee. ESHS Congress, 934-941.
R.Pisano, 2008. The role played by mechanical science in the architects and engineers of Renaissance, 2 Voll., Ph.D Thesis, op. cit.University of Roma "La Sapienza"
R.Pisano, 2009. “Continuity and discontinuity. On method in Leonardo da Vinci’ mechanics”, in Organon, in press.
R.Pisano, 2009. “Galileo Galilei. Riflessioni epistemologiche sulla resistenza dei corpi”, in Proceedings SISFA 2008, in press.
R.Pisano, 2009. “On method in Galileo Galilei’ mechanics”, in Proceedings of ESHS 3rd  Conférence, in press.
R.Pisano, Capecchi D., 2009. Galileo Galilei: Trattato di Fortificazione, proceedings”, First Roma Workshop on Past and Present Perceptions of Science Galileo  and the Renaissance Scientific Discourse, Roma, 6 May, in press.
R. Pisano, D. Capecchi, 2008. “La meccanica in Italia nei primi anni del Cinquecento. Il contributo di Niccolò Tartaglia”, XXV  Congr.  SISFA 2005, C17.1-C17.6
R. Pisano, D. Capecchi, 2008. “Leonardo da Vinci. Recenti riflessioni storico-epistemologiche sulla deformabilità dei corpi”, Atti XLVI Congr. nazionale AIF, 120-129
R. Pisano 2009. “Galileo Galilei. Epistemological reflections on resistance  of bodies”, in Proceedings SISFA 2008, in press.
R. Pisano 2009. “Il ruolo della scienza archimedea nei lavori di meccanica di Galilei e di Torricelli, Proceedings of XXVI  Congr. SISFA 2006, 65-74
R. Pisano, D. Capecchi, 2009.“Il ruolo della meccanica ne Le Fortificazioni di Buonaiuto Lorini”, AISI 2010, Napoli, in press.

Next >