Post-Galilean Thought and Experiment in Seventeenth-Century Italy: The Life and Work of Vincenzio Viviani

While this is the case for most recent, especially Anglophonic, studies of the period, there have been several Italian historians during the nineteenth and twentieth centuries who have published biographical studies of Vincenzio Viviani and certain of his colleagues. Some of these authors will be mentioned in this paper, in particular: Bonelli M. L. , “L'ultimo discepolo: Vincenzio Viviani”, in Maccagni C. (ed.), Saggi su Galileo (2 vols, Florence, 1972), ii, 656–88; and Favaro A. , Amici e corrispondenti di Galileo, ed. by Galluzzi P. (Florence, 1983), 1009–155.

This was the view held by several historians, led by Martha Ornstein, writing during the early and mid-twentieth century about the rise of scientific institutions. See Ornstein M. , The role of scientific societies in the seventeenth century, 3rd edn (Hamden, 1963). More recently, this focus on experiments and the organization of science has been shared by several historians, including Shapin S. Schaffer S. , Leviathan and the air-pump (New Jersey, 1985); Emerson R. , “The organisation of science and its pursuit in early modern Europe”, in Olby R. C. , Cantor G. N. Christie J. R. R. Hodge M. J. S. (eds), Companion to the history of modern science (London, 1990), 960–79; Biagioli M. , “Scientific revolution, social bricolage and etiquette”, in Porter R. Teich M. (eds), The Scientific Revolution in national context (Cambridge, 1992), 11–54; Shapin S. , A social history of truth: Civility and science in seventeenth-century England (Chicago, 1994); Dear P. , Discipline and experience: The mathematical way in the Scientific Revolution (Chicago, 1995); and Beretta M. , “At the source of Western science: The organization of experimentalism at the Accademia del Cimento (1657–1667)”, Notes and records of the Royal Society of London, liv (2000), 131–51. The historiographical positions of these authors and others will be discussed later in this paper.

Magalotti L. , Saggi di naturali esperienze fatte nell'Accademia del Cimento sotto la protezione del serenissimo principe Leopoldo di Toscana (Florence, 1667). As cited in Abetti G. Pagnini P. (eds),Le opere dei discepoli di Galileo Galilei, i: L'Accademia del Cimento, Part 1 (edizione nazionale, Florence, 1942), 86–87. This style of presentation in the Saggi was probably imposed upon the author, Lorenzo Magalotti, by the Cimento's patron, Prince Leopoldo de'Medici. In order to avoid attention from the Catholic Church because of some potentially controversial experiments published in the text, Leopoldo seemingly adopted a policy of self-censorship for the publication of the Cimento's work, ruling out any mention of the academicians' theoretical discussions. See Galluzzi P. , “L'Accademia del Cimento: ‘Gusti’ del principe, filosofia e idelogia dell'esperimento”, Quaderni storici, xlviii (1981), 788–844.

For detailed studies of the emergence of mechanical philosophy as a viable alternative to scholasticism, see Schuster J. , “The Scientific Revolution”, in Olby (eds), op. cit. (ref. 2), 217–42; Schuster J. and Watchirs G. , “Natural philosophy, experiment, and discourse: Beyond the Kuhn/Bachelard problematic”, in LeGrand H. E. (ed.), Experimental inquiries: Historical, philosophical and social studies of experimentation in science (Dordrecht, 1990), 1–48.

Dear P. , Discipline and experience: The mathematical way in the Scientific Revolution (Chicago, 1995), 89; and Gaukroger S. Schuster J. Sutton J. , “Introduction”, in idem, Descartes' natural philosophy (London, 2000), 1–25, p. 7.

Gaukroger S. Schuster J. , “The hydrostatic paradox and the origins of Cartesian dynamics”, Studies in history and philosophy of science, xxxiii (2002), 535–72.

Dear also attributes this elevation in status of the mixed-mathematical disciplines, to the arguments expounded by Francis Bacon, which called for the use of practical knowledge in natural philosophy. Dear P. , Revolutionizing the sciences: European knowledge and its ambitions, 1500–1700 (Princeton, 2001), 72–73.

Viviani V. , Vita di Galileo, ed. by Borsetto L. (Bergamo, 1992), 214.

Galluzzi R. , Istoria del Granducato di Toscana sotto il Governo della Casa Medici (5 vols, Milan, 1974), iv, 127.

Bonelli , op. cit. (ref. 1), 660.

Biblioteca Nazionale Centrale di Firenze, Manoscritti Galileiani (hereafter: BNCF, Ms. Gal.) 155, f. 1r.

Favaro , Amici e corrispondenti (ref. 1), 1015; Bonelli , op. cit. (ref. 1), 661; and BNCF, Ms. Gal. 155, f. 2r.

BNCF, Ms. Gal. 155, f. 2r.

Galileo expressed this in a letter written in 1637 to Father Micanzio Fulgenzio in Favaro Venice A. (ed.), Le opere di Galileo Galilei (edizione nazionale, 21 vols, Florence, 1890–1909; hereafter: Galileo, Opere), xvii, 125–6.

Viviani , op. cit. (ref. 8), 105; and Favaro , Amici e corrispondenti (ref. 1), 1017.

In particular, as has been shown by Wolfgang Lefèvre, Galileo examined scholastic issues related to practical mathematics, such as kinematics and hydrostatics. But from the beginning of his career, as a student in Pisa, he had been attempting to search for dynamical solutions, incorporating theories on force and causes, to problems in motion. Lefèvre W. , “Galileo engineer: Art and modern science”, in Renn J. (ed.), Galileo in context (Cambridge, 2001), 11–27.

Galilei G. , On motion and On mechanics, ed. and transl. by Drake S. Drabkin I. E. (Madison, 1960), 63.

Galileo , Opere, viii, 205. As translated by Drake Stillman in Discourses and mathematical demonstrations concerning two new sciences pertaining to mechanics and local motion (Madison, 1974), 162.

Galileo , Opere, viii, 205–6.

Ibid., 208–14.

“… appena ebbi scorsi i primi Elementi, che impazziente di vederne l'applicazione, passai alla scienza de'moti naturali nuovamente promossa da Galileo, e che allora appunto era uscito in luce: Et arrivato a quel principal supposto, che le velocità de'mobili naturalmente descendenti per piani d'una medesima elevazione sieno uguali tra loro, dubitai, non già della verità dell'assunto, ma dell'evidenza di poterlo supporre come noto”. Viviani , op. cit. (ref. 8), 215.

Ibid., 216.

Galileo , On motion and On mechanics (ref. 17), 171–2.

Viviani , op. cit. (ref. 8), 105–6.

Drake S. , “Galileo gleanings, XXIII: Velocity and Eudoxian proportion theory”, Physis, xv (1973), 49–64, p. 51.

Heath T. L. , The thirteen books of Euclid's Elements (3 vols, New York, 1956), ii, 113.

Viviani narrated these demonstrations, including the arguments based on the refutation of Pappus, in a dialogue form to suit Galileo's style of presentation and inserted an additional section into the crucial Third Day of the text for subsequent editions.

Galileo and Viviani used Euclid's notion of ‘same ratios’ to conclude “that the time along the incline has to the time along the vertical the same ratio that the incline has to the vertical”. Galileo , Opere , viii, 218–19. This is the theorem concluding the added scholium. It is intended to demonstrate Galileo's postulate in Two new sciences, and in the process, to provide a new dynamical solution to a problem in kinematics.

Ibid., xviii, 126, as translated by Drake S. , Galileo at work: His scientific biography (Chicago, 1978), 405. See also Favaro , Amici e corrispondenti (ref. 1), 1017.

Viviani V. , Quinto libro degli Elementi d'Euclide (Florence, 1674). As cited by Bonelli , op. cit. (ref. 1), 658.

See ref. 41 below.

Borsetto , “Introduction”, in Viviani , Vita (ref. 8), 64.

Bonelli , op. cit. (ref. 1), 665–6.

Viviani , Vita (ref. 8), 66.

Viviani's search extended from 1656 until 1677, and enlisted the help of Lorenzo Magalotti, Michelangelo Ricci, as well as friends and colleagues in Paris, Rome, Bologna, Venice and various other cities. Favaro , Amici e corrispondenti (ref. 1), 1112. Favaro goes into a detailed description of Viviani's searches in Documenti inediti per la storia dei manoscritti galileiani nella Biblioteca Nazionale di Firenze (Rome, 1886), 211, n. 14.

Favaro , Amici e corrispondenti (ref. 1), 1120.

Favaro, Documenti inediti (ref. 35), 41; and Procissi A. , “Imanoscritti superstiti dell'Accademia del Cimento” in Celebrazione della Accademia del Cimento nel tricentenario della fondazione (Pisa, 1957). Viviani has also been credited in recent writings, for elevating Galileo's status after death to great heights. See especially Segre M. , “Viviani's life of Galileo”, Isis, lxxx (1989), 207–31.

See Bonelli , op. cit. (ref. 1), 658.

Favaro , Amici e corrispondenti (ref. 1), 1011.

Bonelli , op. cit. (ref. 1), 683.

From all available manuscript sources, it would seem that the formation of this academy was solely Leopoldo's initiative. It was seemingly the Prince's decision to gather his Court philosophers to participate in a formal setting. The Cimento's members included: Viviani, Giovanni Borelli (1608–79), Rinaldini Carlo (1615–98), Alessandro Marsili (1601–70), Francesco Redi (1626–97), Alessandro Segni (1633–97), Antonio Uliva (d. 1668), and the del Buono brothers, Candido (1618–76) and Paolo (1625–59). For a comprehensive account of how the Cimento was established, see Middleton W. E. K. , The Experimenters: A study of the Accademia del Cimento (Baltimore, 1971), 17–82.

Ferdinando's academy, according to Targioni Tozzetti, was operating from as early as the beginnings of the 1640s and in its first few years enlisted the participation of Galileo's best known students still alive in Florence, including Torricelli Targioni Renieri G. Tozzetti , Notizie degli aggrandamenti delle scienze fisiche accaduti in Toscana nel corso di anni LX del secolo XVII (3 vols, Florence, 1780), ii, 163–80. According to Middleton, it is possible that Ferdinando even continued running this academy after Leopoldo established the Cimento. Considering that there are two manuscript diaries of experiments carried out at the Court with variations in the types of experiments and the dates of the entries, it is possible that Ferdinando continued to supervise sessions parallel to those of the Cimento. Middleton , op. cit. (ref. 41), 46–47. Both these diaries are kept amongst the Galilean papers in the Biblioteca Nazionale Centrale in Florence. There are also three other diaries related to the Cimento, the first (BNCF, Ms. Gal. 260, ff. 2r-32r) appears to be an incomplete copy of the official Cimento diary, while the second (BNCF, Ms. Gal. 260, ff. 34r-39r) is believed to have belonged to Rinaldini. The last diary is in Viviani's handwriting (BNCF, Ms. Gal. 260, ff. 226r-281r).

The Cimento did not record its first meeting until June 1657, several months after Viviani's sound experiments. Nevertheless, Viviani's work on the topic was included in the Cimento's publication, Saggi di naturali esperienze, in 1667. Magalotti , op. cit. (ref. 3), 243–5.

BNCF, Ms. Gal. 268, ff. 155r-158v; and Abetti Pagnini , op. cit. (ref. 3), 449–52. The letter is undated so we cannot be entirely sure of when it may have been written. Judging from the references to Gassendi's “Philosophy”, meaning, presumably, the Syntagma philosophicum, published in 1658, it is possible that Viviani wrote the letter that same year.

“… da ciò che ne dice detto Gassendi”. BNCF, Ms. Gal. 268, ff. 156v; Abetti Pagnini , op. cit. (ref. 3), 450. If Viviani did indeed refer to Gassendi's opinion on the topic in this conversation in 1656, we can only assume that this reference was from private correspondence with Gassendi or from a manuscript of Gassendi's Syntagma philosophicum, in which he discussed the movement of sound.

As Viviani revealed in this letter, Ferdinando had measured the time it takes for sound to travel between the nearby Medici villa of Petraia, and the Grand Ducal palace in Florence. Ferdinando's attempt to perform his own experiments shows his genuine interest in natural knowledge. BNCF, Ms. Gal. 268, ff. 156v; Abetti Pagnini , op. cit. (ref. 3), 450.

BNCF, Ms. Gal. 268, ff. 156v; Abetti Pagnini , op. cit. (ref. 3), 450.

Nelli G. B. C. , Saggio di storia letteraria fiorentina del secolo XVII scritta in varie lettere (Lucca, 1759), 110–11. Although Viviani and Borelli performed these experiments together, Viviani ensured that there would be no mistaking the identity of their inventor by mentioning them in this list. This shows the academicians' concerns about intellectual ownership and suggests that they might not have been entirely comfortable with the anonymity of the experiments' authors in the Saggi.

“Le conseguenze poi che si pretendono di cavare da questa equabilità sono, fra l'altre, che per via di lampi e di suoni di diversi tiri potremo aver l'esatta misura delle distanze de'luoghi, e particolarmente in mare… Sarà ancor facile e curioso a sapersi quanto da noi siano lontane le nuvole, e in che distanza da terra si creino i tuoni, misurando i tempi da che si vede il baleno a che quegli si sentono…. Con questo stesso mezzo del suono potremo raggustar le carte de'luoghi particolari, e formar piante di diversi paesi, pigliando prima gli angoli di posizione delle città, castelli e villaggi per situarli acconciamente a' lor luoghi”. Magalotti , op. cit. (ref. 3), 243–4.

Galileo and Torricelli faced a similar challenge when they worked on projectile motion during the 1640s. Galileo and Torricelli argued for a geometrical explanation of the parabolic trajectory of a projectile, but also had to demonstrate the practical value of such work to the Medici Court by applying the geometrical calculations to the techniques of firing artillery. See Hall A. R. , Ballistics in the seventeenth century (Cambridge, 1952), 91; and Rose P. L. , “Galileo's theory of ballistics”, The British journal for the history of science, iv (1968), 156–9, p. 156.

BNCF, Ms. Gal. 268, ff. 155v–158v; Abetti Pagnini , op. cit. (ref. 3), 450–1.

Gassendi P. , Opera omnia (6 vols, Lyons, 1658–75), i, 420–2.

Magalotti , op. cit. (ref. 3), 242.

Ibid. These experiments were recorded in the official diary: BNCF, Ms. Gal. 262, f. 132r.

Brundell B. , Pierre Gassendi: From Aristotelianism to new natural philosophy (Dordrecht, 1987), 54–59; and Osler M. J. , Divine will and the mechanical philosophy (Cambridge, 1994), 182–94.

The academicians spent most of their time together working on their experiments regarding pneumatics and the freezing process. The publication of these experiments also filled the majority of the Saggi's pages.

For lengthy analyses of the Cimento's experiments concerning pneumatics, as well as the freezing process, and for an examination of the natural philosophical issues debated within the Cimento, see Galluzzi , “L'Accademia del Cimento” (ref. 3); Boschiero L. , “Natural philosophizing inside the late seventeenth-century Tuscan Court”, The British journal for the history of science, xxxv (2002), 383–410; and Boschiero L. , “Natural philosophical contention inside the Accademia del Cimento: The properties and effects of heat and cold”, Annals of science, lv (2003), 329–49.

Apollonius of Perga was a student of Euclidean geometry in the third century b.c. and before his death circa 190 b.c., he managed to complete his writing on the geometrical properties of cones with circular sections, that is, conic sections. While Apollonius's first four books of the Conics were available to Renaissance scholars, the last four books had been missing since Antiquity. In fact, the entire second half of Apollonius's work on conics might still be missing today had it not been for the ancient Arabic translators of classical Greek geometrical texts, who preserved seven of the eight books in their translations. The last three of these were translated into Latin by Borelli in 1661. The eighth book remains missing today.

See Micheli G. , “L'assimilazione della scienza greca”, in idem (ed.), Storia d'Italia, Annali 3: Scienze e tecnica nella cultura e nella società dal Rinascimento a oggi (Turin, 1980), 215–57.

Ibid., 217.

Maurolico F. , Emendatio et restituio conicorum Apollonii Pergaei (Messina, 1654). See Baldini U. , “Giovanni Alfonso Borelli e la rivoluzione scientifica”, Physis, xvi (1974), 97–128, p. 120, n. 65.

Galileo , Opere, viii, 269–70.

According to Pappus of Alexandria, Aristaeus's treatise on conics, Solid loci, no copy of which has ever been found, was written before Apollonius began working on his Conics. Clagett M. , Archimedes in the Middle Ages (4 vols, Philadelphia, 1980), iv, 74.

As a result of this rivalry, some animosity existed between Viviani and Borelli. In a letter to a fellow academician in December 1657, Viviani referred to Borelli as “deceitful [artificiosissime]” and “disgusting [stomocato]”. Tenca L. , Le relazioni fra Giovanni Alfonso Borelli e Vincenzio Viviani (Milan, 1956), 112.

It is curious how these manuscripts arrived in Tuscany and why they were not previously translated. In 1590, Cardinal Ferdinando de'Medici, who was soon to take over the Grand Ducal crown from his brother Francesco I, visited Rome and became acquainted with a learned Arab by the name of Ignazio Naheme. Naheme handed Ferdinando a collection of Arabic manuscripts that the future Tuscan Grand Duke took back to Florence. Despite some interest shown in the manuscripts by Tuscan mathematician, G. B. Raimondi, towards the end of the sixteenth century, and by Michelangelo Ricci in 1645, they were not translated and remained untouched in the Grand Duke's archives until Borelli recognized their importance in 1658. See Giovannozzi G. , “La versione borelliana dei Conici di Apollonio”, in Memorie della Pontificia Accademia Romana dei Nuovi Lincei (2 vols, Rome, 1916), ii, 1–32, pp. 4–5.

Ibid., 7.

BNCF, Ms. Gal. 254, ff. 105r–106v; and Barbensi G. , Borelli (Trieste, 1947), 30.

As translated by Middleton , op. cit. (ref. 41), 313. “Tiri pure avanti, e goda di questo benefizio, del quale io dubito di non poter godere, ancorchè abbia presso di me un compeniosissimo trattato dei Conici disteso tutto di mia mano….” BNCF, Ms. Gal.254, f. 107r; and del Gaizo M. , “Contributo allo studio della vita e delle opere di Giovanni Alfonso Borelli”, Atti della Accademia Pontaniana, xx (1890), 1–48, p. 14.

Barbensi , op. cit. (ref. 67), 30.

Middleton , op. cit. (ref. 41), 314. This letter was to Melchisadec Thevenot. BNCF, Ms. Gal. 282, f. 57r.

This point was also made by Middleton , op. cit. (ref. 41), 314.

As translated by Middleton , ibid., 313. “Io similmente concorro, e approvo la soluzione di V.S. e di tutti i suoi amici di mandare alle stampe le sue invenzioni intorno ai conici, et io potrò testificare fra gli altri, che ella non ha avuto notizie di questi ultimi libri”. BNCF, Ms. Gal. 254, f. 107r; and Bonelli, op. cit. (ref. 1), 676.

Borelli's correspondence to Viviani during this period can be read in BNCF, Ms. 254, ff. 103r–114r.

Natucci A. , “Vincenzio Viviani”, in Dictionary of scientific biography, x, 48–50, p. 49.

Borelli used Euclidean and Apollonian geometry to reach his conclusions on the mathematical demonstrations of planetary movement in Theoricae mediceorum planetarum ex causis deductae (Florence, 1666). While he was working on celestial motion, Borelli was also collaborating with anatomists and physiologists in Pisa, in order to find the mechanical structure and movements of the body. This work eventually resulted in his last publication, De motu animalium (Rome, 1680).

This appointment came as Borelli left Tuscany to continue his career in southern Italy, thus vacating the position.

See Drake , Galileo at work (ref. 29), 421–36.

Favaro , Amici e corrispondenti (ref. 1), 1071.

Viviani V. , Discorso al Serenissimo Cosimo III Granduca di Toscana intorno al difendersi da'riempimenti e dalle corrasioni de'fiumi applicato ad Arno (Florence, 1688).

Viviani V. , De locis solidis secunda divinatio geometica in cinque libros iniuria temporum amissos Aristaei Senionis Geometrae (Florence, 1701).

Shapin Schaffer , op. cit. (ref. 2). Shapin continued with this theme in A social history of truth (ref. 2); and to a slightly lesser extent in The Scientific Revolution (Chicago, 1996).

For a thorough critical analysis of this historiographical position, see Schuster J. A. Taylor A. B. H. , “Blind trust: The gentlemanly origins of experimental science”, Social studies of science, xxvii (1997), 503–36.

Biagioli , op. cit. (ref. 2); Tribby J. , “Dante's restaurant: The cultural work of experiment in early modern Tuscany”, in Bermingham A. Brewer J. (eds), The consumption of culture: 1600–1800 (London, 1995), 319–37; Findlen P. , “The economy of scientific exchange in early modern Italy”, in Moran B. T. (ed.), Patronage and institutions: Science, technology, and medicine at the European court, 1500–1750 (Rochester, Suffolk, 1991), 5–24; and Beretta, op. cit. (ref. 2).

Findlen P. , “Controlling the experiment: Rhetoric, court patronage and the experimental method of Francesco Redi”, History of science, xxxi (1993), 35–64.

Beretta , op. cit. (ref. 2), 148.