WILLIAM A. WALLACE
1 Galileo's Pisan studies in science and philosophy
The aura surrounding Galileo as founder of modern science disposes many of those writing about him to start in medias res with an account of his discoveries with the telescope, or with his dialogues on the world systems and the two new sciences, or with the trial and the tragic events surrounding it. Frequently implicit in such beginnings is the attitude that Galileo had no forebears and stands apart from history, this despite the fact that he was forty-six years of age when he wrote his Sidereus Nuntius and then in his late sixties and early seventies when he composed his two other masterpieces.
Attempts have recently been made by scholars to dispel this myth by giving closer scrutiny to the historical record – closer, that is, than one gets from perusing the National Edition of Galileo's works.1 This was a masterful collection, but begun as it was in the last decade of the nineteenth century and completed in the first decade of the twentieth, it perforce could not benefit from the historiographical techniques developed in our century. During the past twenty years, in particular, much research has been done on Galileo's manuscripts, and it sheds unexpected light on what has come to be known as Galileo's “early period” – that covering the first forty-five years of his life.2 This period has been singularly neglected by historians, and to their disadvantage, if the adage parvus error in initio magnus in fine may be applied to the history of ideas.
PERSONS AND PLACES IN TUSCANY
Galileo's father, Vincenzio Galilei, was born in Florence in 1520 and flourished there as a teacher of music and a lutanist of ability (Drake 1970). Having studied music theory for a while with Gioseffo Zarlini in Venice, he married Guilia Ammannati of Pescia in 1563 and settled in the countryside near Pisa. There their first child, Galileo Galilei, was born on February 15, 1564. The family returned to Florence in 1572, but the young Galileo was left in Pisa with a relative of Guilia by marriage, Muzio Tedaldi, a businessman and customs official.
Two years later, Galileo rejoined his family in Florence and was tutored there by Jacopo Borghini until he could be sent to the Camal-dolese Monastery at nearby Vallombrosa to begin his classical education. While at that monastery, Galileo was attracted to the life of the monks and actually joined the order as a novice. Vincenzio was displeased with the development, so he brought his son back to Florence where he resumed his studies at a school run by the Camal-dolese monks but no longer as a candidate for their order.
Vincenzio's plan for Galileo was to become a physician, following in the footsteps of a fifteenth-century member of the family, also named Galileo, who had achieved great distinction as a physician and also in public affairs. Accordingly, he arranged for his son to live again with Tedaldi in Pisa and had him enrolled at the university there as a medical student in the fall of 1581 (Drake 1978).
The next four years of his life Galileo spent at the University of Pisa, studying mainly philosophy, where his professors were Francesco Buonamici and Girolamo Borro, and mathematics (including astronomy) under a Camaldolese monk, Filippo Fantoni. He probably went back to Florence for the summers, however, and this provides a key to the way Galileo supplemented the instructions he received in mathematics from Father Fantoni.
It was the custom of the Tuscan court to move from Florence to Pisa from Christmas to Easter of each year, and the court mathematician at the time was Ostilio Ricci, a competent geometer who is said to have studied under Niccolo Tartaglia (Settle 1971, Masotti 1975). During the 1582–1583 academic year, Galileo met Ricci while the latter was at Pisa and sat in on lectures Ricci was giving on Euclid to the court pages.
The following summer, when Galileo was back home, supposedly reading Galen, he invited Ricci to meet his father. Vincenzio was impressed with Ricci and the two became friends. Ricci told Vincenzio that his son was little interested in medicine, that he wanted to become a mathematician, and sought permission to instruct him in that discipline. Despite Vincenzio's unhappiness with this request, Galileo was able to avail himself of Ricci's help and devote himself more and more to the study of Euclid and Archimedes, probably with the aid of Italian translations prepared by Tartaglia.
By 1585, Galileo dropped out of the University of Pisa and began to teach mathematics privately at Florence and at Siena, where he had a public appointment in 1585–1586, and then at Vallombrosa in the summer of 1585. In 1587, Galileo traveled to Rome to visit Christopher Clavius, the famous Jesuit mathematician at the Collegio Romano. And in 1588, he was invited to the Florentine Academy to give lectures on the location and dimensions of hell in Dante's Inferno.
In 1589, Fantoni relinquished the chair in mathematics at Pis a and Galileo was selected to replace him, partly because of the favorable impression he had made on the Tuscan court with his lectures on Dante and partly on the recommendation of Clavius and other mathematicians who had become acquainted with his work. Galileo began lecturing at Pisa in November 1589, along with Jacopo Mazzoni, a philosopher who taught both Plato and Aristotle and was also an expert on Dante, and the two quickly became friends (Purnell 1972, DePace 1993).
Mazzoni is of special interest because of his knowledge of the works of another mathematician, Giovan Battista Benedetti, and because he is given special mention by Galileo in a letter from Pisa addressed to his father in Florence and dated November 15, 1590. In it, Galileo requests that his seven-volume Galen and his Sfera be sent to him at Pisa and informs his father that he is applying himself “to study and learning from Signor Mazzoni,” who sends his regards (EN10:44–5).
Galileo then taught at the University of Pisa until 1592, when financial burdens put on him as the eldest son at the death of his father in 1591 required him to obtain a better salary than the 60 florins he was being paid. He sought and received an appointment at the University of Padua at a salary of 180 florins, where he delivered his inaugural lecture on December 7, 1592.
He spent the next eighteen years in the Republic of Venice, which he later avowed were the happiest years of his life. Then he returned to the Florentine court in 1610 as mathematician and philosopher to Cosimo II de’ Medici, the Grand Duke of Tuscany.
MANUSCRIPTS AND THE EXPANDED DATA BASE
We have touched on places and persons in Tuscany that played a significant role in Galileo's intellectual development. The principal locations are Pisa and Florence, with Vallombrosa and Siena of secondary importance, along with the outside trip to Rome, which fortunately gave rise to materials that greatly enlarge the data base on which we can work. Galileo left a number of manuscripts dating from about 1580 to 1592, most in his own hand and in Latin, much of it on watermarked paper. Antonio Favaro transcribed some of the manuscripts for the National Edition and made a few notations regarding Galileo's peculiar spelling of Latin terms.
He also was able to identify two sources Galileo used for note taking, both translations of Plutarch's Opuscoli Morali, one published at Venice in 1559 and the other at Lucca in 1560 (EN9:277–8). Apart from this, Favaro could only conjecture about Galileo's sources and the periods during which he composed the various manuscripts that make up his Tuscan heritage, most of which are still conserved in Florence's Biblioteca Nazionale Centrale.
Serious work on these materials began around 1970, when Stillman Drake worked out a technique for dating Galileo's manuscripts through a study of the watermarks on the paper on which they were written and when other scholars, myself included, began to uncover the source materials on which the natural philosophy contained in one of the manuscripts was based.3 Over the past twenty-five years, this research has expanded to include full studies of watermarks (Camerota 1993), detailed paleographical studies of Galileo's handwriting and word choice (Hooper 1993), and analyses of the ink he used when writing the manuscripts (Hooper 1994).4
Research on the sources of Galileo's philosophy proved particularly fruitful, since it turned out that a large part of that philosophy was appropriated from notes of lectures given in Rome by Jesuit professors of the Collegio Romano – the prestigious university established in that city by the founder of the Jesuits, Ignatius Loyola. Although Galileo did not attend those lectures, he somehow obtained copies of them and then appropriated selected materials for his own use. Since the Jesuit notes can be dated, the discovery in them of passages with correspondences in Galileo's writings offers an additional way to determine the time and place of Galileo's compositions.
The manuscripts most important for this enterprise are all in Galileo's hand and are four in number. One is a special collection, Filza Rinuccini 2, and contains Galileo's lectures on Dante's Inferno; this was given in Florence and is written on paper bearing a Florentine watermark. The other three are in the group of manuscripts at the Biblioteca Nazionale entitled Manoscritti Galileiani and bear the numbers 27, 46, and 71.
Manuscript 27 is labeled Dialettica, the term used for the whole of logic in Galileo's day, and contains two treatises on logic. Antonio Favaro regarded this as a “scholastic exercise” of Galileo and only transcribed its titles and a sample question in the National Edition (EN9:275–82). It gives many indications of having been copied or appropriated from one or more sources, and many of its folios bear watermarks, all of Pisan origin.
Manuscript 46 bears the notation that it contains “an examination of Aristotle's De cáelo made by Galileo around the year 1590” (EN1:9). This manuscript is essentially a notebook and it contains five treatises on different subjects, which Favaro transcribed and published in their entirety under the title Juvenilia, regarding it as a youthful composition (EN1:15–177). It, too, shows signs of copying, and its folios bear a variety of watermarks, most of either Pisan or Florentine origin.
Manuscript 71 differs from the other two in that there are crossouts and emendations in the manuscript but no signs of copying. It apparently contains original drafts of essays by Galileo on the subject of motion, on this account, is referred to as the De Motu Antiquiora, the “older” science of motion, to distinguish it from the “new” science of motion published by Galileo in 1638. The folios of this manuscript, like the others, bear watermarks, a majority from Pisa but a significant number from Florence. Favaro also transcribed and published this manuscript (EN1:251–408), but in so doing he changed the ordering of the essays as they occur at present in the manuscript.
There are errors of Latinity in some of the noted manuscripts and also peculiarities of spelling. There are also internal references that serve to show temporal connections between them. And, finally, there is now a substantial collection of possible source materials, some in print, others still in manuscript, on which Galileo could have drawn when writing them. Evaluating all of this material is the task one must face when trying to assess Galileo's intellectual formation. This took place mainly at the University of Pisa, but it was an ongoing process during the entire Tuscan period, prior to Galileo's move to the Veneto in 1592.
GALILEO'S APPROPRIATION OF JESUIT LEARNING
Of the material surveyed thus far, the most surprising is that associated with the Jesuits of the Collegio Romano, a source completely unsuspected for over four centuries.
I started my research on that subject at about the same time Drake was beginning his work on watermarks and have reported my findings in publications since then, principally 1981, 1984a, 1990, and 1992a, b. The path was tortuous and need not be reviewed here. The main conclusions were that the two manuscripts with the closest connections to the Jesuits, 27 and 46, were both composed at Pisa, the first in early 1589 and the second in late 1589 or early 1590 (Wallace, 1992b:39, 57).
The logic notes of manuscript 27 consist of two treatises relating to Aristotle's Posterior Analytics, one dealing with foreknowledge required for demonstration and the other with demonstration itself. Both treatises clearly derive from a course taught by Paulus Vallius in Rome, which did not conclude until August of 1588, and from which Galileo could not have appropriated his version until early 1589. Nothing in the watermark evidence and that derived from peculiarities in spelling alters this conclusion.
The situation is more complex with regard to Manuscript 46, labeled Physical Questions (Wallace 1977) to differentiate them from the Logical Questions of Manuscript 27. This is composed of three parts, the first containing portions of a questionary on Aristotle's De caelo, the second portions of a questionary on Aristotle's De generatione, and the third of series of memoranda on motion that are related to the composition of Manuscript 71, to be considered later. There are three treatises in the part pertaining to De caelo, the first concerning the subject of that work, the second on the universe as a whole, and the third on the heavens.
All three of these are written on paper with Pisan watermarks and show few peculiarities of spelling. Since they presume knowledge of the logic contained in Manuscript 27 and show signs of improved Latinity, their writing is best located at Pisa around 1590, within a year after the questions on logic. The particular Jesuit set of notes Galileo used for his appropriation is not known with certainty, but a good possibility is that taught by Antonius Menu on De caelo in 1580. This source clears up a problem in the dating of Manuscript 46 based on the chronology given in it by Galileo (Wallace 1977:42, 258–9) and otherwise fits in with considerations presented in Wallace (1981:217–28) and Wallace (1984a:89–96).5
The second part of Manuscript 46 contains three treatises pertaining to De generatione, the first on alteration, the second on the elements, and the third on primary qualities. These are written on paper different from the first part, with Florentine watermarks, and they contain irregularities in spelling. The irregularities relate to word forms that are written differently in Italian and Latin, as, for example, santo and sancto, and occur in words with letter grouping like -nt- and -st-. Thus for elementum Galileo will sometimes write elemenctum; for contra, conctra; for momentum, momenctum; for distantia, dixtantia; and so on. These variants have been studied by Wallace Hooper (1993) who sees them as evidence of Galileo's learning when, and when not, to insert a c or an x when changing from an Italian to a Latin spelling.
Apparently, Galileo overcompensated at first and inserted too many c's or changed an s to an x too often, for these forms quickly disappear in his later compositions. Their presence, therefore, is a good indication that their author, who had been accustomed to writing in Italian, was beginning to write in Latin as he prepared himself for an academic career. On the basis of this evidence it seems likely that these treatises were written in Florence and at a date even earlier than Manuscript 27, probably 1588.
Which of the Jesuit courses Galileo used for his appropriation is difficult to decide, but the best candidate is that on De generatione, offered in Rome by Paulus Vallius, the same Jesuit whose logical questions were used by Galileo when writing his Manuscript 27. Unfortunately, the exemplar of Vallius's work on the elements that shows close correspondences with Galileo's Manuscript 46 is found in a codex that is undated. We do know, however, that Vallius taught De generatione there in 1585,1586, and 1589, and, of these, the 1586 version would fit best with the new evidence.
As I have argued in Wallace (1984a:91–2, 223–5), Galileo first gained access to all these lecture notes through his visit to Christopher Clavius in 1587. At that time, he left with Clavius some theorems he had composed on the center of gravity of solids. In correspondence between the two in 1588, which involved Guidobaldo del Monte also, Clavius questioned Galileo's proof of the first theorem on the grounds that it contained a petitio principii (EN10:24–5, 29–30).
Since this type of question pertains to the foreknowledge required for demonstration, and at that time Vallius was teaching the part of the logic sequence dealing with foreknowledge and demonstration, it seems reasonable to suppose that Clavius would have put Galileo in touch with Vallius and that the latter would have made his lecture notes available to the young mathematician. Also, Galileo could well have had queries for Clavius on gravitas and levitas as these pertain to the elements, and Vallius would again be the best resource to whom Galileo could turn for information on these topics. This would explain how Galileo obtained not only the materials on which Manuscript 27 were based but also how the earlier version of Vallius's De Elementis (say, that of 1586) came to be incorporated in his Manuscript 46.
From the point of view of philosophy, Galileo's Manuscript 27 contains some very sophisticated information on scientific methodology, especially on the use of suppositions in scientific reasoning and on the role of resolution and composition as employed in the demonstrative regressus. Scholars have tended to overlook the regress, a powerful method of discovery and proof developed at the University of Padua, which reached its perfection in Galileo's lifetime (Wallace 1995). These areas of logic have been described in detail in my study of Galileo's sources (Wallace 1984a: Chapters 3, 5, and 6), which documents the recurrence of expressions found in Manuscript 27 in all Galileo's later writings. The implications of these logical teachings are more fully delineated in my examination of Galileo's logic of discovery and proof (Wallace 1992a), the first part of which (logica docens, Chapters 1–4) systematically analyzes the logic contained in his logical treatises and the second part (logica utens, Chapters 5–6) how he used it in his works on astronomy and mechanics.
Manuscript 46 is almost four times longer than Manuscript 27, being composed of 110 folios as opposed to the latter's 31. Its material content covers the universe, the celestial spheres, and the elemental components of the terrestrial region, topics that engaged Galileo's attention throughout his life.
Two of its questions on the celestial spheres are clearly extracted from Clavius's commentary on the Sphere of Sacrohosco, either the 1581 or the 1585 edition. They show that Galileo was acquainted with Copernicus's teaching on the number and ordering of the spheres, even though he there defended the Ptolemaic teaching. He continued to teach Ptolemaic astronomy until the early 1600s, as is seen in his Trattato della Sfera, student copies of which were prepared from an original in Galileo's own hand between 1602 and 1606. The autograph has been lost, but Drake speculates that it was begun as early as 1586–1587, in conjunction with Galileo's private teaching of astronomy (Drake 1978:12). More likely, it was composed toward the end of 1590, when he wrote to his father requesting that his copy of the Sfera be sent to him at Pisa (Sfera here meaning the text with Clavius's commentary), and when he was writing the De caelo portion of Manuscript 46 containing the extract from Clavius (Wallace 1983, 1984a:255–61).
A striking but often unnoticed feature of Galileo's thought is his extraordinary grasp of Aristotelian teaching and his ability to engage the Peripatetics of his day on fine points of their interpretations. Such knowledge was not simply intuited by Galileo, he had to work to acquire it. He himself wrote to Belisario Vinta on May 7, 1610, when seeking the title of philosopher be added to that of mathematician to the Grand Duke of Tuscany, that he had “studied more years in philosophy than months in pure mathematics” (EN10:353). Surely the study and laborious appropriation of these lecture notes from Collegio Romano, a major portion of which is found in Manuscript 46, is to be counted among the “years in philosophy,” to which Galileo there refers. As far as his use of the Jesuit questionaries on De caelo and De generatione is concerned, these have been partially investigated in my translation of Manuscript 46 (Wallace 1977:253–314) and more fully in later works (Wallace 1981, 1984a, 1991, and 1992a).
THE PHILOSOPHICAL AMBIENCE AT PISA
Galileo's formal study of philosophy, of course, took place at the University of Pisa from 1581 to 1585, and he had further contacts with the philosophers there when teaching mathematics at the university between 1589 and 1592. Possibly because Galileo later voiced his disagreement with the views of his teachers at Pisa, scholars have tended to undervalue his philosophical training there.
This may prove to be a mistake, since a number of studies are now available that connect his studies at the university with the manuscripts we have already discussed, as well as with Manuscript 71, which will occupy our attention in the following section. To lay the groundwork for that exposition, we now sketch the philosophical ambience at Pisa, with particular reference to Francesco Buonamici, Girolamo Borro and his influence on Filippo Fantoni, and Jacopo Mazzoni and the way in which he may have put Galileo in contact with the thought of Giovanni Batista Benedetti.6
Correspondences between the contents of Manuscripts 46 and 71 and the teachings of Buonamici have long been recognized and have been analyzed in some detail by Alexandre Koyré (1978). More helpful for our purposes is Mario Helbing's (1989) study of Buonamici's philosophy. This provides the complete background of Galileo's studies at Pisa, a full analysis of the contents of Buonamici's De Motu, and valuable reflections on his relations with Galileo. Helbing calls attention to the fact that the De Motu was already completed by 1587, though it was not published until 1591. Its importance derives from the fact that it records the fruits of Buonamici's teaching at the University of Pisa, where he taught natural philosophy from 1565 to 1587. His occasion for putting out the volume was, in Buonamici's own words, “a controversy that had arisen at the university among our students and certain of our colleagues on the motion of the elements” (Helbing 1989:54).
To appreciate the import of this statement one must be aware, Helbing points out, that professorial lectures were not the only means of transmitting knowledge to students at the time. Disputations were an additional component, and many of these seem to have centered on precisely the problems that interested Galileo. It could well be, therefore, that Galileo was one of the students to whom Buonamici refers. The colleagues mentioned most certainly include Borro, who published a treatise on the motion of heavy and light bodies in 1575, to which Galileo refers in Manuscript 71, and probably Fantoni, who left a manuscript on the same subject that shows Borro's influence.
Helbing's thesis is that Buonamici's teaching exerted a substantial influence on the young Galileo, so much so that his own writings reflect a polemic dialogue with his teacher that continued through the years. The subjects and problems that preoccupied him were all contained in Buonamici's massive treatise, whose technical terminology Galileo took over as his own, even though his investigations led him to markedly different results.
Buonamici's project was to write a definitive treatise on motion in general that would explain its many manifestations in the world of nature on the basis of philological and scholarly research. Galileo's project, by way of opposition (EN1:367), was to concentrate on only one motion, essentially that of heavy bodies, and to make a detailed study of that using mathematical techniques to reveal its true nature. In his lectures, Helbing argues, Buonamici probably introduced Galileo to the atomism of Democritus, to Philoponus's critiques of Aristotle's teachings, to Copernicus's innovations in astronomy, to Archimedes and his use of the buoyancy principle to explain upward motion, to Hipparchus's theory of impetus, and to the writings of many others, including those of Clavius and Benedetto Pereira at the Collegio Romano – references to all of which can be found in his De Motu.
Galileo, without doubt, explicitly rejected many of Buonamici's teachings. Helbing notes that this rejection is particularly evident in Galileo's early writings, where Buonamici's arguments against Archimedes are definitely his target. Galileo also makes references to his former teacher in terms that are far from complimentary, in both the Two Chief World Systems (EN7:200, 231–2) and the Two New Sciences (EN8:190).
But despite these negative reactions, Helbing also records several areas of substantial agreement between Buonamici and Galileo, two of which are relevant to our study. The first is the general methodology they employ in their study of motion. Both wish to use a methodus to put their science on an axiomatic base, imitating in this the reasoning processes of mathematicians (De Motu 3A-B). Both regard sense experience as the foundation of natural science, taking this in a sense broad enough to include experiment in the rudimentary form it was then assuming at Pisa. And both see causal reasoning and demonstration, with its twofold process of resolution and composition, as the normal road to scientific conclusions.
The second and more important area of agreement is the status each accords to mathematics both as a science in its own right and as an aid in investigating the secrets of nature. Buonamici lists the three speculative sciences as physics, mathematics, and metaphysics, and he insists that students should begin their study with mathematics, then proceed to physics, and ultimately to metaphysics.
Again, mathematics for him is the discipline that can raise one to divine science. It is also a true science that satisfies the requirements of the Posterior Analytics, against the teachings of Pereira, whom he cites explicitly. Its demonstrations are not limited to reductions to the impossible but include ostensive demonstrations of all three types: of the fact, of the reasoned fact, and, most powerful, making it the most exact of the human sciences. Buonamici further accords validity to the middle sciences (scientiae mediae) which he lists as optics, catoptrics, harmonics, astronomy, navigation, and mechanics, and he sees them as valuable adjuncts for the study of nature. This part of Buonamici's instruction seems to have deeply influenced Galileo and set him on the course that would bring him ultimately to Clavius and the Collegio Romano.
Two additional professors at Pisa, Borro the philosopher and Fantoni the mathematician, seem to have had less positive influence on Galileo. Borro was the type of philosopher against whom Galileo reacted most violently. Very different from Buonamici, he took most of his knowledge of Aristotle from medieval authors, especially Averroes in Latin translation. His writings show him much opposed to Platonism and the attempts being made in his day to reconcile Aristotle's ideas with those of his teacher.
Borro's anti-Platonism, coupled with his attraction to Averroes, are further revealed in his vehement rejection of mathematics and of the use of mathematical methods in the study of nature. He focused instead on the empirical side of Aristotelian philosophy, stressing the importance of observation and experience in uncovering the secrets of nature, and in this respect he undoubtedly exerted an influence on Galileo. This influence is seen in Manuscript 71, where Galileo shows his acquaintance with an experiment performed by Borro and described by him in De Motu Gravium et Levium (1575).
Fantoni is important for two quaestiones he left in manuscript form, one on the motion of heavy and light bodies, the other on the certitude of the mathematical sciences. His De Motu is of some significance for the fact that he wrote it not as a philosopher, as did Borro and Buonamici, but while teaching mathematics, and in so doing set a precedent for Galileo to prepare a similar treatise when he took over Fantoni's post. Actually, it presents little more than the kind of Averroist analysis found in Borro's book. The treatise on mathematics is also unoriginal, taking up positions similar to those defended by Buonamici in his massive text. What is noteworthy about it is that it is explicitly directed against Pereira. Fantoni argues that mathematics is a true science, that it fills all the requirements of the Posterior Analytics for certain knowledge, that it demonstrates through true causes, and that it can even achieve demonstrations that are most powerful – conclusions consonant with those of Clavius and the mathematicians at the Collegio Romano.
Possibly the strongest influence on Galileo from his years in Pisa, however, came not from his professors there, but from the colleague he encountered when he started teaching there, Jacopo Mazzoni. In 1590, when Galileo told his father that he was studying with Mazzoni, he was probably composing the notes on De caelo and De generatione, a course Mazzoni had taught the previous year.
Unlike his Pisan colleagues in philosophy, Mazzoni was not a monolithic Aristotelian. He also had Platonic sympathies, and in the summer of 1589 he had introduced a course in Plato's thought at the university. One of his major interests was comparing Aristotle with Plato, for he had made a concordance of their views in an early treatise published at Cesena in 1576. His major work on that subject, the Praeludia, did not appear until 1597, but there are indications Mazzoni was working on it over the intervening years. After its publication at Venice, in fact, Galileo wrote to him and remarked how their discussions at the beginning of their friendship were detectable in its composition (EN2:197).
Like Buonamici, Mazzoni takes a favorable view of the “mixed sciences,” the scientiae mediae, and is explicit that Ptolemy's work pertains to that genre and also the work of Archimedes. It was Aristotle's shunning the use of mathematical demonstrations in physics, Mazzoni states, that caused him to err in his philosophizing about nature.
As an example, he cites Aristotle's teaching on the velocity of falling bodies. In detailing its particular errors and how they can be corrected, he turns to the work of Benedetti and particularly the way the latter used Archimedian principles to rectify Aristotle's teachings. Mazzoni's own treatment of the velocity problem, it turns out, more resembles that given by Galileo in Manuscript 71 than it does Benedetti's. This gives reason to believe that it was precisely these matters that Galileo and Mazzoni were studying late in 1590, the period during which it is commonly agreed Galileo was working on his De Motu Antiquiora.
Another comparison made by Mazzoni comes from his interest in pedagogy and concerns the relative merits of Plato and Aristotle for removing impediments encountered in the study of nature. Galileo discusses such impediments in his early writings and the various suppositions one may use to circumvent them. It is not unlikely that his studies with Mazzoni were seminal also in this respect.
With regard finally to Benedetti's work on falling motion, Koyré suspected a connection between it and the positions taken in Manuscript 71 but had little textual evidence for it, since Galileo nowhere makes any mention of Benedetti. In particular, the anti-Aristotelian tone Galileo adopts in his Manuscript 71 resonates strongly with the tone of Benedetti's major work on falling motion, Diversarum Speculationum Mathematicarum et Physicarum Liber, printed at Turin in 1585.
Since this was available before 1590 and figures prominently in Mazzoni's Praeludia, it seems reasonable to suppose that Benedetti's text was itself the object of Galileo's study with Mazzoni referred to in the letter to his father. As I have pointed out elsewhere (Wallace 1987), Benedetti's basic disagreement with Aristotle was over the latter's not using mathematical principles and methods in the study of nature, a theme recurring in both Mazzoni and Galileo. Benedetti's work likewise abounds in suppositions and thought experiments, many of which are similar to Galileo's, and he, like Galileo, is particularly intent on discovering the causes of various properties of local motion – what they both call the verae causae, the true causes, as opposed to those proposed by Aristotle.
Information gleaned from the philosophical ambience at Pisa thus complements the materials contained in Manuscripts 27 and 46 and provides a fuller understanding of Galileo's intellectual development during his years at Pisa. His interest in Archimedes undoubtedly dates from his studies with Buonamici and Ricci, the latter particularly because he helped Galileo hone his argumentative skills against his former teacher. His respect for Plato and his privileging Plato over Aristotle in some of his writings are at least partially explicable in terms of his contacts with Mazzoni (DePace 1992; Dollo 1989, 1990).
Nor does this type of influence from Mazzoni work at cross purposes with the materials Galileo appropriated from the Collegio Romano. In some matters, the Jesuits actually preferred Platonic teachings to those of Aristotle. For, as Crombie (1977) has amply demonstrated, they saw Platonism as fostering interest in the study of mathematics – which Calvius by 1589 had succeeded, over the objections of Pereira, in making a part of the Ratio studiorum at the Collegio Romano.
THE ARCHIMEDEAN – ARISTOTELIAN STUDY OF MOTION
This brings us back to Galileo's Manuscript 71 and his first sustained attack on the problem of falling motion, where, like Benedetti, he hoped to correct Aristotle with the aid of Archimedes. This manuscript has a number of components and the problem of ordering and dating these, partially explored by Favaro (EN1:245–9), has been the subject of renewed research on the basis of the new clues they present (Fredette 1972, 1975; Drake, 1986; Wallace, 1990; Camerota, 1993; Hooper 1993). We first review this development and then assess its import for the subsequent development of Galileo's science. The memoranda or jottings that Galileo made in preparation for his De Motu are found at the end of Manuscript 46, after the treatise on the elements, and this serves to tie the contents of Manuscript 71 to the physical questions.
These aside, the components of Manuscript 71 pertaining to the early De Motu are five in number and in the following order: a plan for the treatise, a dialogue on motion, a ten-chapter treatise on motion, a twenty-three-chapter treatise on motion, and variants of the first two chapters. In transcribing and publishing these, Favaro rearranged them, and the memoranda, in an order different from their appearance in the manuscripts, as can be seen from the following listing, which shows the foliation of the manuscripts on the left and the pagination of the National Edition on the right:
| MS 46 102r–110v | Memoranda | EN1:408–17 | ||
| MS 71 3v | Plan for De Motu | EN1:418–9 | ||
| MS 71 4r–35v | Dialogue on motion | EN1:367–408 | ||
| MS 71 43r–60v | 10-chapter treatise | EN1:344–66 | ||
| MS 71 61r–124v | 23-chapter treatise | EN1:251–340 | ||
| Ms 71 133r–134v | Variants of first two chapters | EN1:341–3 | ||
Inserted into this material and occupying folios not listed above, are two items which Favaro decided to publish in volumes two and nine of the National Edition:
| MS 71 39r | De Motu Accelerato EN2:259–66 |
| MS 71 132v–125r Latin transl. of Greek Isocrates | EN9:283–4 |
The last item here is bound in backwards, which explains its folio ordering.
Favaro's arrangement in EN1 suggests that, of the three main items, the twenty-three-chapter treatise on motion was written first, followed by the ten-chapter treatise, and the dialogue on motion last. To these, he inserted the variants between the first two items and appended the memoranda on motion and the plan at the end.
This ordering has been contested in all recent scholarship, starting with Drabkin and Drake (1960) and Fredette (1972). Both proposed the order of dialogue, twenty-three-chapter version, and then ten-chapter version, though they offered different reasons in its support.
To these, Drake (1986) added the evidence he was able to glean from watermarks and on that basis made further decisions regarding the time and place of their composition. In his view, the dialogue was written first, at Siena, between 1586 and 1587; then came the ten-chapter treatise, composed at Florence in 1588, and finally the twenty-three-chapter treatise, also at Pisa, between 1590 and 1591. His dating of the last item was based on my dating of the logical questions (Manuscript 27), whose influence he could also detect in the longer De Motu.
In my response to Drake's proposal, I agreed that the dialogue was written first, but at Pisa and in 1590, and I maintained that the other versions were composed there also, but in 1591 or 1592, before Galileo left for Padua (Wallace 1990:42–7).
This is the way things stood before Camerota began his detailed study of watermarks in Manuscript 71 and Hooper examined its various components for peculiar spellings of Latin terms. Their most important finding was that the ten-chapter De Motu was written on paper with the same Florentine watermarks as that of Galileo's lectures on Dante's Inferno (and Manuscript 46’s treatise on the elements) and had many irregularities in spelling, suggesting that it was the first item of those preserved in Manuscript 71, written in 1588 or shortly thereafter. Of the remaining pieces, all but the last four chapters of the twenty-three-chapter treatise bear Pisan watermarks. These chapters, surprisingly, are written on sheets with Florentine watermarks. The ensemble shows very few peculiar spellings, with the exception of the variants of the first two chapters, which have more than half the percentage of irregular spellings in the ten-chapter treatise and are probably of early composition also.
Data such as these have led Hooper (using Camerota's data) to propose the following as the preferred order of the materials in Manuscript 71: the ten-chapter treatise, composed at Florence as early as 1588, the variants on the first two chapters, written at Pisa in 1590, the Dialogus, written at Pisa also in 1590, the first nineteen chapters of the twenty-three-chapter De Motu, likewise written at Pisa but in 1591–1592, and the last four chapters of that work, written at Florence in 1591–1592 (Hooper 1993, Camerota 1993).
As supporting evidence for their Pisa 1590 dating of the dialogue, Hooper-Camerota detect the influence of Mazzoni in that work. These results are in substantial agreement with my own datings (Wallace 1990, 1992b). The most important consideration is that the latest research confirms my line of reasoning to establish that the major part of the De Motu Antiquiora, and particularly the twenty-three-chapter version, was written after the composition of Manuscripts 27 and 46 (Wallace 1984a). This allows for an influence of the materials Galileo appropriated from the Jesuits on that work, with consequences I shall now explain.
The key teaching of Manuscript 27, already noted, is that on the demonstrative regressus, a type of reasoning that employs two demonstrations, one “of the fact” and the other “of the reasoned fact” (Galilei 1988, Berti 1991, Wallace 1992b:180–184). Galileo refers to these demonstrations as “progressions” and notes that they are separated by an intermediate stage.
The first progression argues from effect to cause and the second goes in the reverse direction, thus “regressing” from cause to effect. For the process to work, the demonstration of the fact must come first, and the effect must initially be more known than the cause, though in the end the two must be seen as convertible. The intermediate stage effects the transition to the second demonstration.
As explained in Galileo's time, this stage involved “a mental examination of the cause proposed,” mentale ipsius causae examen, the wording used by Jacopo Zabarella.7 The Latin examen is significant because it corresponds to the Greek peira, a term that is the root for the Latin periculum, meaning test, the equivalent of experimentum or experiment (Olivieri 1978:164–6, Wallace 1993). Thus the main task of the intermediate stage is one of testing, of investigating and eliminating other possibilities, and so seeing the cause as required wherever the effect is present.
Note here Galileo's major innovation in the regressus: It was his use of the periculum in the intermediate stage to determine the “true cause” of the phenomenon under study. In the case of the De Motu Antiquiora that phenomenon was the speed of a body's fall in various media. Here Galileo's major use of Archimedes was his replacement of Aristotle's concept of absolute weight by that of specific weight, that is, the weight of the body as affected by the medium in which it is immersed, and so corrected for the buoyancy effect of the medium.
This was Benedetti's contribution, of course, and is not original with Galileo. What was original was Galileo's use of the inclined plane to slow the descent of bodies under the influence of gravity. The basic insight behind this experiment is found in Chapter 14 of the twenty-three-chapter version of De Motu (EN1:296–302, Drabkin and Drake 1960:63–9) and may be stated as follows: If the effective weight of a body can be decreased by positioning it on an incline (analogous in some way to the decrease of effective weight by buoyancy), then its velocity down the incline will be slowed proportionately.
The demonstration Galileo offers is geometrical and consists in showing that the forces involved with weights on an inclined plane actually obey the law of the balance. It also invokes several suppositions and on this account may be seen as a demonstration ex suppositione. If these suppositions are granted, the conclusion follows directly: The ratio of speeds down the incline will be as the length of the incline to its vertical height, because the weight of the body varies precisely in that proportion.
Galileo uses the term periculum for test or experiment five times in the De Motu treatises (Schmitt 1981:VIII, 114–23). One occurrence is in connection with the basic supposition behind his reasoning, the Aristotelian principle that speed of fall is directly proportional to the falling body's weight, amended now to be its weight in the medium as opposed to its absolute weight. Galileo says that if one performs the periculum the proposed proportionality will not actually be observed, and he attributes the discrepancy to “accidental causes” (EN1:273).
Moreover, for the inclined plane reasoning to apply, one must suppose that there is no accidental resistance occasioned by the roughness of the moving body or of the plane or by the shape of the body; that the plane is, so to speak, incorporeal, or at least that it is very carefully smoothed and perfectly hard; and that the moving body is perfectly smooth and of a perfectly spherical shape (EN1:298–9). Under such conditions, one may suppose that any given body can be moved on a plane parallel to the horizon by a force smaller than any given force (EN1:299–300). Here Galileo states that one should not be surprised if a periculum does not verify this for two reasons: External impediments prevent it (which elicits the previous supposition) and a plane surface cannot be parallel to the horizon because the Earth's surface is spherical (EN1:301).
A more interesting periculum to which Galileo makes reference occurs in Chapter 22 of the De Motu, where he speaks of dropping objects from a high tower (EN1:333–7, Drabkin and Drake 1960:106–10). Here, he contests the results of Borro's experimentum which purported to show that when two equal bodies of lead and wood are thrown simultaneously from a window, the lighter body invariably reaches the ground before the heavier one.
Galileo's tests, which he says were often repeated, show the opposite. Although the lighter body moves more swiftly at the beginning of its motion, the heavier one quickly overtakes it and reaches the ground far ahead. The reasons Galileo offers is that the lighter body cannot conserve its upward impetus as well as the heavier body. Thus it falls quickly at first, but the heavier body then overcomes its upward impetus and so catches up with, and then passes, the lighter body.
This solution actually depends on Galileo's argument in Chapter 19 of De Motu, directed against Aristotle, to explain why bodies increase their speed, or accelerate, during fall (EN1:315–23, Drabkin and Drake 1960:85–94). There, Galileo bases his explanation on an upwardly directed impetus or levity impressed on the body that is self-expending with time. As opposed to Aristotle's cause, Galileo sees the vera causa of the velocity increase to lie in the decrease of effective weight throughout the body's fall.
All of these suppositional demonstrations, we now know, pertain to Galileo's Pisan period. They all can be put in the form of the demonstrative regressus as this is set out in Manuscript 27, samples of which are given in Wallace (1992a:241–7). Galileo wanted to publish the treatise on motion, but he clearly had doubts about the “true causes” he had proposed in it because of his failure to obtain experimental confirmation of his results. He kept the manuscript in his possession, nonetheless, and when he finally did discover the correct law of falling bodies, he inserted a draft of his discovery among the folios of Manuscript 71, thus signaling its role in the discovery process (Fredette 1972, Camerota 1992). This is the De Motu Accelerato fragment we have listed above, which Favaro correctly judged was composed in 1609, at the end of Galileo's early period, and so he published it in the second volume of the National Edition.
CONTINUATION AT PADUA, AND BEYOND
We move now to the next period of experimental and observational activity, this time at Padua and extending to 1610, at the end of which Galileo made his important discoveries with the telescope. In his teaching at Padua, he continued to use his treatise on the sphere, the Trattato della Sfera, also called the Cosmografia, which is significant for its showing how the demonstrative regress works in astronomy.
The simplest context is Galileo's explanation of the aspects and phases of the Moon and the ways these vary with the Moon's synoptic and sidereal periods (EN2:251–3). These phenomena depend only on relative positions within the Earth-Moon and Earth-Sun systems and do not require commitment to either geocentrism or heliocentrism, being equally well explained in either. Basic to the explanation is the conviction that these aspects and phases are effects (effetti) for which it is possible to assign the cause (la causa, EN2:250). Among the causes Galileo enumerates are that the Moon is spherical in shape, that it is not luminous by nature but receives its light from the Sun, and that the orientation of the two with respect to Earth is what causes the various aspects and the places and times of their appearances.
The argument is typically that of a scientia media and follows closely the paradigm provided by Aristotle in Posterior Analytics (Bk. I, Ch. 13) to show that the Moon is a sphere. It involves only one supposition, that light travels in straight lines, and this is what governs the intermediate stage of the regress. It allows one to use projective geometry to establish the convertibility condition, namely that only external illumination falling on a shape that is spherical will cause the Moon to exhibit the phases it does at precise positions and times observable from the Earth. The reasoning is summarized in regress form in Wallace (1992a:194–7).
Galileo's first attempt at a science of mechanics followed soon after his De Motu Antiquiora and built on the progress he had made at Pisa in the study of the inclined plane. The earliest version of his mechanics, based on what was thought at the time to be Aristotle's Quaestiones mechanicae, survives in two early versions, one probably dating from 1593 and the other certainly from 1594.
The main point is to show how all the primary machines – the lever, the capstan, the pulley, the screw, and the wedge – can be reduced to the simplest of them – the lever – and this itself can be reduced to the balance. In it, Galileo uses a concept he had already mentioned in the De Motu, namely, that of a minimum force, or a force smaller than any given force, to prove that a force of 200 will move a weight of 2,000 if applied with a leverage of 10 times the distance of application. If one considers, he says, that any minimal moment added to the counterbalancing force will produce a displacement, by not taking account of this “insensible moment,” one can say that motion will be produced by the same force as sustains the weight at rest.
The use here of what is clearly a supposition, one permitting the mathematical physicist to neglect insensible forces in his calculations, opened the door for him to treat both dynamic and static cases by the same mathematical principles. Thus, by this early date, he had begun to bridge the gap between Archimedean statics and the Aristotelian dynamical tradition of De ponderibus recently revived by Tartaglia, and he was moving in the direction of a unified science of statics and dynamics.
Galileo's more fully developed treatise on mechanics, written in Italian and titled Le meccaniche in some manuscripts, was completed by 1600 or 1602 and was modeled on Tartaglia's works. In it, Galileo attacked the difficult problem of the force required to move an object up an inclined plane. By invoking his principle that the force required to move a weight need only insensibilmente exceed the force require to sustain it, he was able to solve not only the problem of the inclined plane but that of the wedge and the screw also (EN2:183–4, Drabkin and Drake 1960:175–7). Again, this line of reasoning made use of the demonstrative regress, invoking in the intermediate stage suppositions of the type described above (Wallace 1992a:262–3).
Shortly after this, Galileo engaged in an extensive period of experimentation that is recorded in the folios uncovered by Drake and that enabled him finally to obtain empirical confirmation of his calculations for motion down an incline and in free fall. This required him to relinquish the Archimedean-Aristotelian ratios for velocity versus specific weight he had been employing at Pisa and, ultimately, by 1609, to arrive at the conclusion that in motions that are naturally accelerated the velocity increases uniformly with time of fall. The major steps in this program, which involved the so-called table top experiments (completely unknown before Drake's discoveries) employed demonstrations that can be arranged in the format of the regressus, as will be documented below.
Momentous as these investigations were, they were quickly surpassed by Galileo's discoveries with the telescope in late 1609 and 1610. Fortunately, the paradigm he had used for demonstrating the aspects and phases of the Moon was at hand for explaining the novelties he had revealed. Others before him had constructed telescopes, and some had even looked at the heavens with them, but none would formulate the “necessary demonstrations” Galileo would propose on the basis of his observations.
Within months, he established that there were mountains on the Moon, that Jupiter was carrying along four satellites in its twelve-year passage across the heavens, and, later, that Venus exhibited phases – a sure indication it was orbiting the Sun and not the Earth. So spectacular were these results, all of which could be shown to be demonstrations through the use of the regressus, that they changed Galileo's life in a most profound way. His “early period” was completed and he set out on the fateful course of convincing his fellow scientists (and the Church) that the Copernican system actually portrayed the true construction of the world. This would not only occupy his “middle period,” but it would determine the tragic course of his “later period” as well.
When we add these Paduan accomplishments to their Pisan beginnings, however, we can see how fruitful these times leading to Galileo's forty-fifth year had been. His spectacular results in astronomy, no more important than his laying the foundations of modern mechanics, as yet unknown to the world, had behind them the strong logical base contained in Manuscript 27, one of his first Pisan manuscripts. Precisely how he accomplished this is documented in Wallace (1984a, 1992a), the first providing textual selections that connect Manuscript 27 with the various discoveries, and the second showing how all employ a search for causes using a method of resolution and composition that fits into the general schema for the demonstrative regress. The results are tabulated below, with the subjects of proof indicated in the center, the page numbers in 1984a on the left, and those in 1992a on the right:
| Text (1984a) | Subject of proof | Manuscript 27(1992a) |
| 230 | 1 Fall in Various Media (EN1) | 242 |
| 233 | 2 Fall and Specific Weight (EN1) | 248 |
| 236 | 3 Speed in Different Media (EN1) | 250 |
| 239 | 4 Motion on Inclined Planes (EN1) | 253 |
| 235 | 5 Speed Increase in Fall (EN1) | 256 |
| 248 | 7 Aspects and Phases of | 195 |
| the Moon (EN2) | ||
| — | 8 Mountains on the Moon (EN3.1) | 199 |
| — | 9 Satellites of Jupiter (EN3.1) | 202 |
| — | 10 Phases of Venus (EN10) | 202 |
Of these, the first five, all from the De Motu Antiquiora, were not strictly demonstrations, although Galileo originally proposed them as such. It surely is to his credit that he ultimately recognized this and withheld them from publication, undoubtedly for empirical reasons, because of their failure to meet the limited pericula he used to test them at Pisa. Of the remainder, and particularly the last four, he never doubted their apodictic character.
There remains now a final consideration, namely, whether Galileo's use of demonstrative techniques terminated in 1610 at the end of his early period or whether it extended into the other periods as well. There are excellent reasons to prefer the second alternative, especially when one sees Galileo as amending the Manuscript 27 doctrine to make of it a logic of discovery that can employ probable arguments as well as demonstrative proofs.
The first indication we see of this is his tentative proof for the Earth's motion based on the ebb and flow of the tides, which he presented to his friend Cardinal Alessandro Orsini on January 8, 1616 (EN5:377–95). There, Galileo speculates that “the cause of the tides could reside in some motion of the basins containing the seawater,” thus focusing on the motion of the terrestrial globe as “more probable” than any other cause previously assigned (EN5:381). In concluding his proof, Galileo notes that he is able to harmonize the Earth's motion with the tides, “taking the former as the cause of the latter, and the latter as a sign of and an argument for the former” (EN5:393). This is an elegant way of reformulating the first and last stages of the demonstrative regress, while leaving the intermediate stage open for probable arguments as well as for those that would establish conclusive proof.
Using this enlarged understanding of the regressus, it is possible to analyze the key proofs Galileo worked out in his middle and later periods. These are presented below in a format similar to that used above for the early period:
| Text (1984a) | Subject of proof | Manuscript 27 (1992a) |
| 284 | 1 True Cause of Flotations (EN4) | 277 |
| 288 | 2 Nature of Sunspots (EN5) | 209 |
| 294 | 3 Early Tidal Argument (EN5) | 212 |
| 300 | 4 Unity of the Universe (EN5) | 220 |
| 303 | 5 Earth's Daily Rotation (EN5) | 223 |
| 306 | 6 Earth's Annual Revolution (EN5) | 225 |
| 308 | 7 Later Tidal Argument (EN5) | 229 |
| 315 | 8 True Cause of Cohesion (EN8) | 281 |
| 320 | 9 Breaking Strength of a Beam (EN8) | 283 |
| 322 | 10 Naturally Accelerated Motion (EN8) | 287 |
| 330 | 11 Motion of Projectiles (EN8) | 292 |
The first of these, as well as the eighth to eleventh, Galileo seems to have proposed as demonstrative. The rest he proposed only as probable arguments, surely because of the Church's prohibition against Copernican teaching, but also because he may have recognized some of their logical limitations. By the time he came to the last two, however, there can be no doubt that he made the transition from scientia media to nuova scienza (Olivieri 1995) and it is for this we celebrate him as the Father of Modern Science.
Only sixteen months before his death, on September 14, 1640, Galileo wrote a letter to Fortunio Leceti, explaining what it meant to be a true follower of Aristotle and stating that, in matters of logic, he had been an Aristotelian all his life (EN18:248). In light of his many invectives against the Peripatetics of his day, this statement by Galileo is puzzling and has given rise to many interpretations, some calling into question his honesty and sincerity.
When the letter is read in light of the materials just presented, however, it is a simple matter to absolve Galileo of charges of this type. In effect, he does not commit himself to any of Aristotle's conclusions in the physical sciences but states instead that he has consistently followed Aristotle's logical methodology in his own scientific work.
This is what enabled him, he says, to reason well and to deduce necessary conclusions from his premises; coupled with what he has learned from pure mathematicians, it has given him skill in demonstration and the ability to avoid mistakes in argumentation. He concludes on the note that, if one takes reliance on Aristotle's logical canons to be the sign of a Peripatetic, he can rightfully be called a Peripatetic himself.
When the letter to Liceti is read in light of what is available in the National Edition alone, of course, the background required for its understanding is missing. But then the true problem posed by the letter becomes quite clear: It is not Galileo's identifying himself as an Aristotelian but rather how he could possess sufficient knowledge of Aristotelian logic to be able to employ it in the way he claims. The problem is insoluble when the manuscripts of his early period, and particularly his Manuscript 27, are overlooked or are not taken into account. Such omission is the parvus error in initio to which I referred at the outset of this essay. Only when it is rectified do we gain an understanding of the man within his full historical context.
NOTES
1 Le Opere di Galileo Galilei, ed. Antonio Favaro, 20 vols, in 21, Florence: G. Barbera Editrice, 1890–1909, henceforth cited as EN: Vol. No., page no(s).
2 Following the lead of W. R. Shea (1972), the chronology of Galileo's life is now commonly divided into three periods – the early period, from his birth in 1564 to 1610; the middle period, from 1610 to 1632; and the later period, from 1632 to his death in 1642.
3 The pioneering study of the sources of Galileo's natural philosophy was that of Alistair Crombie (1975), who first discerned its connection with teachings of the Jesuits. He followed that essay with a study of the place of mathematics and Platonism in Jesuit educational policy (1977) and then with a fuller examination of Jesuit ideas of science and of nature that are reflected in Galileo's writings, which he coauthored with his student Adriano Carugo (1983). For a detailed account of my early investigations and their relationships to the work of Crombie and Carugo, see Wallace (1984b:xii–xiii, 1986b, 1986c, and 1992b:xi–xv).
4 Here, Hooper reported early results of a project at the Instituto Nazionale di Fisica Nucleare in Florence, in which accurate physical analyses are being made of the chemical composition of Galileo's inks and papers using nondestructive proton induced x-ray emissions (acronym PIXE).
5 Favaro dated the compositions of Manuscript 46 at 1584, on the basis of the internal evidence he gathered from that chronology (EN1:27), where he added the number of years Galileo gives “from the birth of Christ to the destruction of Jerusalem, 74; from then up to the present time, 1510,” to get the result 1584. Apparently, Favaro was unaware that exegetes in Galileo's time had already established that Christ was born in the year 4 B.C., and thus he should have obtained the result 1580. What he also could have done was add A.D. 70 (a well-established date among historians for the destruction of Jerusalem) to 1510, and this would have given him 1580 directly. If Galileo used Menu's notes for the chronology, this would serve to explain the sum of 1580 in his appropriation. Part of Favaro's reason for defending his erroneous 1584 dating of Manuscript 46 seems to have been his opposition to Pierre Duhem, who used Galileo's mention of the Doctores Parisienses in that manuscript to connect him with medieval authors who were his so-called Parisian precursors. For details of the dispute between Favaro and Duhem, see Wallace (1978) which is enlarged and reprinted in Wallace (1981).
6 Works on the authors and subjects mentioned and on which I have drawn in what follows include Camerota (1989), DePace (1990, 1992), Lennox (1986), Machamer (1978), Manno (1987), Masotti (1976), and Schmitt (1981).
7 The expression occurs in Zabarella's Opera logica, Cologne: Zetzner, 1597, 486. For details of the connection between Galileo and Zabarella, see Wallace (1988), reprinted in Wallace (1991).