The Problems of Christoph Grienberger (1564-1636)


Michael John Gorman


from The New Science and Jesuit Science: Seventeenth Century Perspectives, ed. Mordechai Feingold, Dordrecht: Kluwer, 2003 (Archimedes vol. 6), pp. 1-120



CENODOXUS: Wakeful and easeless are

my days and nights, consumed in careful studies

SELF-LOVE: But time cannot consume what all men's praises render immortal.

CENODOXUS: Yet how easily such honours can be gained.

My life's whole purpose is therefore this: by glorious deeds

to ensure that I and all my glory never perish. This die I've cast.


Jakob Bidermann, Cenodoxus, I. iii, transl. D. G. Dyer and C. Longrigg, Edinburgh, 1975, p. 47



In 1609 Jakob Bidermann's "Comico-Tragedy" Cenodoxus, or the Doctor of Paris was performed on the stage of the Jesuit college in Munich. The play, first produced seven years earlier in Augsburg, deals with the story of a Parisian scholar who, despite maintaining an ascetic public demeanour, privately prided himself on his unparalleled erudition. In Bidermann's graphic account, based loosely around the legend of St Bruno, the eleventh-century founder of the Carthusian order, Cenodoxus, recast as a Renaissance humanist, is finally condemned to eternal torment for the sin of kenodoxia or vaingloriousness[1]. The Munich production of the play provoked a memorable reaction, described in the preface to the first collected edition of Bidermann's dramatic works.[2] At first the audience laughed at the opening comic scenes, but as the play progressed the mood gradually changed to one of astonishment and horror as the spectators realised the enormity of the sins portrayed and became aware of the power of hell. By the end of the play, the terrified members of the audience were contemplating their own sins in stunned silence. The impact of the play was immediate. Fourteen members of the audience went into retreat to perform the Spiritual Exercises of St Ignatius, just as in the play Bruno retreated into the wilderness to found his monastery and lead a life of spiritual contemplation. The actor who played Cenodoxus himself then joined a Jesuit novitiate, and passed the rest of his life in the religious modesty of the Society of Jesus.[3]


It is difficult to find a more poignant example of the way the Jesuit order in general, and the Jesuit spiritual teachings embodied in the Spiritual Exercises in particular, were perceived amongst the ruling elites of early modern Europe as constituting a powerful antidote to pride, superbia, or vaingloriousness. Ignatius himself, following Gregory the Great and Thomas Aquinas, frequently emphasized the interdependence of modesty and obedience in his writings, arguing that disobedience, the ultimate enemy to the social fabric of the Jesuit order that he had founded, was an inevitable consequence of vaingloriousness.[4] The Rules of the Society of Jesus, first published in 1582 as a guide to the different functions and modes of social behaviour of Jesuits, contained a series of Rules on Modesty due to Ignatius. These rules, originally composed around 1555,[5] and well entrenched by the 1580s, really amounted to rules of bodily deportment. Members of the Society, in order to display modesty, humility and religious maturity, had to keep their heads pointing straight forward, with their necks inclined slightly downward. Eyes were to be kept down, especially when talking to others, wrinkling of the nose was to be avoided, walking more quickly than necessary was discouraged, and all gestures were to display humility and move the observer to devotion.[6] Speech too was to display modesty and edification.[7] Biographical writings about eminent Jesuits, taking their lead from Ribadeneyra's widely read biography of Ignatius[8], laid great emphasis on the qualities of modesty, humility and self-abnegation advocated by the Jesuit Constitutions and Rules.


Deportment and Scientific Practice


Before the development of societies and institutions exclusively devoted to scientific pursuits in Europe from the 1660s onwards, and the subsequent emergence of codified and tacit forms of professional ethics specific to such institutions, natural philosophers and mathematicians attempting to make novel claims about the natural world were obliged to look outside science for models of acceptable conduct in the prosecution and presentation of their work. Rather than being obliged to acquiesce into a single model of personhood, scientific practitioners were free to make their own creative synthesis from a smorgasbord of religious and  courtly models, to name just two of the more obvious options. Steven Shapin has emphasised the extent to which Robert Boyle drew on the social mores of the English gentleman in order to provide a social basis for credibility in the reporting of scientific observations. In a similar vein, Mario Biagioli has argued that Galileo fashioned himself as a natural philosopher by successfully deploying the vocabulary of Medicean dynastic emblematics.[9]


Whereas the court environment in which Galileo worked for at least part of his life promoted visibility and authorship -- the attachments of texts, inventions and observations to a proper-name[10] --, the cultural values promoted in the Jesuit order generally emphasised invisibility and self-abnegation, and denied 'authorship' to all but a relative few, sometimes denoted by the term scriptor in the catalogues of the Jesuit houses. Individual glory was, in general, to be shirked in favour of the collective glory of the order. In disciplining their adversaries in theological and philosophical disputes, Jesuit authors made frequent use of terms like jactantia and jactatores, using the inappropriate deportment of opponents to discredit their arguments. The playwright Jakob Bidermann himself, after the successes of his theatrical castigations of superbia, was brought to Rome to act as General Revisor for Jesuit literary works, where he had the opportunity to police the humility of a large number of learned Jesuit writers in person for almost twenty years.[11]


Admittedly many Jesuit mathematicians also worked in a courtly environment. Galileo's opponent in the dispute over sunspots, Christoph Scheiner, is one example.[12] Nonetheless, careers such as Scheiner's manifest the deep tensions between the type of deportment suitable to a court and the ready-made, modest "personality" provided by the Jesuit prescriptive literature and inculcated through the practice of the Spiritual Exercises.[13] Precisely for this reason I would like to look more closely in the present article at a Jesuit mathematician who worked almost exclusively within Jesuit-controlled institutions. I believe that the strategies of self-abnegation[14], deployed by the Jesuit mathematician Christoph Grienberger, who availed himself of every opportunity to remove his name from texts written with his pen and optical and astronomical instruments designed by him and built with his own hands, can reveal much about what it was to be both a Jesuit and a skilled mathematical practitioner in the early seventeenth century. At the outset, this may appear to be a task of some difficulty, as the 'person' that we would like to understand is a person who manifests himself by disappearing - erasing his tracks in the history of science with remarkable dexterity and even managing to avoid an entry in the Dictionary of Scientific Biography. However, through the indiscretions of some of his Jesuit colleagues, through his own epistolary confessions to his senior mathematical colleague, Christoph Clavius, and through the existence of a significant number of anonymous manuscripts that I attribute to Grienberger, some of which are published in the appendix, the public and private selves of this elusive individual begin to emerge. Where Galileo found a source of legitimation for certain types of mathematical practice in the colourful world of the Medici court in Florence, his exact contemporary Grienberger found his Archimedean point for the upward leverage of the status of mathematics deep within the complex bureaucratic structure of the Jesuit order.


Who was Christoph Grienberger?


Bamberga, Bamberger, Banbergiera, Gamberger, Ghambergier, Granberger, Panberger - the list of names used by his contemporaries to refer to Christoph Grienberger goes on and on.[15] Print has a tendency to fix the orthography of proper names, and Grienberger's name was one that, with the exception of a slim book of star-charts and a set of trigonometric tables[16], rarely appeared in print during his life. In approaching the question "Who was Christoph Grienberger?", I do not aim to provide anything like a biography of the sort that Charles Coulston Gillespie might have chosen to include in the DSB[17]. Instead, I would like to look at how people wrote about Grienberger and how Grienberger wrote about himself. I would like to examine Grienberger's own production in terms of texts and instruments, and his moderation of the productions of others, in his work as a revisor of mathematical works written by Jesuits and in his strategies of engagement in epistolary relationships with natural philosophers and mathematicians outside the Jesuit order.[18]


Christoph Grienberger died on 11 March 1636. Before his death he was in charge of the technical censorship of all mathematical works written by Jesuit authors. Often Grienberger would send detailed calculations and corrections to an author, demanding that they be incorporated before allowing the work to be published. In some cases, as in Gregorius a St. Vincent's attempt to square the circle, Grienberger advised the Jesuit General Muzio Vitelleschi to refuse publication altogether, on the grounds that the errors contained in the proofs would damage the reputation of the Society of Jesus.[19] When Grienberger died, he clearly lost control over the mathematical publications of his fellow Jesuit mathematicians. Perhaps more interestingly, he lost control over his own authorial presence, or rather, absence. A case in point is Mario Bettini's Apiaria, an encyclopedic collection of mathematical curiosities.[20] The censorship of the book took place in the mid-1630s, but publication was held up, possibly through a lack of a suitable patron.[21] The book finally appeared in 1645, and unlike other works, which merely incorporated Grienberger's corrections unacknowledged, Bettini takes great pains to highlight the contributions of the late Revisor, whom he hails at the outset of his book as having the stature of an "Archimedes of our time", combining "most ingenious practices and wonderful machinery" with "very acute theories".[22] Later in the work, Bettini confessed that "I have benefited, my Reader, from the mind and industry of the very learned and exceedingly modest man, Grienberger, who, while he would have discovered many marvellous things by himself, preferred to make himself serviceable to other people's inventions and other people's praises".[23] In his Aerarium, published three years later, Bettini included a Scholion Parergicon eulogising Grienberger, and continuing to compare him to Archimedes, adding that "Grienberger has no greater enemy than his own modesty, by which it has come to pass that his ingenious inventions have been neglected, and he will be consigned to oblivion".[24] Bettini added, echoing the Apiaria, that "It was a remarkable characteristic of [Grienberger] that, following the example of Archimedes, he combined most acute theories with extraordinary practices"[25], and his claims for Grienberger's achievements in designing instruments and machines are closely echoed by other contemporary mathematical authors.[26]




Instruments and Invisibility

And yet Archimedes possessed such a lofty spirit, so profound a soul, and such a wealth of scientific theory, that although his inventions had won for him a name and fame for superhuman sagacity, he would not consent to leave behind him any treatise on this subject.

Plutarch, Life of Marcellus, XVII.3-4


When Ernst von Wittelsbach, Prince-Archbishop of Cologne, sought a telescope to replace the instrument sent to him by Galileo with which Kepler had first observed the Medicean stars, it was to Grienberger that he turned. The Galileian instrument, Wittelsbach elaborated, showed stars to be triangular or four-pointed, depending on how it was oriented, and also distorted terrestrial objects viewed from a distance. Grienberger, Wittelsbach presumed, could provide him with a more accurate instrument. As Mario Biagioli points out, shortly after the publication of the Sidereus Nuncius Grienberger possessed a more powerful telescope than anything Galileo had constructed.[27]


In Bettini's Apiaria, we see Grienberger's instrumental proficiency forcibly exposed to the public gaze. In composing his corrections to the Apiaria, in his role as Revisor, Grienberger had noticed that a scenographic instrument described by Bettini could be improved in a way that would make it easier to use and more accurate. The instrument (fig. 1), rather similar to Christoph Scheiner's pantograph (fig. 3),[28] allowed the user to make accurate drawings from life with little effort and less skill. Grienberger wrote to Bettini in 1635 to describe his modifications:


On experimenting [tentando], I discovered that Your Reverence's instrument might be made more easily. I removed the directing rod that moved transversely, until now the part of the instrument that appeared to obstruct its operation. I added cursores in my own way, as you will see below, and completed the job by means of four small beams, making a parallelogram. I took care that the line of sight [radius visualis] and the line of writing [radius scriptorius] would both depart from one of its points, and that both points would exist in a single straight line, namely the axis around which the parallellogram will be rotated continuously.[29]


In addition to providing a lengthy description of the device, arguably at least as different from Bettini's own rude contraption as Scheiner's pantograph, Grienberger sent Bettini two copper-plate engravings[30] for inclusion in his book, one showing a schematised form of the instrument accompanied by Grienberger's trademark cursores, and the other showing the instrument manipulated by the eyes and hand of an invisible Grienberger (see figs. 1 and 2). Grienberger's pathological modesty is at work here again. Ever keen to divest himself of any vestige of authorship, he writes to Bettini of the modified scenographic instrument that


I could have sent this Bettinian Instrument to the Emperor recently, but I did not wish to do this without the permission of Your Reverence. I would rather receive that permission which Your Reverence would bestow if [the instrument] were first published in the Apiaria.[31]


Another work in which Grienberger's instrumental manipulations in the Collegio Romano lie tantalisingly in the shadows is Christoph Scheiner's voluminous 1630 book on sunspots, the Rosa Ursina.[32] The dichotomy between court and Curia that characterised the work of Scheiner and of many other Jesuit astronomers is eloquently expressed by Daniel Widman's etching of the different techniques for observing sunspots (fig. 4). At the top we see Scheiner in the company of various members of the Orsini household, observing the sun on an ersatz viewing platform, complete with obelisks, on the banks of the Lago di Bracciano, close to the Orsini Castle, which can be seen in the left background. At the bottom we see Scheiner in duplicate, compasses still in hand, making observations from his room in the Jesuit Domus Professa in Rome.[33] The instrument used by Scheiner in the lower vignette is the telescope that he claimed to have used to discover sunspots before Galileo observed them in 1611, and suffered from the disadvantage of being difficult to move from a fixed position, thus making protracted observations over any length of time a very awkward business.


To cope with this problem, Grienberger developed a "telescopic heliotrope" or "heliotropic telescope", an instrument (fig. 5) which avoided the difficulties of the other device by being simultaneously mounted on two axes around which it could rotate freely to follow the trajectory of the sun, like the sunflower from which it took its name. Again, Grienberger seems to have been responsible for the engraving of this device published by Scheiner. Again, Grienberger as machine-operator is invisible, in marked contrast to the multiple representations of Scheiner in the previous figure. Scheiner, ever one to emphasise the collective nature of the scientific enterprise,[34] asked Grienberger to provide him with a description of his instrument, but he refused, to Scheiner's surprise:


And thus this machine is not entangled in as many difficulties as the other one; and additionally [Grienberger's] machine is more convenient, and carried out the work more quickly than that one. For this reason, it will be worthwhile to write a short explanation of its nature, since the Architect of the Machine himself seemed to be unwilling to furnish this: despite having later edified many things with his demonstrations, and hastened and urged me to finish the work, [as well as having] helped me most opportunely with similar services that were virtually necessary to me in such a short space of time.[35]


Undoubtedly the polemic between Scheiner and Galileo was part of the reason for Grienberger's attempt to distance himself from the text of Scheiner's work. The rift between Galileo and the Jesuit mathematicians of the Collegio Romano that followed Galileo's attacks on Orazio Grassi's public disputation on the comets of 1618 was a source of much distress to Grienberger,[36] who could not see any reason for this turnaround.[37] In fact, Galileo's gesture seems to have been the result of a cynical, and rather unsuccessful attempt to cultivate the patronage of Archduke Leopold of Austria, also a patron of Scheiner.[38] Nonetheless, Grienberger's participation in the Rosa Ursina, performing observations (not with Scheiner in the Domus Professa, but in the Collegio Romano only a few hundred yards away – see fig. 7) and refining observational instruments is characteristic of the way he chose to present himself in other works. To understand the development of this pattern of effacement of claims to intellectual ownership, I would like to turn to Grienberger's earlier career in the Jesuit order.


Private Lessons 


On 15 September 1590, Grienberger, then mathematics teacher and student of theology at the Jesuit College in Vienna, wrote the earliest of his surviving letters to Christoph Clavius in Rome. Although Grienberger, who had spent the ten years since he first entered the Jesuit order in Prague and Olmütz,[39] had not yet met Clavius face to face, his letter betrays an unexpected degree of intimacy:


Why should I not love my teacher? And indeed so much mine that he seems almost to be mine alone. Are you not mine, who are so present to me always, that I began immediately to love you and now for almost the four years for which I have known you have hardly ever placed a foot outside my bedroom? [40]

Grienberger is, of course, cohabiting with Clavius's textual body - his commentaries on Euclid's Elements and the Sphere of Sacrobosco as well as other works.[41] Nonetheless, a short time after this letter was sent, along with the demonstratiunculae on spherical trigonometry that Grienberger, like a good pupil, sent to his virtual master,[42] Grienberger was summoned to Rome so that the two mathematicians could really live under the same roof.[43] The pattern was to become relatively common - Giuseppe Biancani and Odo van Maelcote were also brought to Rome to assist Clavius (and to be fashioned as mathematicians in his image) after sending unsolicited solutions to celebrated problems or instruments to the famous professor in Rome,[44] and many others sent demonstrations hopefully.


In 1595 Clavius went to Naples, leaving Grienberger in charge in Rome. Grienberger wrote to Clavius shortly after his departure:


Now the Mathematical Museum has put on new clothes, nor does it cry out for anything other than the speedy return of its master. In the meantime it will have me as a custodian. On Monday next I will give my old [room] to two others[45].


The bedroom was a multifunctional space for the Jesuit mathematician. Generally, the rooms of Jesuits were not provided with keys, but, along with the rooms of the Superiors, the Procurator (responsible for the financial affairs of the College), the room of the senior mathematician of the College formed an exception.[46] The added security of a key meant that the mathematics professor could store valuable mathematical instruments in his domestic space, which was often referred to as a mathematical museum, or musaeum mathematicum.[47] Later, while in Lisbon, Grienberger would tell Clavius of a valuable clock that he had kept for several months in the privacy of his bedroom.[48] As well as constituting a space for the storage and construction of instruments, the mathematician's bedroom was the focus for the studies carried out by the private mathematical academy of the college.[49] Printed books currently being used by the academy, manuscripts of mathematical works and, perhaps most crucially, the letters sent to successive professors of mathematics in the Collegio Romano, were all stored in this space.[50] Whereas the private papers of a Jesuit were generally destroyed after his death unless deemed to be of particular importance,[51] the mathematicians of the college enjoyed the security of a place apart, allowing the correspondence and manuscripts accumulated by successive professors to constitute what Athanasius Kircher and his colleagues were later to use as a private mathematical archive.[52]



Humdrum Mathematical Culture



During Clavius's absence in Naples, Grienberger kept him informed with regular bulletins on the vicissitudes of college life. These allude to his own research, the work of the private mathematical academy under his guidance and the normal mathematics classes of the College. Grienberger's letters are punctuated by descriptions of humorous events, such as Fabricio Mordente's pompous display of his beautiful, but imprecise, geometrical compasses to the mathematicians of the college[53] and a rather excessive number of ponderous jokes about Clavius's penchant for Neapolitan pastries.[54]


On 12 January 1596 Grienberger told Clavius of a possible addition to his other duties:


I fear that perhaps I may have to teach privately to a certain Count whose name escapes me. But I hear that he has studied little else, and it appears to me that he is rather young, not to say a boy, so I hope for little profit, even on my side, as I do not know how to deal with that type of person correctly.[55]


Shortly afterwards, Grienberger's fears came true, making unfair demands on both his time and his character:


I do not have much free time, apart from in the mornings. For after lunch all is taken up by the class and the academies, of which there is the domestic one, as you know, and another at the Gate, to which Count St. George, as he's known, comes, a boy with a reasonable mind, together with a certain other [boy] of around the same age, called Orazio, from Perugia, also of good family. Both of these asked the Fr. General if I could lecture them privately. Your Rev. will wonder that I am suitable for this task, as it should really require not a German but a Tuscan, who would be more affable than me. But seeing that it has pleased them thus I hope that they will have patience with me.[56]


Grienberger, unlike his more famous Tuscan contemporary Galileo,was clearly no courtier, and elsewhere diagnosed himself as having a particularly frigid nature, when speculating that Clavius might be prolonging his stay in Naples because Grienberger was occupying his bedroom:


But is [Clavius] perhaps excluded from his bedroom? On the contrary, it is so ready that it would invite him him there freely even against his will. For I will easily find another one that is equally cold, unless perhaps all rooms are cold that are occupied by exceedingly cold [frigidissimus] me.[57]


Despite pandering on occasions to a cardinal's desire for a sundial[58], or to the wishes of young aristocrats to have private tuition, Grienberger's concerns lay more with the well-being of his young disciples in the mathematical academy, bound to him by a common love of mathematics, than with courtly aspirations.


Unless the Superiors change their plans, I believe that I will be freed from the ordinary domestic academy. [...] The other private academy is creeping forward slowly [in the study] of Clocks. Out of the three pupils, one (Janos Nagy, of course) as he was trying impetuosly to go up two steps at a time four or five days ago, almost suffocated on his catharr. However, Nature won, and made herself a way forcibly, but not without blood, as together with the phlegm he vomited up no small quantity of blood.[59]


The impetuous mathematician clearly pays a price. Grienberger went to visit Nagy in the college infirmary, where he found two other indisposed mathematical practitioners:


As I was visiting Nagy today, I found Fr. Villalpando and Fr. Mario (the one who saluted you in Naples when you were in your sedan chair) in the same place [i.e. the infirmary]. Reading your letter they rejoiced to hear of your good health, and indeed we sensed some unknown fragrance from your letter, and some unknown pleasant odour, but without a taste.[60]


Although the convalescent mathematicians might have detected the smell of the Neapolitan sweetmeats that Clavius hoarded in his bedroom in Naples, imbibed by his writing paper, Grienberger is suggesting with lumbering jocularity that the elderly mathematician had kept the taste of the pastries for himself.[61]




Public mathematics in the Collegio Romano: The Problemata



Shortly after Clavius left Rome for Naples, Grienberger castigated him for suggesting to the Rector that Grienberger might give a public oration to mark the commencement of studies in the Collegio:


I do not know what Your Reverence expected when you promised our Rev. Fr. Rector that I would give an oration [Praefatio], for I happened to hear this from him at least twice, in the presence of others. For you know extremely well that, to me, that has always seemed an extremely difficult task. Certainly, if they expected an oration they did not get one, but instead I explained the dimension of the circle from Archimedes so slowly that it could not be completed in half an hour.[62]


Grienberger did not enjoy speaking in public. No great surprise here, but what might appear initially to represent something of a paradox is a statement made in Mario Bettini's Aerarium, when concluding his eulogy of Grienberger and "correcting" Giuseppe Biancani's entry on Grienberger in his Chronology of Illustrious Mathematicians, appended to his 1615 Aristotelis loca mathematica.[63] Listing Grienberger's extant manuscript works, Bettini writes:


There are many optical and mechanical [machinaria] experiments present in our Roman College that were once exhibited to the eyes and admiration of princely men visiting that place.[64]


To understand how Grienberger's modesty and distaste for public speaking might be reconciled with his authorship of a large number of experimental problems presented publicly to the applause of princes visiting the Collegio Romano, I would like to consider the emergence of a highly specific genre - the Problemata.[65]


As discussed above, the 1586 first edition of the Jesuit Ratio Studiorum had proposed that Clavius should give private lessons in mathematics to eight or ten Jesuits, selected from all the different provinces of the order, in order to furnish the provinces with mathematics teachers.[66] The next published edition of the Ratio  (1591) suggested that in addition to this private academia,


once or twice a month one of the students should recount [enarret] an illustrious [illustre] mathematical problem in a large gathering of philosophers and theologians, having first been instructed [edoctus], as is proper, by the master.[67]


Some of the surviving mathematical problems presented in the Collegio Romano are published in the appendices to the present article. Although these Problemata are generally anonymous, a significant amount of evidence in addition to Bettini's attribution, discussed in the notes accompanying each problem, ranging from references in letters, literary style, internal evidence and Grienberger's distinctive handwriting, points to Grienberger as the author of all of these Problemata, which range in date from 1591, the year of Grienberger's arrival in Rome, to 1614. As a ceremonial form of culture, such presentations clearly had much in common with the extravagant public defenses of philosophical theses made by aristocratic students in the Collegio and so disparaged by Federico Cesi. In the thesis defenses at the Collegio, studied in detail by Louise Rice,[68] the script read by the student was generally written by one of the professors, although if the theses (or the odes composed for the occasion) were printed, they were accompanied by the student's name. The same practice seems to have been adopted for the mathematical Problemata, as suggested by the "instruction" by the master advocated by the Ratio Studiorum. Publication was a rarer matter in the mathematical presentations, but when it happened, it followed the same patterns. The Roman publishers Zannetti and Mascardi, favourites for such philosophical "vanity publications", were also used for the mathematical problems.[69]



Mixed mathematical themes in the Problemata


It should perhaps be stressed that the individual modesty that I ascribe to the behavioural patterns of Christoph Grienberger was utterly different from the prescriptions of cognitive humility with regard to the mysteries of the natural world that characterised much theological discourse of the late sixteenth century discussed by Carlo Ginzburg.[70] Indeed, Grienberger's refusal to accept authorial dignities, and his confessions of bodily weakness[71] coexisted with the flow from his pen of a series of claims for the exalted powers and cognitive capacities of mathematicians with respect to the natural world. Such a combination of individual modesty with elevated claims for the power of a collectivity is a feature that can be found elsewhere in Jesuit culture, perhaps reaching its zenith the 1640 Image of the First Century of the Society of Jesus published to mark the centenary of the order.[72] As Marc Fumaroli has shown, the anonymous Jesuit compilers of this work excused its rather immodest claims for the achievements of the Society by attributing these achievements indirectly to Jesus, in whose hands the Society that took his name was merely a passive instrument. This relationship was captured emblematically by a device in which the Society of Jesus was the moon, reflecting the light of the Sun, representing Christ[73]. Another emblem in the same book reinforces the idea of the Society of Jesus as a passive, mechanical device, manipulated by Divine Love to raise the earth towards heaven by means of conversion (fig. 7). The device used is similar to one which forms the topic for one of Grienberger's most spectacular mathematical Problemata, dating from 1603 (fig. 8).[74] The problem in question, later plagiarized unashamedly by Gaspar Schott (fig. 9),[75] provides a graphic example of the enormous power over nature which Grienberger ascribed to the collectivity of mathematical practitioners.


Grienberger's speaker intends to demonstrate to his audience that "by means of no more than 24  wheels with toothed axes, the Earth's globe, even if it were made entirely of gold, could be driven away from the centre [of the universe], by the force of only one Talent".[76] The demonstration of this highly Archimedean claim is preceded by a long passage extolling the virtues of mathematics that is anything but modest.

"The boldness of Mathematicians," Grienberger begins, "has always been great, as has their power, Most Religious Fathers and other most honourable members of the audience; and they possess so much spirit in a small number of people, that there is nothing in the whole universe either cloaked in darkness or buried in difficulties that has been able to escape their ingenuity and that has not been investigated with their machines”.[77] Although nobody could doubt that the motions of the heavens had been translated into the laws of mathematics [leges Mathematicorum], someone might still query the dominion of mathematicians over the elementary world. However, "the elements themselves", Grienberger continues, "love to be governed by mathematics as much as they love their own dignities and powers, and prefer to be ornamented by mathematicians than to be reduced to almost nothing by natural philosophers".[78] The Naturales dress the elements poorly, in the different qualities of heat, cold, wetness and dryness, and imprison them in concentric spheres.

Why should [the elements] not be miserable, then, being so poorly dressed, confined in prisons and constrained to serve people that treat them so badly. They dig into the earth with ploughs, and utterly disembowel it even to wrench out a handful of gold. They make water wash all the filthiest people; condemn air to the mills and grindstones, and fire to the furnaces. There is no service that is so vile that [the elements] are not subjected to it [...] It should not seem strange, then, if the elements would happily resort to the Mathematicians, who care for their dignity, and whose works often free them from prison, and bring them into the gardens and palaces of kings.[79]


The elements are happier under the dominion (imperia) of mathematicians than that of physicists, or natural philosophers. As the passage cited shows, in Grienberger's text, the social and cognitive status of the mathematical disciplines are inextricably entangled. Archimedes’ reputed military exploits at the siege of Syracuse with the aid of giant burning mirrors provide Grienberger with a vivid demonstration of the quasi-Promethean ability of mathematicians to steal Fire from heaven. Rather than invoking the astrological assistance of Jupiter, Archimedes wrought destruction on the Roman fleet by sheer mastery of the science of conics.[80] Moving on to the elements of Water and Air, Grienberger suggests that his audience need only read Heron’s De Spiritualibus to see their mathematical manipulation, or look at the device constructed by Giannello Torriano in Toledo to raise the water of the Tagus to the level of the city, the bird-fountains in the gardens of the Villa d’Este at Tivoli, or the hydraulic organ in the gardens of the papal Palazzo del Quirinale in Rome “in which merely by the flow of water, which provides the air and moves the wheels, the sound of an organ is reproduced without anybody playing”.[81] It is the remaining Aristotelian element -- namely Earth -- that Grienberger wishes to “exalt” on this particular occasion, however. As knowledge of the weight of the true terraqueous globe is the prerogative of God alone, Grienberger manufactures a false “geometrical” earth for his spectators, made entirely of gold, which he then attempts to raise by means of a system of 24 wheels at a mutual gearing of 1:10. Grienberger calculates that if the first wheel of this device (see fig. 8), which he borrows from Pappus’ Mathematical Collections, is rotated 40,000 times in one hour [i.e. around 11 times per second] the final wheel, attached to the rope lifting the earth will still take 100 million million years to complete a single revolution.[82] Grienberger suggests that the power for his earth-lifting device might be provided by a man in a treadmill, perhaps taking Archimedes’ reported claim over-literally, but cautions humourously that “I will not weave those ropes, or prescribe the material for the wheels or the place from which the machine shall be suspended: as these are other matters I leave them for others to find”.[83]


The high social status of the mathematical disciplines is a pervasive theme in Grienberger’s other Problemata. When Grienberger first arrived in the Collegio Romano in 1591, he delivered an oration on the mathematical disciplines, much of which was taken up with establishing the nobility of the family made up by the seven mathematical 'sisters': Arithmetic, Geometry, Music, Astronomy, Mechanics, Geodesy, Perspective and Practical Arithmetic (Supputatrix).[84] In the midst of a rather labyrinthine account of the resemblances and quasi-incestuous interrelations between the different 'sisters', he mentions an experiment to show that the study of perspective furnishes the causes of appearances that would otherwise remain a mystery, an experiment that is taken up and performed by the narrator of the following Problema.[85] Despite the iconic status of Archimedes’ performance at Syracuse, mathematical wonders were not limited to the military domain, and Grienberger also describes a trick-picture, possibly an anamorphosis, which he had heard of, in which a forest landscape seen from one position is transformed into a picture of the Emperor with his brother when one looks through a specially constructed hole.[86] As well as being an ancestral mathematical powermonger, Archimedes also provided a source for the credibility of the early-modern mathematical practitioner, and Grienberger makes much of the story (recounted by Proclus) that Hieron, King of Syracuse, ordered that everything Archimedes said should be believed.[87]



Knowing the world through mathematics



Describing the audience of his 1595 oration to mark the beginning of studies to Clavius, Grienberger wrote that


Our Reverend Father General was there, unexpectedly, along with several other unexpected people, and he seemed to apprehend the matter with some delight, as I understood afterwards from Father Pereira, who complained to me because I didn't invite him.[88]


 Pereira was unhappy not to be invited to hear Grienberger's discourse (one of the very few public speeches that he seems to have given in person), and indeed the statements about mathematics made at the beginning of the 1595 oration were little short of anathema to Pereira's perception of the cognitive impotence of the mathematical disciplines, discussed above:


You know that the whole of Philosophy is divided chiefly into three kinds of Sciences: Natural, Mathematical and that divine one that is called Metaphysical. The first one verifies for itself things immersed in matter, that is, abstracted neither from reality nor from reason. The last one assumes as its objects things that are utterly alien to matter. Even if the other two might seem to have all things distributed between them, the middle one, however (which, even by virtue of being the middle one can be said to be more excellent than the others), finds that in [treating] the same matters it ascribes them to itself in such a way that in its object it nevertheless in no way defrauds the other [sciences]. [89]


Although mathematics considered quantity abstracted from any specific material incarnation, such abstraction rendered mathematical truths universal in their application, rather than inapplicable to the natural world as Pereira and others wished to suggest[90]. The theme, later to be central to Giuseppe Biancani's De mathematicarum natura dissertatio (1615)[91] recurs frequently in the other Problemata, which Biancani may have had the opportunity to read during his time as one of the academicians in the Collegio Romano.[92] Mathematical conclusions made about quantity in general were applicable to any physical quantity, including motion; and Grienberger completes his oration with the suggestion that the possibility of incommensurable lengths implied the possibility of real incommensurable motions. The other Problemata put the application of mathematics to natural motions into action, and include one dealing with the motion of a weight attached to a rod, influenced by the medieval calculatores and Tartaglia, and another on the reality of the motions of the heavens described by astronomers.[93] In the latter, Grienberger, furthering an argument put forward in Clavius's Commentary on the Sphere of Sacrobosco, considers the motion of an ant on a moving table, to demonstrate, against the views of Pereira and the other "homocentrists",[94] that a single body, could possess two real motions simultaneously without involving a contradiction. This allowed Grienberger to argue for the reality of the convoluted motions ascribed to the planets by astronomers, although he avoids confronting the vexed question of the Aristotelian distinction between natural and violent motion. As geometry pervades Grienberger's depiction of the natural world, so it inhabits the artificial domain of buildings and other institutions necessary to civic life. In one Problema, Grienberger writes that


Without doubt that Bolognese structure [i.e. the Torre degli Asinelli in Bologna] had an outstanding mathematician as its architect [delineator] by whose vigilance Geometry has come to inhabit that tower.[95]


Another problem was prompted by the disagreement between a group of Spanish sailors and a group of Portuguese sailors who arrived simultaneously in Lisbon, having circumnavigated the world in opposite directions, and unable to decide which day was Sunday,[96] and indeed the Gregorian Calendar, co-authored by Clavius, is an obvious example of an enormous mathematical artifice of a religious and civic nature.



Performing physico-mathematics: the floating-bodies debate



On February 5th 1612, Christoph Grienberger interrupted a letter that he was writing to Galileo to report the news of Clavius's death in "real time":


While I pause from writing for a moment, behold here is someone who rushes to announce that our Clavius is about to be given his Travelling money, which he accepted this very evening at the first hour of the night. So do not be surprised that I break off this letter in a rather untimely fashion - such news does not allow me to linger any longer on these matters. You will learn more from the bearer of the letter, Father Odo van Maelcote, who, by returning to Flanders has shackled me once more to the mathematics classes.[97]


Grienberger's relationship with Galileo had been strengthening steadily since 1611, as the physical powers of his senior colleague Clavius decreased. The Ad benevolum lectorem introducing Grienberger's 1612 star-charts eulogises Galileo's telescopic observations in highly charged language[98]. The decline of Clavius brought the Austrian and the Tuscan ever closer; and after Galileo's triumphal visit to the Collegio Romano Grienberger spoke eagerly to Galileo of future reunions of the aging Clavian telescope of the Collegio with Galileo's instrument.[99] Galileo's anger at the criticism of his opinions on the heights of lunar mountains by a Jesuit in Mantua led him to write a long letter to Grienberger to defend his position in detail[100]. Replying on the "anniversary of the death of our most beloved Clavius", Grienberger displayed a prudence that brings into relief the boundary of the corporate culture within which he carried out his work:


Do not be surprised that I am silent about your [letter]: I do not have the same liberty as you do.[101]


To have entered the dispute on Galileo's side would have constituted a breach of discipline for Grienberger, and would have been incompatible with his institutionalised modus procedendi.  Instead, as ever, he breaks his silence through the words of others. A young former pupil of Galileo's studying in the Collegio Romano, Giovanni Bardi, wrote to him to describe a meeting with Grienberger:


I visited Father Grienberger on behalf of Your Lordship and saluted him in your name. He returns your salutations doubled. I asked him for his opinion on that book [i.e. Galileo's Sunspot letters] which he had already seen and he said that he thought very well of it, and that on this subject, as on the other matter of things that float on water, he was of [the opinion] of Your Lordship.[102]


Galileo had spent much of 1612 embroiled in a bitter dispute with a group of Florentine Aristotelians about the cause of flotation of flattened bodies having a “weight” greater than that of water. As the early part of the debate has been discussed at length elsewhere[103] I shall limit my discussion to a brief summary. Vincenzo di Grazia's claim that ice was condensed water was attacked by Galileo, who pointed out that in this case ice would sink, as is patently contrary to experience. Di Grazia replied that ice floated because of its flat shape, and a dispute quickly flared up about the true cause of the flotation of bodies. Ludovico delle Colombe then joined the debate, and began performing experiments in public with chips of ebony to demonstrate that, in this case, shape, not heaviness, was the cause of flotation. Galileo's Discorso intorno alle cose che stanno in sù l'acqua was published in 1612[104], and attempted to explain the flotation of the anomalous ebony chips in terms of a small dip in the surface of the water, leading the the combined weight of ebony and air to be less than that of water.

Bardi complained to Galileo that, although Grienberger was very much in agreement with the Archimedean conclusions of the Discorso, students with only half a year of philosophy were pronouncing ridiculous judgements on the work, and the remaining professors were not yet discussing it.[105]

Grienberger’s backstage participation in the polemic surrounding Galileo’s Discorso illustrates both the possibilities and the limitations of the new public space for mathematical and experimental demonstrations provided by the Problemata in the Collegio Romano, a space that Grienberger had by now made his own. Previous problemata, particularly that concerning the nova of 1604[106] and the Nuntius Sidereus Collegii Romani recited by Odo van Maelcote in 1611[107] had demonstrated that the mathematicians of the Collegio Romano were prepared to risk conflict with the professors of Aristotelian natural philosophy by openly endorsing observations that challenged Aristotelian teachings concerning the incorruptibility of celestial matter. The dispute on galleggianti demonstrated that, under Grienberger’s guidance and instruction, they were willing to extend the domain of conflict to the most Archimedean domain of hydrostatics.

Bardi served as Grienberger’s public mouthpiece on this occasion.  On 20th June 1614, Bardi wrote to Galileo sending him the text of the presentation in defence of Galileo's position that he was to make in the Collegio Romano.

As one of these Problems had to be done, and it was allocated to me, Fr. Grienberger asked me what I would like to treat, proposing some other things to me. I told  him that I would have liked to deal with some matter similar to this, so he took this, which I think will please you no small amount, because it conforms entirely with your opinion, or rather it is your opinion, with the addition of those two experiments that cannot but support your view. And Fr. Grienberger told me that if he hadn’t had to have respect for Aristotle, whom they are not allowed to oppose in any way by order of the General, but must always save, he would have spoken more clearly than he did, because in this [matter] he is entirely on your side; and he told me that it is no wonder that Aristotle is in opposition, because he was most clearly mistaken in that which Your Lordship told me once about those two weights falling earlier or later[108]

The wording of Bardi’s letter is slightly ambiguous with regard to the authorship of the text he was to recite three days later. Nonetheless, Bardi’s claim that Grienberger “would have spoken more clearly than he did” clearly refers to the immediate context of the floating bodies debate, as shown by the remainder of the letter. Grienberger and Galileo had not met since the outbreak of the debate, and none of the previous surviving letters from Grienberger to Galileo mentions the dispute on floating bodies. I would like to suggest that Bardi is telling Galileo that Grienberger “would have spoken more clearly than he did” in the enclosed Problema, due to be recited by Bardi, but written by Grienberger on Bardi’s suggestion. This interpretation is consonant with a significant amount of additional evidence. The only surviving manuscript of Bardi’s presentation, entitled De ijs quae vehuntur in aquis, is preserved amongst Grienberger’s papers, where it is bound between rough trigonometric tables and a draft of his Problema on the basic principles of algebra. The differences between this text and the printed version suggest its priority – the manuscript contains corrections which are incorporated in the printed text. The handwriting of this Problema is identical to Grienberger’s other Problemata. Despite Bardi’s professed studies with Galileo and Grienberger no other evidence of his mathematical ability exists besides this single Problema and before its appearance Galileo dismissed his hydrostatic concerns as puerile.[109] The most recent discussion of Bardi’s text suggests that Bardi was subsequently unproductive, despite this prodigious beginning, due to eye-problems[110], but an attribution to Grienberger seems a more economic explanation. The sources cited in the Problema, including the works of Marino Ghetaldi and Juan Bautista Villalpando, are also cited elsewhere in Grienberger’s writings. Stylistically, the Problema De ijs quae vehuntur in aquis is also entirely in accordance with Grienberger’s other Problemata, as demonstrated by the excerpts published in the appendix.[111] From what we have seen of Grienberger’s behavioural patterns, it is unsurprising that Grienberger made no attempt to arrogate the work for himself, and indeed, as Bardi’s letter indicates, the  Jesuit system of censorship made it more convenient for such a work to appear under the name of a lay-person.

Grienberger’s caution seems to have been grounded on fact. On 14 December 1613 the ageing Jesuit general Claudio Acquaviva had issued a lengthy Ordinance for the solidity and uniformity of doctrine to all of the Jesuit provinces. While strenuously criticising departures from Thomist theology, Aquaviva also condemned the introduction of new opinons in philosophy, and ordered the Provincials to ensure “that the opinions that are taught in philosophy are subservient to theology, and that our philosophers follow Aristotle alone, wherever his teachings are not at variance with catholic truth”.[112] An attempt by the Jesuit mathematician Giuseppe Biancani to publish a similar work supporting Galileo’s position in the floating-bodies debate fell foul of the Jesuit censors shortly after Bardi’s presentation because it was “an assault on, not an explanation of Aristotle […]. And the conclusion and arguments of the work are not those of the author, but of Galileo: it would have been enough to have read them in Galileo’s work. To transcribe in the books of Ours [i.e. Jesuits] the discoveries of Galileo, especially those by which he attacks Aristotle, seems neither decent nor expedient”[113]. These were accusations to which “Bardi”’s work would have clearly been equally prone, had they not avoided Jesuit censorship altogether.

Bardi, I am suggesting, did little more than provide the occasion for Grienberger to give public legitimation to Galileo’s explicitly anti-Aristotelian conclusions in the Collegio Romano in the courtly and collegiate context of a Problema. Without delaying more on the question of attribution, I would like to move on to the content of Bardi’s theatrical hydrostatic performance. Bardi described the planned event in some detail in his letter to Galileo

There will be, in addition to the paintings [dipinte] and printed sheets [stampate], all of these experiments on a table, so that they can be seen by everybody, in such a way that they cannot deny what they see with their eyes[114]

The reference to dipinte suggests either a large panel bearing the picture (fig. 10) appended to the end of the manuscript, or possibly small copies distributed to each member of the audience which could be taken away as souvenirs. Bardi's reference to stampate is not so clear, but may refer to a printed list of his Archimedean conclusions, handed out to the members of the audience, possibly accompanied by schematic diagrams bearing the letters that he cites in his talk. Shortly after the event Stelluti wrote to Galileo giving a full report of Bardi's performance. He described his delight in seeing Galileo's opinion defended to rapturous applause, and admired the "experiments made in the presence of everybody by Father Christoph Grienberger, after he had brought all of the instruments which you can see in the enclosed picture into the room where the Problem was recited”. Stelluti observed that "although there was the odd Peripatetic who shook his head... everything was made quite clear by the end". Stelluti also provides crucial information on the audience, which included, as well as Stelluti himself and Federico Cesi, the brother of the latter, Bartolommeo Cesi, the mathematicians Luca Valerio[115] and Johannes Faber and other Prelates and "signori letterati". All of these spectators were, Stelluti continues,  "extremely satisfied to see such a "good Jesuitical demonstration" towards Galileo, to the annoyance of his imitators.[116]

The opening of Bardi’s talk recounts Galileo’s recent metamorphosis from sidereal messenger into Neptune. Announcing his aim to “uncover the cause by which things that should sink in water […] are discovered to float in water” in accordance with Galileo’s explanation, Bardi frames the polemic in distinctly  violent terms:

[F]rom this dissertation of ours it is to be hoped that every victory and every trophy of truth will be in your possession. The material will be abundantly supplied by Experience which, as it fights for the cause of this serious dispute, as in a battle, gathers soldiers, provides them with weapons, and urges them to war, and, like anyone who wishes to encourage people to fight vigorously, must take up a position on the front line itself.[117]

The wonderful drawing appended to Bardi’s presentation (fig. 10) illustrates the extent to which Grienberger’s mathematical problemata drew on Jesuit traditions in emblematics. The use of putti to perform experiments, later to become widespread, was a convention first adopted a year previously by Rubens in his illustrations for the Jesuit Francois Aguilon’s collosal work on optics, the Opticorum libri sex.[118] Rubens appears to have drawn some of his inspiration from the iconographic conventions of the profusion of Jesuit emblem books representing divine and profane love that flourished in the late sixteenth century.[119] In our case, as we are informed that the experiments described by Bardi were actually carried out by Grienberger, the performing putti might be said to represent his ultimate act of iconographic self-effacement - Grienberger's only surviving self-portrait, one might say.


Pictures, as well as words, formed essential tools for persuasion in the Jesuit rhetorical tradition.[120] Works such as Jeronimo Nadal’s Evangelicae Historiae Imagines used carefully crafted engravings to reinforce the gospel message, and played a crucial role in Jesuit missionary work.[121] Grienberger’s lavish  illustration, far more elaborate than the few schematic diagrams present in Galileo’s own Discorso, also formed an integral part of the persuasive artillery of Bardi. Central to the illustration is the phenomenon that formed the focus of Galileo’s dispute with the Florentine Aristotelians: a flat metal disc floating in a circular dish full of water, accompanied by two putti locked in discussion. The Galileian conclusion – namely that the plate floats because of a small dip in the water’s surface – a “well” (puteus) in the language of Bardi/Grienberger, is assumed in the diagram, which gives the water’s surface a conspicuous hollow. Such a minuscule experimental phenomenon is unlikely to have been easily visible to the grouped aristocratic and ecclesiastic spectators, unless their gaze was carefully shepherded. While Galileo’s Discorso legitimated its own existence by arguing that writing was more efficacious than speech as a means of distinguishing truth from falsehood,[122] Bardi’s oration endorsed direct, shared ocular experience, assisted by instruments.


Some things are heavier than others, others are lighter, and some are of the same weight [as each other]. It is by means of balances [bilances], scales [trutinae] and steelyards [staterae]that weights are conferred on heavy bodies. Although these are common [devices] neither Philosophy nor Mathematics abhorrs them.[123]


Grienberger’s rough manuscript notes and calculations (see fig. 16) reveal that he was no stranger to the balance, and conducted a series of measurements of the specific gravities of different metals in the wake of Marino Ghetaldi’s Archimedes Promotus. A representative excerpt, in coarser style than the public Problemata, reads as follows:


The weight of the cylinder in air according to one of my observations is 1 pound and 11.1/4.1/8.1/128 ounces. In water, however, it is 1 pound and 8 1/8.1/16.1/64 ounces, or, in 128th parts of an ounce, 2993 parts in air and 2586 parts in water, and since the difference is 407 parts a cylinder of water equal to the cylinder of tin will thus be of 407 parts, and the proportion of the weight of tin to the weight of water will thus be 2993 to 407.[124]


Returning to the public stage of Bardi’s Problema, it might be opportune to consider the remaining experiments illustrated in his diagram (fig. 10). On the left we have a floating brass ‘boat’ (scapha), which the weight of the putto is insufficient to submerge. On the right is a further “miracle of nature”: a cylindrical tube, beneath which a lead plate remains suspended when plunged into water. Grienberger suggests that this additional experiment, taken from Simon Stevin, provides additional evidence that a cylindrical “well” of air can lead bodies heavier than water not to sink. The device in the upper-middle is another experiment derived from Stevin – a scales in which 10 pounds of lead are balanced by only 1 pound of water, through the insertion of a cylinder fixed to the wall which occupies the space of 9 pounds of water.  Grienberger/Bardi suggests that since the shape of the immersed body is arbitrary, this provides further evidence in favour of Galileo, and in direct opposition to the Florentine Aristotelians, that “in similar experiments no account whatsoever should be taken of shapes or resistances of the medium”.[125]


Bardi hoped that the publication of “his” text would provide a non-Italian public with a Latin compendium of the central teachings of Galileo’s Discorso.[126] Federico Cesi, to whom Bardi wished to dedicate the work was unhappy with the dedicatory letter, complaining obliquely to Galileo that “when one is dealing with men who are truly great, I would like them to be treated in a fitting manner”.[127] Stelluti elaborated to Galileo that Cesi objected to the dedication “both because he did not state that it was recited in the said College [i.e. the Collegio Romano] and because he does not give your Lordship the mention that your valour deserves, passing over it with most languid expressions”.[128] Again, Grienberger speaks through Bardi to Galileo to emphasize his subjection to Jesuit discipline:


And [Grienberger] asked me to send you his greetings, and to say to you that if he could have spoken in his own way, he would have said even more, but that he could not do otherwise, and perhaps he may have done more than he should have. For this reason he avoided becoming at all involved in the printing process, and I was obliged to show myself to be resolved to print it, because otherwise it might easily not have come about, because there were some who inclined more towards ‘no’ than ‘yes’.[129]


Deprived of the essential diagram and, perhaps even more importantly, the endorsement of the Collegio Romano of the Society of Jesus, Bardi’s Problema made far less stir as a publication than as a public performance, and Grienberger retreated once more from the public sphere.[130]




This paper has aimed to demonstrate Grienberger’s deployment of pedagogy, bureaucracy and anonymity to effect significant changes in the way the natural world was understood by his peers. In spite of the increasing dangers involved in public opposition to Aristotle in the Jesuit context, Grienberger was prepared to use the public forum offered by the mathematical problemata to attack a number of key tenets of Aristotelian natural philosophy, and to defend the legitimacy of mathematics as a key instrument for the investigation of the natural world.  Institutionalised Jesuit modesty provided Grienberger with a powerful resource which he used to great effect to discredit Aristotelian natural philosophy from behind the scenes, to strengthen the arguments of the books of Jesuit mathematicians and to perfect the observational and mathematical instruments of his colleagues from his cubiculum in the Collegio Romano.


George Fortescue, an alumnus of the English college in Rome, provides a rare example of a literary portrait of Grienberger which may serve us as a fitting closing image. Fortescue, who resided in Rome between 1609 and 1614, stages an imaginary meeting between Galileo, Grienberger and Clavius in the Roman residence of the Mantuan Cardinal Ferdinando Gonzaga. After Galileo had finished displaying the two magical wonders he brought with him to Rome, the phosphorescent Bologna stone and his “new opticon” -- the telescope --, it was Grienberger’s turn to show his wares:


As I see that this is an arena of subtleties I bring to you an experiment on the most clear, distinct and eloquent Voice that I recently imparted to a statue, while removed from more serious studies.  The statue was made not of brass or of solid marble, but of plaster, in which the coiled receptacles of the voice, as if contained in a cavity, received the percussions of sounds and rendered them more felicitous. When words were introduced into this voice-duct, punctuated by breathing, and I transmitted others to the machine successively after similar breathing intervals and closed the point of entrance of the voice tightly, then at length, after the various by-roads, turnings and hinderances that really gave assistance, the oration arrived at the head [of the duct] and the boundary of the statue.  The acute power of the words and the succession of breaths moved the gullet and mobile tongue most easily to produce the diversity of syllables. But how much I see myself to disappoint my companions, equal to the stars, who perhaps smile at their Grienberger, studiously forming voices from plastered blocks[131]



Surprisingly, Fortescue’s attribution of the invention of a speaking-statue to Grienberger is somewhat plausible. Much later Athanasius Kircher had such a device in his bedroom in the Collegio Romano, which he later transferred to his museum, where it was baptised the “Delphic oracle”. In response to English claims to priority in the invention of the speaking-tube, Kircher never claimed its invention but merely stated that it had been invented years before “in the Collegio Romano”.[132] Whether or not it was really built by Grienberger, however, is of little importance -- a mechanical orator, a machine which moved its tongue and appeared to speak, amplifying the voice of the hidden operator, could hardly have been more appropriate to his favoured mode of self-expression.






* I thank Jill Kraye, Simon Schaffer, Rob Iliffe, Mario Biagioli, Moti Feingold, Ann Blair and Nick Wilding for helpful comments on previous drafts of this paper. I am grateful to the Pontifical Gregorian University for permission to publish documents from their archives.



APUG = Archivio della Pontificia Università Gregoriana, Rome

ARSI = Archivium Romanum Societatis Iesu, Rome

BN = Bibliothèque Nationale, Paris

BNR = Biblioteca Nazionale “Vittorio Emmanuele II” , Rome

CC = Christoph Clavius: Corrispondenza, ed. Ugo Baldini and Pier Daniele Napolitani, Pisa: Università di Pisa, Dipartimento di Matematica, Sezione di Didattica e Storia della Matematica; 1992

F.C. = Fondo Curia

F.G. = Fondo Gesuitico

GW = Johannes Keplers gesammelte Werke, ed. Walther von Dyck and Max Caspar, München, C. H. Beck, 1937-

MP = Monumenta Paedagogica Societatis Iesu, Nova editio penitus retractata, ed. Ladislaus Lukács, Rome: Institutum Historicum Societatis Iesu, 1965-

OG= Le Opere di Galileo Galilei, Edizione Nazionale, ed. A. Favaro (1890-1909)

Sommervogel = Augustin de Backer, Aloys de Backer and Auguste Carayon, eds., Bibliothèque de la Compagnie de Jésus, Nouvelle éd. par Carlos Sommervogel, 12 vols., Brussels: O. Schepens, Paris: A. Picard (1890-1932), repr. Louvain (1960).

[1]The Vulgate translates kenodoxia as "inanis gloriae cupido" (Gal. 5, 26, Phil. 2,3).

[2]Jakob Bidermann, Cenodoxus, in Bidermann, Ludi theatrales sacri, sive Opera comica posthuma, Munich: J. W. Schell; 1666, 2 vols. Reprinted (Herausgegeben von Rolf Tarot) Tübingen: Max Niemeyer Verlag; 1967, Band 1, pp. 78-159. On Cenodoxus, see also Roland Mayer, Personata Stoa: Neostoicism and Senecan Tragedy. Journal of the Warburg and Courtauld Institutes, 1994; 57: 151-174, on p. 166.

[3]Bidermann, Ludi theatrales, cit., I, sig. [(†) 8 ] v - sig. (††)1 r.

[4]For pointers to the more important Ignatian sources, see the excellent introduction to Rolf Tarot's critical edition of Cenodoxus, cit., particularly pp. XXI-XXIII.

[5]See Dionysius Fernández Zapico (ed.), Regulae Societatis Iesu (1540-1556). Monumenta Historica Societatis Iesu. Rome; 1948. pp. 514- 527.

[6]In a critique of court-based accounts of the development of European civility, Dilwyn Knox situates the Jesuit rules of modesty in the context of a medieval monastic tradition of disciplina. See Dilwyn Knox, Disciplina: The Monastic and clerical origins of European Civility in John Monfasani and Ronald G. Musto, eds. Renaissance society and culture: Essays in honour of Eugene F. Rice, Jr. New York: Italica Press; 1991: 107-135, especially on pp. 126-8.

[7]Unpublished versions extended this rule to the written word, see Zapico, cit., p.526 (Regularum modestiae complementum (1555): "In loquendo vel scribendo nulla detur significatio arrogantiae", but the published versions of the Regulae restricted their attention to the body.

[8]Pedro Ribadeneira, Vita Beati Patris Ignatii Loyolae, Antwerp, 1610. In so far as Ignatius's life story and spiritual disciplining after his injury at the battle of Pamplona came to serve as a model for those entering the order, it is perhaps worth mentioning in the context of self-effacement that Ignatius never allowed his portrait to be painted while General of the Society - future portraits had to rely heavily on sketches made at his deathbed and several death masks. See Thomas M. Lucas (ed.), Saint, Site and Sacred Strategy: Ignatius, Rome and Jesuit Urbanism, Vatican City: Biblioteca Apostolica Vaticana; 1990, p. 63 and Fontes Narrativi de S. Ignatio de Loyola et de Societate Iesu (Monumenta Historica Societatis Iesu), 4 vols., Rome: Institutum Historicum Societatis Iesu; 1943-1965, Vol. III, pp. 240-1.

[9]Steven Shapin, A Social History of Truth: Civility and Science in Seventeenth-Century England, Chicago and London: University of Chicago Press; 1994 , especially Chapter 4, and Mario Biagioli, Galileo Courtier: The practice of science in the culture of absolutism, Chicago: University of Chicago Press; 1993. Through a peculiarly reflexive twist, both Biagioli and Shapin have recently been castigated for intellectual deportment inappropriate to the exalted station of the historian. On Biagioli, see Michael Shank, Galileo's Day in Court, Journal for the History of Astronomy, 25 (1994), 236-243, answered in Mario Biagioli, Playing with the Evidence, Early Science and Medicine, 1 (1996), 70-105, followed by Shank's lengthy rejoinder, How shall we practice history? The case of Mario Biagioli's Galileo Courtier, Early Science and Medicine, 1:1 (1996), 106-150. On Shapin, see Mordechai Feingold, When Facts Matter, Isis, 1996, 87: 131-139, Peter Dear's response (Isis, 1996, 87: 505-6), Shapin's response (Isis, 1996, 87: 681-4) and Feingold's rejoinder (Isis, 1996, 87: 684-7).

[10]The work of Roger Chartier, in particular, has provided a renewed critique of the problems related to early modern authorship raised by Foucault's celebrated 1969 essay Qu'est-ce qu'un auteur?. See especially Roger Chartier, Figures of the Author, in Chartier, The Order of Books: Readers, Authors, and Libraries in Europe between the Fourteenth and Eighteenth Centuries, Stanford, CA: Stanford University Press; 1994.

[11]See Jacob Bidermann, Cenodoxus, ed. and transl. D.G. Dyer, Edinburgh: Edinburgh University Press, 1975, p. 8.

[12]On Scheiner's troublesome courtly deportment, see Steve Harris, Les chaires de mathématiques. in Luce Giard, Les jésuites à la Renaissance. Système educatif et production du savoir. Paris: Presses Universitaires de France; 1995: pp. 239-261, and also M.J. Gorman, A Matter of Faith? Christoph Scheiner, Jesuit censorship and the Trial of Galileo. Perspectives on Science. 1996; 4(3): 283-320.

[13]Studies of Ignatian spirituality include David Lonsdale, Eyes to See, Ears to Hear: An Introduction to Ignatian Spirituality, London: Darton, Longman & Todd; 1990. For the connections between the development of the Jesuit spiritual programme with the organizational structure of the order see especially John W. O' Malley, The First Jesuits, Cambridge MA, Harvard University Press, 1993.

[14]Of course, self-abnegation, or 'self-cancellation', in Greenblatt's terminology, is really just a form of self-fashioning. See Stephen Greenblatt,  Renaissance self-fashioning from More to Shakespeare, Chicago and London: The University of Chicago Press; 1980.

[15]A cursory examination of the Edizione Nazionale of Galileo's Works and the Clavius correspondence revealed no less than nineteen current variants. See OG, s.v. 'Grienberger' and CC, passim.

[16]Catalogus veteres affixarum Longitudines ac Latitudines conferens cum novis. Imaginum Coelestium Prospectiva duplex. Altera rara Ex Polis mundi, in duobus Hemisphaerijs Aequinoctialibus, per Tabulas Ascensionum Rectarum et Declinationum. Altera nova Ex mundi Centro, in diversis planis globum Caelestem tangentibus, per Tabulas Particulares. Utraque Caelo et accuratioribus Tychonis observationibus quam simillima. Christophori Grienbergeri Oeni Halensis, e Societate Iesu, Calculo ac Delineatione, elaborata. Romae: Apud Bartholomaeum Zannetum; 1612, and Euclidis sex primi Elementorum Geometricorum libri, cum parte undecimi, ex majoribus Clavii Comment. in Commodiorem formam contracti, rerumque mathematicarum Christophori Grienbergeri Oenhallensis e Societate Jesu Opusculum primum. Romae, apud Haeredes Bartholomaei Zanetti, 1629 respectively. A manuscript version of the latter work, is in the Biblioteca Nazionale Centrale in Rome (BNR, Fondo Gesuitico 594 (2723) A manuscript of the second part of the latter work, Elementa trigonometrica, id est sinus Tangentes Secantes in Partibus Sinus totius 100000. Opusculum Secundum. Romae, per Haered. Barthol. Zannetti, 1630, containing Muzio Vitelleschi's original letter of approval, is in the Biblioteca Medicea-Laurenziana in Florence (Ms. Ashburnam 1650). For information on later editions of both works see Sommervogel, Vol. III, coll. 1810-1811. Grienberger’s star charts are of particular interest in their use of Tycho’s data, fifteen years before the publication of Kepler’s Rudolphine Tables. See Kepler to Wilhelm Schickard in Nuertingen, Linz, 11 March 1618, GW 17 pp. 256-259, on 257.

[17]A useful summary biography has been published in CC I.2, pp. 55-7. Detailed discussions of Grienberger can also be found in Baldini, Legem, cit., Chapters V and VI.

[18]Apart from the letters published in OG and CC,  the codex APUG 534 contains numerous unpublished letters sent to and from Grienberger, a list of which is published in Ugo Baldini, Legem impone subactis. Studi su filosofia e scienza dei gesuiti in Italia, 1540- 1632. Rome: Bulzoni; 1992, p. 200. For further details see CC I.2, p. 57.

[19]See Paul P. Bockstaele,Four Letters from Gregorius a S. Vincentio to Christopher Grienberger.  Janus. 1969; 56: pp. 191-202 and William B. Ashworth Jr, The Habsburg Circle. in Bruce T. Moran, ed., Patronage and Institutions. Science, technology and medicine at the European Court 1500 - 1750. Rochester, New York: The Boydell Press; 1991: 137 - 167.

[20]Mario Bettini, Apiaria Universae Philosophiae Mathematicae  Bononiae: Io. Baptistae Ferronij; 1645.

[21]See Stefano Ghisoni to Giannantonio Rocca, Bologna; November 23 1636, "Ed avendolo io sentito molto lamentarsi, che sia in così poca stima la Matematica, dal modo di esagerar questo punto, ho congetturato, che non abbia trovato persona, che faccia la spesa per il suo libro", published in Lettere d'uomini illustri del secolo XVII a Giannantonio Rocca. Modena: Società Tipografica; 1785, pp. 62-4.

[22]"Qui nostri aevi alter Archimedes a doctioribus sine controversia est habitus, quippe qui acutissimis theorijs ingeniosissimas praxes, & mirificas machinationes adiungeret." Bettini, Apiaria Universae Philosophiae Mathematicae  Bononiae: Io. Baptistae Ferronij; 1645, Sig. C2 recto.

[23]"Fruerem mi Lector ingenio, & industria doctissimi, ac modestissimi viri Griembergeri, qui cum plura haberet apud se a mirifice inventa, maluit tamen alienis, inventis, & alienis laudibus inservire", Bettini, Apiaria Universae Philosophiae Mathematicae  Bononiae: Io. Baptistae Ferronij; 1645 Apiarium V, Caput VI, pp. 44-6.

[24]"Sed nihil sibi magis inimicum habuit Griembergerus, quam suam ipsius modestiam, qua factum est ut ingeniosissima sua inventa neglectui, & obliuioni habuerit" Bettini, Aerarium Philosophiae Mathematicae,. Bononiae: Io. Baptistae Ferronij; 1648, p. 75. Bettini provides much information on Grienberger's manuscript heritage here that Sommervogel incorrectly ascribes to Gaspar Schott.

[25]"Singulare in eo id fuit, quod Archimedis exemplo acutissimas theorias mirificis praxibus iungebat", Bettini, Aerarium , loc. cit.

[26]E.g. Juan Bautista Villalpando, "Is vero in examinandis mechanicis instrumentis tanta est sollertia praeditus [Griembergerus], ut nemini debeat haberi secundus",(J. B. Villalpando, Apparatus Urbis ac Templie Hierosolymotani. Rome; 1604, p. 436) and Gaspar Schott, describing an oil-spouting lantern designed by Grienberger, "Sequens Lucerna tametsi vulgaris appareat, suos tamen habet admiratores, quia artificio non caret, & ab ingeniosissimo excogitata constructaque fuit Mathematico. Is fuit P. Christophorus Grünbergerus, Germanus, Clavij in Mathematicis discipulus, & in Romano Collegio quondam illarum scientiarum Professor; qui suis eam manibus (erat enim simul Mechanicus eximius) construxit affabre e ferreis laminis colore obductis, & adhuc asservaur in Kircheriano Museo, & aquâ infusâ exhibet nunc illum effectum, quem oleo repleta exhibere deberet, non sine adventantium admiratione ac voluptate" (G. Schott, Mechanica hydraulico-pneumatica. Würzburg: Henricus Pigrin; 1657, p. 290).

[27] Galileo to Belisario Vinta, 19 March 1610, OG X, 298-9, Ernst von Wittelsbach to Grienberger, 1 April 1611, APUG 534 f. 81r in OG XX 601-2, Grienberger to Galileo, Rome, 11 January 1611, OG XI 31-35, Biagioli, Replication or monopoly? The economies of invention and discovery in Galileo’s observations of 1610, forthcoming in Science in Context.

[28]See Christoph Scheiner, Pantographice seu Ars delineandi res quaslibet per parallelogrammum lineare seu cauum, mechanicum mobile, Romae; 1631.

[29]"Tentando inueni instrumentum V. R. facilius effici posse. Hastam directoriam, quae movetur in transversum abstuli, atque adeo illam instrumenti partem, quae videbatur operationem remorari. Cursores meo modo, ut inferius videbis, adieci, & quatuor tigillis parallelogrammum constituentibus opus absolui. Curavi ut & radius visualis, & radius scriptorius uterque ex suo puncto egrederentur, & utrumque punctum existeret in una linea recta, nempe in axe, circa quem parallelogrammum perpetuo circunducitur." Bettini, Apiaria, cit., Apiarium V, p. 44.

[30]It seems highly plausible that the engravings were made by Grienberger himself, whose published Catalogus shows him to have been an extremely accomplished draughtsman, as do the drawings and engravings that accompany several of the Problemata discussed later in the present study.

[31]"Potuissem nuper hoc ipsum Bettinianum instrumentum mittere ad Imperatorem, sed id facere sine licentia Rev. Vestrae nolui. Mallem habere eam licentiam, quam Rev. Vestra daret si quam primum Apiaria in lucem daret", Bettini, Apiaria, cit., Apiarium V, Caput VI, pp. 44-6.

[32]Christoph Scheiner, Rosa ursina, sive, Sol, ex admirando facularum et macularum suarum phaenomeno varius. Bracciani: Apud Andream Phaeum Typographum Ducalem; 1630.

[33]The relationship between Scheiner and the Orsini household was not so harmonious as this vignette might seem to suggest, as revealed by letters sent by Scheiner to Archduke Leopold of Austria during this time. See Franz Daxecker, Briefe des Naturwissenschafftlers Christoph Scheiner SJ an Erzherzog Leopold V von österreich Tirol 1620-1632, Innsbruck: Publikationsstelle der Universität Innsbruck, 1995, pp. 135, 152, 156, 159.

[34]On Scheiner's "collectivist" approach to natural investigation (apparently cramped somewhat by his unpopularity amongst other Jesuits) see Rivka Feldhay, Galileo and the Church: Political Inquisition or Critical Dialogue? Cambridge: Cambridge University Press; 1995, p. 288.

[35]"Itaque Machina haec tot difficultatibus non implicatur, quot illa; & insuper sua expeditius, & in praxi celerius absoluit quam illa. Unde operae precium erit, eius naturam aliquantulum scriptione explicare, siquidem id ipsemet Machinae Architectator visus est praestare noluisse: quamuis postea non pauca suis demonstrationibus egregiè illustrarit, meque festinantem, atque ad finem operis properantem, similibus officijs, mihi in tanta temporis angustia poene necessarijs, peropportune adiuuerit", Christoph Scheiner, Rosa ursina, sive, Sol, ex admirando facularum et macularum suarum phaenomeno varius. Bracciani: Apud Andream Phaeum Typographum Ducalem; 1630, p. 348

[36]See C. Grienberger to Ricardo de Burgo, [Rome], [June-July 1619], "Rebus denique Galilaei vellem me non immiscere si possem postquam tam male de Mathematica Collegii Romani est meritus a qua non semel et quidem in praesentia tam bene quam sincere est habitus", published in Baldini, Legem impone subactis, cit., pp. 194-5, on p. 195. Surprisingly, before the election of Urban VIII to the Holy See, Federico Cesi made the rather strange suggestion that Galileo's Il Saggiatore, a work that was far more critical of the mathematicians of the Collegio Romano, should be dedicated to none other than Grienberger. See Giovanni Ciampoli to Galileo, Rome; 1620 Jul 17 in OG XIII, p. 44 "Il Sig.r Pinc.e Cesi mi ha mandato aperta l'inclusa: vi era una poliza, nella quale adduceva alcune ragione per le quali giudicava bene il dedicar l'opera al P. Bamberger [i.e. Grienberger], e rimette a noi il mandarla, i quali, essendo qua in paese, assolutamente non giudichiamo bene il farlo per non mettere in fastidi quel povero Padre, come certamente sappiamo ab exemplo che seguirebbe."

[37]After Galileo's trial, Grienberger is reported to have said that "If Galileo had maintained the affection of the Fathers of this College, he would live gloriously to the world and none of his disgraces would have come about. He would have been able to write freely on any subject, even on the motion of the earth etc.". Galileo interpreted this statement  as a confirmation of his suspicions that the Jesuits had engineered his downfall, but the material presented here might suggest an alternative interpretation - Grienberger had hoped that together Galileo as 'author' and the Jesuit astronomers as 'expert' corroborators of his observations might produce a reformed cosmology sanctioned by the Catholic church. See Galileo to Elio Diodati, Florence; 25 July 1634, in OG XVI, p.117. Grienberger's remarks in his notes for the censorship of Giuseppe Biancani's cosmography (Sphaera mundi, Bononiae: Typis Sebastiani Bonomij; 1620) also suggest that Grienberger was in favour of a new cosmography being written by someone outside the order, to replace the outdated commentaries on the Sphere of Sacrobosco: "Laudabile est in primis studium Auctoris, quod potissimum tyronibus in rebus mathematicis prodesse conatur, quibus Cosmographia nova necessaria videtur, eo quod vetus plurimum hoc tempore immutata sit eique non pauca accesserint ornamenta. Sed dubium est expediat necne, ut id per Nostros fiat", ARSI FG 655, f. 118r, in Baldini, Legem impone subactis, cit., p. 235 (emphasis added).

[38]See M.J. Gorman, A Matter of Faith? Christoph Scheiner, Jesuit Censorship and the Trial of Galileo. Perspectives on Science. 1996; 4(3): 283-320 on p. 312. That Galileo’s attempt was unsuccessful is apparent from a letter from Johannes Remus Quietanus to Grienberger of 20 June 1620, APUG 534 f. 34r, cit. in Baldini, Legem impone subactis, cit., p. 213 note 22

[39]See CC I.2, pp. 55-7.

[40] "Quid ni ergo meum amem Praeceptorem? et quidem tam meum, ut mei pene solius esse videatur. An non meus sis, qui tam mihi semper praesens es, ut iam pene quatuor ab annis quibus te nosse unaque statim amare caepi, meo ex cubiculo vix unquam pedem extuleris", Grienberger to Clavius, Vienna, 15 September 1590, in CC II.1, pp. 158-162, on p. 158.

[41]Christoph Clavius, Euclidis Elementorum libri XV. Accessit XVI. de Solidorum Regularium comparatione. Omnes perspicuis demonstrationibus, accuratisque scholiis illustrati, Rome: Apud Vincentium Accoltum; 1574, Christoph Clavius, In Sphaeram Ioannis de Sacrobosco Commentarius, Rome: Apud Victorium Helianum; 1570 (first edn.). See CC I.3 pp. 5-11 for a full bibliography of Clavius's works.

[42]"Nunc quoniam id discipulorum quoque est muneris ut non solum lectionem quisque recitet suam, quod quidem hisce demonstratiunculis, fero licet, facere caepi", Grienberger to Clavius, Wien, 15 September 1590, cit., on p. 158.

[43]Mario Biagioli has recently pointed to the importance of the homosocial bond in the activities of the Accademia de' Lincei, but the connection between homosociality and epistolary links, clearly evinced in the Jesuit order well before the creation of the Lincei and stemming from the Ignatian conception of the importance of epistolary relationships to the "union of hearts" in the Society, has yet to receive adequate attention. See M. Biagioli, Knowledge, Freedom, and Brotherly Love: Homosociality and the Accademia dei Lincei. Configurations. 1995; 2: 139-166.

[44]Biancani sent Clavius a proposed solution to the problem of measuring longitude at sea. He suggested that a large number of accurate clepsydras could be used to constitute a shipboard clock which, in conjunction with accurate measurements of a particular fixed star, ideally lying close to the equator, could be used to calculate longitudes accurately. The Rector  of the Jesuit College of Padua sent an accompanying letter pleading with Clavius to help Biancani, to allow the College to have a mathematics teacher, which it had lacked since Marc' Antonio de Dominis, Biancani's teacher, had become Bishop of Segna. See Biancani to Clavius, Padova, 28 February 1598 in CC IV.1, pp. 34-37. Maelcote sent an astrolabe of his own design, prompting Clavius to suggest his transfer to Rome. See Clavius to Maelcote, Roma, 16 February 1601, in CC IV.1 pp. 124-5 on p. 124 "Si tui Superiores cum P. N. Generali agerent, ut in urbem vocaveris, donec vivo, res mihi esset gratissima".

[45]"Iam novam vestem induit musaeum mathematicum nec aliud clamare videtur nisi ut cito redeat patronus. Me interim custodem habebit. Die lunae proximo vetus meum tradam duobus aliis”, Grienberger to Clavius (in Naples), Rome, 6 October 1595, in CC III.1, pp. 137-8, on p. 137.

[46]ARSI Rom. 150, I. 36r, cit. in CC III.2, pp. 54-5, note 2.

[47]Such "mathematical museums" were also to be found in other Jesuit colleges, including the college of Prague, where  Jakob Johann Wenceslaus Dobrzensky de Nigro Ponte  saw a a hydro-magnetic clock-fountain made by Kircher's disciple Valentin Stansel. See J.J.W.  Dobrzensky de Nigro Ponte, Nova, et amaenior de admirando fontium genio (ex abditis naturae claustris, in orbis lucem emanante) philosophia. Ferrara: Alphonsum, & Io. Baptistam de Marestis; 1657, p. 46.

[48]"Exspecto proximam studiorum interruptionem, ut diligentius perquiram et conscribam fabricam cuiusdam Machinae quam iam ab aliquot mensibus mecum habeo in cubiculo". Grienberger to Clavius (in Rome), Lisbon, 24 March 1601, CC IV.1, pp. 136-9 on p. 137.

[49]On the different levels of mathematical tuition in the Collegio Romano, ranging from the private mathematical academy for the training of future teachers to the normal public classes, see CC I.1 59-89.

[50]See CC III.1, p.138.

[51]This practice was formalised in 1636, when Muzio Vitelleschi wrote to Francesco Piccolomini, the Roman Provincial, that the papers of a Jesuit should be examined by the Superiors after his death and only papers of special interest should be preserved. According to Baldini and Napolitani, this was more or less what went on beforehand. See Muzio Vitelleschi to F. Piccolomini, Rome; 9 August 1636, cited in  CC I.1, p. 30.

[52] Athanasius Kircher, Magnes, sive de arte magnetica opus tripartitum, Romae: Ex Typographia Ludovici Grignani, 1641, Lib. II, Cap. II, p. 431, "[P]artim è literis ab ijs, qui iter in Indias susceperant, vel oretenus ab ijs, qui inde peregrini Romam advenerant; partim ex literarum Mathematicarum è diversis orbis terrae partibus ad Clavium, Grimbergerum, aliosque Romanos Societatis IESU Mathematicos praedecessores meos datarum, quod penes me est, Archivio; multas sanè, circa declinationes Magneticas haud spernendas observationes collegi", Gaspar Schott, Mechanica Hydraulica-Pneumatica, Würzburg: Pigrin, 1657, pp. 300 and, esp., 339: "In Manuscriptis doctissimi viri P. Christophori Grünbergeri, olim in Romano Collegio Mathematicae Professoris, quae in Archivio Clavij & Grünbergeri reperi, haec habentur verba circa praesentem Bettini Machinam, & de motu perpetuo opinionem..." [emphasis added].

[53]Grienberger dismisses the compass, celebrated by Giordano Bruno in two poems, as a pretty plaything: "Nempe in rebus exactioribus esse inutile instrumentum at in apparentia et operatione vulgari pulchrum simul et iucundum immo quod multum faciat mirari spectantes", Grienberger to Clavius (in Naples), Rome, 23 February 1596, CC III.1, pp. 161-9, on p.164.

[54]E.g. "O felices barattolas, o dulces mustacciulos. eoque feliciores quo minus deficient", Grienberger to Clavius (in Naples), Rome, 27 October 1595, in CC III.1, pp. 139-142 on p. 139, "Saltem optarem, ut ne Roma una cum Clavio abisse videatur Mathematica, et Neapolim veluti in novam Coloniam transmigrasse. Quam spero redituram propediem ubi nimia quae illic est dulcedo nauseam attulerit. Quod si ita dulcedo delectat, ut eius satietas sit nulla, saltem meminerit extra patriam se vicere...". Clavius's gluttony was later lampooned by Joseph Scaliger: "Clavius qu'on m'avoit dit estre un grand personnage & que i'ay trop loué, est une beste. Monsieur Dabin m'a dit qu'il luy faut tous les matins un morceau de jambon & un verre de vin Grec. C'est un gros ventre d'Aleman...", Joseph Scaliger, Scaligerana. Editio altera. ad verum exemplar restituta, Coloniae Agrippinae: Apud Gerbrandum Scagen; 1667 p. 51 (s.v. 'Clavius').

[55]"Vereor me fortassis privitam debeam legere cuidam Comiti cuius nomen excidit. Sed ut audio parum aliis studuit, et ut mihi videtur satis est iuvenis ne dicam puer unde parvum spero profectum etiam ex parte mea qui cum eiusmodi hominibus digne tractare nescio", Grienberger to Clavius (in Naples), Rome, 12 January 1596, CC III.1, pp. 146-50.

[56]"Non habeo multum temporis vacui, praeter tempus matutinum. Nam a prandio totum sibi Schola et Academiae vendicant, quarum una domestica ut novit altera est ad Portam, ad quam convenit Comes Sancti Georgi ut vocant puer non mali ingenii. et quidam alius eiusdem fere aetatis Horatius nomine, Perusinus et ipse bonae familiae, quorum uterque apud R.P. Generalem procurarunt ut eis privatim legerem. Cogitet T. Ra. quam sim aptus ad hoc officium, quod non Todescum sed Tuscanum, meque affabiliorem requireret. Sed quoniam eis ita placuit spero mecum habebunt patientiam", Grienberger to Clavius (in Naples), Rome, 23 March 1596, in CC III.1, pp.170-3, on p. 170. It is just possible that "Horatius" may have been the young Orazio Grassi (though he came from Savona rather than Perugia), who joined the Jesuit Novitiate at S. Andrea al Quirinale in 1600 at the age of eighteen.

[57]"Sed exclusus est forte [Clavius] cubiculo? immo vero ita aptum est ut vel nolentem invitet. eodem libenter. facile enim ut puto aliud inveniam quod aeque sit frigidum, nisi forte omnia sint frigida in quibus ego frigidissimus inhabito". Grienberger to Clavius (in Naples), Rome, 24 November 1595, in CC III.1, pp. 142-145 on p. 143

[58]Grienberger to Clavius (in Naples), Rome, 26 January 1596, CC III.1, pp. 151-2: "Nunc parum quiescere cogor, quod mihi in cubiculum allatus sit lapis ut in eo describam horologia pro Cardinali Lanceloto".

[59]"Si superiores non mutent consilium credo me liberum fore ab Academia domestica ordinaria. [...] Altera vero academia privata de Horologiis sensim proprepit. e tribus unus nempe Ioannes Nagius cum ante quatuor vel quinque dies impetuosius binos simul gradus ascendere conaretur, defluente catharro vix non suffucatus est. Vicit tamen natura, viamque sibi fecit vi, sed non sine sanguine, nam una cum phlegmate non parum sanguinis eiecit", Grienberger to Clavius (in Naples), Rome, 23 March 1596, in CC III.1, pp. 170-3, on pp. 170-1.

[60]"Cum hodie visitarem Nagium reperi ibidem tum P. Villalpandum tum P. Marium eum quem dum iret Neapolim T. Ra. salutavit in lectica, qui legentes T. literas laetati sunt de bona valetudine, etenim vero sensimus nescio quam fragrantiam ex ipsis literis, bonique nescio quid odoris sed sine gustu." Grienberger to Clavius (in Naples), Rome, 23 March 1596, in CC III.1, pp. 170-3, on p. 172

[61]ibid., loc. cit. : "Scilicet Clavius Gustum servat sibi nobisque mittit odorem, ut hinc conclusimus quam omnia plana sint in cubiculo Clavii cum etiam chartae dulcem illum odorem hauriant et Romam usque deferant".

[62]"Nescio quo attestante Ro. Patri nostro Rectori T. R.a promiserit me facturum Praefationem, bis enim ut minimum et quidem coram aliis id ex eo audire me, contigit, cum optime noverit quam mihi id muneris, visum sit semper difficillimum. certe si Praefationem expectarunt eam non habuerunt, sed eius loco Dimensionem circuli ex Archimede ita fuse explicatam ut dimidia hora absolvi non potuerit....", Grienberger to Christoph Clavius (in Naples). Rome; 24 November 1595, CC. III.1, pp. 142-6, on p. 143.

[63]Giuseppe Biancani, De mathematicarum natura dissertatio una cum clarorum mathematicorum chronologia. Bononiae; 1615 (bound with idem., Aristotelis loca mathematica, Bononiae, 1615).

[64]"Extant plurea & optica, & machinaria experimenta in Coll. nostro Romano: quae aliquando Principum virorum illuc inuisentium oculis, & admiratione exhibita sunt", Bettini, Aerarium, cit., Def. 10, §3, p. 75

[65]For a rich discussion of the different literary genre of problemata in natural philosophy modelled on the Pseudo-Aristotelian problems, see Ann Blair, The Problemata as a natural philosophical genre, forthcoming in Natural Particulars, ed. Nancy Siraisi and Anthony Grafton, Cambridge MA: MIT Press, 2000, pp. 171-204.

[66]"Professor alter, qui modo P. Clavius esse posset, constituatur, rerum mathematicarum pleniorem doctrinam conferat in triennium, explicetque privatim nostris octo circiter aut decem, qui mediocri saltem sint igenio, nec a mathematicis alieno, et philosophiam audierint; qui ex variis essent convocandi provinciis, unus ex qualibet, si fieri posset [...] Porro ex hac academia eximii prodirent mathematici, qui eam facultatem in omnes provincias, ad quas essent reversuri, disseminarent, et nostrorum tuerentur existimationem, siquando oporteret eos de mathematicis respondere." MP V, p. 110.

[67]"Semel aut iterum in mense auditorum aliquis in magno philosophorum theologorumque conventu illustre aliquod problema mathematicum enarret, prius a magistro, sicut oportet, edoctus", MP V, p. 284. This suggestion was previously made in the unpublished 1586 version of the Ratio Studiorum, MP, V, p. 177. The definitive version of the Ratio Studiorum, published in 1599, also stated “Singulis aut alternis saltem mensibus ab aliquo auditorum magno philosophorum theologorumque conventu illustre problema mathematicum enodandum curet; posteaque, si videbitur, argumentandum”, MP V, p. 402.

[68]Louise Rice, College Art: Prints, Poetry and Music for the Academic Defense at the Collegio Romano, paper given at the conference The Jesuits: Culture, Learning, and the Arts, 1540-1773, May 28 - June 1 1997, Boston College, Chestnut Hill, MA.

[69]Zannetti's close links with the Collegio dated from the extraordinary success of his edition of Bellarmine's 1578 Hebrew grammar. In 1598, the publishing house moved to new premises located adjacent to the Collegio to facilitate the collaboration, and when Bartolomeo Zannetti died in 1621 he left all his printing equipment to the Jesuits. Mascardi moved to occupy his premises shortly after this time, taking over a lucrative and spiritually edifying business relationship between College and printing-house. See Saverio Franchi, Le Impressioni Sceniche. Dizionario bio-bibliografico degli editori e stampatoi Romani e Laziali di testi drammatici e libretti per musica dal 1579 al 1800. Roma: Edizioni di Storia e Letteratura; 1994, pp. 780-805.

[70]Carlo Ginzburg, The High and the Low: The theme of forbidden knowledge in the sixteenth and seventeenth centuries in Ginzburg, Clues, Myths, and the Historical Method, Baltimore and London: The Johns Hopkins University Press; 1989 p. 60-76.

[71]In addition to the confessions of bodily inability found in Grienberger's letters to Clavius cited above, see Christoph Grienberger, Catalogus veteres affixarum Longitudines ac Latitudines, Romae: B. Zannetti, 1612, Ad Benevolum Lectorem: "Quam cum etiam ipse probe perspectam heberem, videremque desiderium meum plurimorum esse; neque spes ulla affulgeret inueniendi ea apud alios quibus levari diuturna nostra sitis posset, ipse meos imbecilles humeros, tandem huic oneri utilitate gravissimo submittendos duxi, & aquam quae meae aliorumque siti extinguendae sufficeret, primo DEO dante & expensas faciente, domum detuli, tum foras ductis rivulis ob commune studium, etiam ad irrigandos aliorum hortulos eduxi" (emphasis added).

[72]Imago Primi Saeculi Societatis Iesu A Provincia Flandro-Belgica eiusdem Societatis Repraesentata. Antwerp: Balthasar Moretus; 1640.

[73]Marc Fumaroli, Baroque et Classicisme: L'Imago Primi Saeculi Societatis Jesu (1640) et ses adversaires. in Fumaroli, L'Ecole du Silence: Le sentiment des images au XVIIe siècle. Paris: Flammarion; 1994: 343-365.

[74] Problema: Terram auream, Talenti potentia movere, 5 November 1603, APUG Fondo Curia 2052 VIII 101r-110r, in Appendix IX

[75]See Schott, Magia universalis, Bamberg: J. M. Schönwetter, 16772 (4 vols.), pars III, pp. 219-228, "Machina II: Glossocomum nostrum, quo talenti potentia movetur Terraqua, si aurea foret". Schott makes no mention of Grienberger's authorship of the problema, but makes only minor changes to the original. Schott's diagram, almost identical to Grienberger's, is reproduced in William B. Ashworth, Jr., Iconography of a new physics, History and Technology, 4, 1987: 267-297, who provides other instances of the iconographic use of earth-moving machinery.

[76]"Dico igitur rotis non amplius 24 et solidem axibus dentatis Globum terrestrem quamuis aureus foret totus, extra centrum propelli posse, uel ab ea potentia, quae Talentum", Problema: Terram auream, Talenti potentia movere, 5 November 1603, APUG Fondo Curia 2052 VIII f.103r, in Appendix IX.

[77]"Magna fuit semper Mathematicorum audacia, magna uis Patres religiosissimi, caeterique Auditores ornatissimi; et tantus in tam paruo numero animus, nihil ut in hac rerum universitate sit vel tenebris obuolutum vel obrutum difficultatibus, quod eorum ingenia effugere potuerit, quod eorum machinas expertum non sit", ibid., on f. 101r

[78] “Verum etiam illa tam amant Mathematicorum imperia, quam suae non oblita dignitatis ac facultatis, rebellia sunt saepe numero illis quibus iure subesse debirent nec mirum. Scilicet ornari malunt a Mathematicis quam parvi et pene nihili fieri a suis”, ibid., f. 101r.

[79]“Quidne igitur misera sint, quae ita misere uestiuntur, misera quae carceribus cohibentur miserrima quae etiam illis ipsis seruire coguntur, a quibus tam male accipiuntur. In terram aratris proscindunt, eamque ut uel pugillum auri extorqueant, penitus euiscerant. Aquam nullis non immunditijs abluendis accommodant; aerem uero ad pistrina et molas, et ignem denique ad coguinas condemnant: nullaque est tam uilis seruitus, quam subire non cogantur. Quare cum talia sint apud Naturales elementa, qualia uidimus, nouum uideri non debet, si apud Mathematicos libenter diuersentur, quibus eorum dignitas curae est, et quorum opera saepius carceribus exuuntur, atque in Regum hortos ac palatia introducuntur", ibid., f. 101v.

[80] “Fulminat Archimedes et placidem et sereno tempore neque is didiciit hanc artem a Jove, sed hausit ex scientijs Conicis”, ibid., ff. 102r-v

[81]“Heronem igitur legat de Spiritualibus, qui diversa aqua ludrica, aeris que nosse cupit. adeat Toletum ubi Tagus summam arcem petit ingenio italico. adeat Tibur ubi garritus auium, ubi mirabiles aquarum strepitus stupebit; excitatos olim arte gallica. et denique si Urbe excedere non libet, montem Quirinalem ascendat et hortos lustret pontificios, in quibus solius aquae decursu, quae aerem subministrat, et rotas mouet, sonis recreabitur organi, nemine ludente”, ibid., f. 102v.

[82] Ibid., ff. 108v-109r. Compare Pappi Alexandrini Mathematicae Collectiones a Federico Comandino Urbinate in Latinum conversae et commentariis illustratae. Pisauri: Apud Hieronymum Concordiam; 1588, ff. 314-5: Problema VI. Propos. X. ... Datum pondus data potentia movere.

[83] “Neque ego hic chordas texuero, aut rotis materiam, locumque machinae praescripsero, ex quo suspendatur, haec enim ut aliena alijs procuranda relinquo”, Problema. Terram Auream, cit, f. 106v.

[84]See Praefatio, [November 1591], APUG Fondo Curia 2052 VIII ff. 67r-70v, in Appendix I below.

[85]See Fieri posse [...] in aliqua mensa lumine, APUG Fondo Curia 2052 VIII ff. 11r-16r, 22v-23r, in Appendix II.

[86] "Hac qui callent Pictores mirabilia omnino efficiunt opera, inter quae non immerito forsan tabella etiam illa extitent, quam ego quidem ipse non vidi, certo tamen exstare ab ijs qui viderunt accepi, estque talis, ut illi qui tam intuentur e directo nihil omnino praeter ferat silvas et alia eiusmodi videant, qui vero eandem ex latere inspiciunt per deformitatum quoddam foramen, ipsum cernant cum Fratro Imperatorem integerrime depictum. Aliud de scenographia quoque adferrem exemplum, nisi ad reliqua adeoque ad finem properarem", in Praefatio, [November 1591], APUG Fondo Curia 2052 VIII f. 70r, Appendix I below.

[87] "In omnibus hisce vel maxime excelluit Archimedes. [...] Per mirabilia vero opera quae efficit illud tandem ab Hierone Rege privilegium est consequutus, ut quidquid tandem affirmaret omnino sibi fides haberetur", ibid. Compare Francesco Barozzi, Proclu Diadochi Lycii in primum Euclidis elementorum librum  commentariorum … libri IIII, Patavii 1560, p. 37.

[88]"Interfuit R.dus Pater noster Generalis cum nonnullis aliis inexpectatus, visusque est rem aprehendisse non sine delectatione, ut ex P. Perierio postea intellexi, qui mecum conquestus fuit quod non invitassem" Grienberger to Clavius (in Naples), Rome; 24 November 1595, in CC  III.1, pp. 142-146.

[89]"Nostis Philosophiam universam, in tria potissimum, distinctam esse Scientiarum genera, Naturalem, Mathematicam, et divinam illam quam vocant methaphysicam. Prior illa res sibi in materia immersas, id est nec re nec ratione abstractas verificat; posterior res a materia prorsus alienos, suo sibi pro obiecti assumit: at vero media illa (quae vel ob hoc quod media est caeteris dici potest esse praestantior) etsi iam reliquae duae res inter se universas distribuisse videantur, inuenit tamen quod in ijsdem rebus ita sibi proprium adscribat, ut suo nihilominus obiecto caeteras nequaquam defraudet", [Problema. De Dimensione Circuli], [27 October - 24 November 1595?], APUG Fondo Curia 2052 VIII f. 126v, in Appendix IV.

[90] On the debate on the epistemological status of mathematics in the Jesuit context, a question which has attracted a great deal of attention from historians, see Paolo Galluzzi, Il "Platonismo" del tardo Cinquecento e la filosofia di Galileo. in Paola Zambelli, Ricerche sulla cultura dell'Italia Moderna. Bari: Laterza; 1973: 37-79, Peter Dear, Discipline & experience: the mathematical way in the scientific revolution. Chicago: University of Chicago Press; 1995 pp. 32-44, A.C. Crombie, Mathematics and Platonism in the Sixteenth-century Italian Universities and in Jesuit Educational Policy. in Y. Maeyama W.G. Daltzer, eds. Prismata: Naturwissenschaftsgeschichtliche Studien (Festschrift für Willy Hartner). Wiesbaden: Franz Steiner; 1977: 63-94. Nicholas Jardine, The forging of modern realism: Kepler and Clavius against the sceptics. Studies in history and philosophy of science. 1979; X: 141-173 and Baldini, Legem impone subactis, (cit.) pp. 45-52.

[91]Giuseppe Biancani, De mathematicarum natura dissertatio una cum clarorum mathematicorum chronologia. Bononiae; 1615 (bound with idem., Aristotelis loca mathematica, 1615), English translation in Paolo Mancosu, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century, New York, Oxford, Oxford University Press, 1996, pp. 178-212

[92]Biancani is recorded as an academician in 1599-1600 (ARSI, Rom. 54 ff. 2v, 12v, 77r, cit. in CC I.2 pp. 18-19).

[93]Grienberger, Problema Mechanicum Circa motus ponderum, [January 1596?], APUG Fondo Curia 2052 VIII 7r-8v (Appendix VI), idem., Problema Circa motus caelorum, APUG Fondo Curia 2052 VIII 111r-117r (Appendix V).

[94]On Clavius's response to homocentric astronomy see James M. Lattis, Between Copernicus and Galileo: Christoph Clavius and the collapse of Ptolemaic cosmology. Chicago and London: University of Chicago Press; 1994, pp. 87-94.

[95]"Habuit proculdubio et Bononiensis illa structura sui delineatorem insignem mathematicum, cuius vigilantia id effectum est, ut Geometria turrim illam inhabitaret", Grienberger, Problema Datis excessibus quibus diameter Quadrati aut figurae, APUG Fondo Curia 2052 VIII 122r-124v, Appendix VII.

[96]De errore qui in denominandis numerandisque diebus in Indicae navigatione commititur, APUG Fondo Curia 2052 VIII 96r-98r, Appendix VIII.

[97] "Dum hic paulisper scribendo subsisto, ecce accurrit qui Clavio nostro dandum Viaticum nunciat, quod etiam hoc vespere, prima noctis hora, accepit. Ne igitur mirere quod intempestivius literas abrumpo: diutius his immorari tanta novitas non sinit. Disces plura ex harum latore, qui est P. Odo Malcotius, qui, Flandriam repetens, scholae mathematicae me iterum alligavit", Grienberger to Galileo, Rome, 5 February 1612,  in OG XI, 272-4, on p. 273

[98] “Et denique, ut brevi absolvam, in paucis illis Numerorum, Figurarumque Descriptionibus, ea contineri affirmabant, quae Expeditioni illi plurimum adiumenti adferre queant, quam nostris hisce temporibus, nova Gygantum Progenies, Machinis novis, & Galileo praeeunte Duce fortissimo aeque ac fortunatissimo, in remotissimas oras, Orbem scilicet octavum, vastissimum, populatissimumque, atque in latissimas reliquorum Planetarum Provincias, iam a biennio, felicibus auspicijs, machinari coepta est”, Grienberger, Catalogus veteres affixarum Longitudines ac Latitudines, conferens cum novis. Imaginum Coelestium Prospectiva duplex. Romae: Apud Bartholomaeum Zannetum; 1612, Sig. A2 verso

[99]"Salutant Dominationem tuam omnes quos toties in Collegio Romano salutavit, et saluto in primis ego, meque D. tuae commendo; et se commendat etiam perspicillum Clavianum, expectatque avide sociari cum Galilaico. Mihi Clavianum sensim consenescere videtur cum Clavio”, Grienberger to Galileo, Roma; 24 June 1611, in OG XI, pp. 130-1.

[100]Galileo to Grienberger, Firenze; 1 September 1611, in OG XI, pp. 178-203.

[101]"Neque mirere quod de tuis sileam: non est mihi eadem quae tibi libertas", Grienberger to Galileo, Rome; 5 February 1613 in OG XI, pp. 479-80.

[102]"Visitai il Padre Gamberger da parte di V.S. et insieme lo salutai in nome suo, il quale rende a V.S. duplicati saluti. Io li domandai quello che gli pareva di questo libro, che già lui haveva visto; e mi disse molto bene, e che in moltissime cose, tanto di questo come di quell'altro delle cose chi stanno sull'acqua, era da quella di V.S."Giovanni Bardi to Galileo, Rome; 24 May 1613, in OG XI,  pp. 512-513.

[103]On the debate about the Gallegianti, see especially Stillman Drake, "The Dispute over Bodies in water", Galileo Studies, Ann Arbor: University of Michigan Press; 1970, pp.159-176, Mario Biagioli Galileo Courtier: The practice of science in the culture of absolutism. Chicago: University of Chicago Press; 1993, Ch.3, pp.159-209 and most recently Francesco de Ceglia, Reazioni romane: L’idraulica galileiana negli scritti di Giovanni Bardi e Giuseppe Biancani, Bari: Laterza, 1997.

[104]Despite the Archimedean conclusions of this work, Galileo's attempts to produce an Archimedean demonstration foundered, due to his assumption that the volume  of the liquid displaced is equal to the submerged bulk of the body. To be consistent with Archimedes, he should have assumed that the volume  of liquid displaced is equal to the bulk of the body below the original level of the liquid. This slip meant that Galileo ended up using the method of the Pseudo-Aristotelian mechanical problems. See William R.Shea, Galileo's discourse on floating bodies: Archimedean and Aristotelian elements, Actes du XIIe Congrès International d'Histoire des Sciences, 1968, Paris: Blanchard;1971, IV, pp. 149-153.

[105]Bardi to Galileo, Rome 24th May 1613, cit.

[106] BNR, Fondo Gesuitico 1186,  ff. 108r-114v. See Baldini, Legem impone subactis,cit. pp. 155-182 and Appendix X to the present article. Although Baldini suggests that this Problema is probably due to Odo van Maelcote there is substantial evidence that it was composed by Grienberger. The evidence is reviewed in the introduction to appendix X.

[107] OG III, 1, 291-298. While there is evidence that Maelcote recited this oration, there is no independent evidence that he was responsible for its composition. The copy preserved in the Vatican library (BAV Barb. Lat. 231, ff. 177r-182r) is not in Grienberger’s hand.

[108] “[D]ovendosi fare uno di questi problemi et essendo stato destinato a me, mi domandò il Padre Ghambergier di che cosa volevo farlo, proponendomi alcune altre cose; hora io gli dissi che haria desiderato di fare di qualche materia simile a questa, e cosi lui prese questa, che non credo che sii per apportarli pocho gusto, perchè è tutta conforme al suo parere, anzi quello istesso, con l’aggiunta di quelle doi esperienze che non possono se non conferire alla sua sentenza. E mi ha detto il Padre Ghambergier, che se non havessi hauto rispetto ad Aristotile, al quale loro per ordine del Generale non possono opporsi niente, ma lo devono sempre salvare, haria parlato più chiaro di quello che ha fatto, perchè in questo lui ci sta benissimo; e mi diceva che non è meraviglia che Aristotile sii contro, perché anchora si è ingannato chiarissimamente in quello che V.S. anchora mi diceva una volta di quei doi pesi che caschano prima o poi”, Bardi to Galileo, Rome, 20 June 1614, OG XII p. 76.

[109] See OG IV, p. 195

[110] De Ceglia, op. cit., p. 44.

[111] See Appendix XV

[112] “Sed insuper videat provincialis diligenter et efficiat, ut opiniones, quae docentur in philosophia, theologiae subserviant, nostrique philosophi unum sequantur Aristotelem, ubicunque illius doctrina nihil a catholica veritate dissidebit”, Claudio Acquaviva S.J., Ordinatio pro soliditate et uniformitate doctrinae, ad omnes praepositos provinciales S.I., Rome, 14 December 1613, in MP VII, pp. 660-664, on p. 663. On the issue of uniformity and solidity of doctrine, see Baldini, Legem impone subactis, ch. 1 and 2.

[113] “Additio illa ad Librum P. Blancani, De his quae moventur in aqua, non videtur edenda: cum sit impugnatio, non autem (ut titulus prae se fert) explicatio Aristotelis. Neque conclusio, aut rationes, quibus illa probatur, sint Autoris, sed Galilaei: satisque fuerit eas apud Galileum legi. Transcribi enim in libros nostrorum inventa Galilaeu, praesertim quibus impugnat Aristotelem, nec videtur decens, nec expediens”, Giovanni Camerota, censure of G. Biancani, Brevis tractatio de iis quae moventur in aqua, 16 February 1615, ARSI FG 662 f. 166r, published in Baldini, Legem impone subactis, cit., p. 232.

[114]"Ci saranno, oltre alle dipinte e stampate, tutte queste esperienze in sur un tavolino, acciò si vegghino da tutti, di maniera che non potranno neghare quello che vegghono congll'occhi", Bardi to Galileo, Rome 20th June 1614, OG XII, p.76.

[115]On Valerio, who left the Society of Jesus in 1580, but maintained close contact with Clavius see Ugo Baldini and Pier Daniele Napolitani, Per una biografia di Luca Valerio. Bollettino di Storia delle Scienze Matematiche. 1991; Anno XI(1): pp. 3-157.

[116]Francesco Stelluti to Galileo, Rome, 28 June 1614, in OG XII, p. 78.ref - EXACT REF]

[117] “[P]enes vos  erit quicquid victoriae, quicquid trophaei veritatis, ex hac nostra dissertatione, sperandum est. Materiam abunde suppeditabit Experientia, quae ut gravissimae pugnae causa exbibit, ita par est, primum ut ipsa locum hac in velitatione obtineat, militem ipsa cogat, armis instruat, ac proemijs invitet; quocuo ad fortiter pugnandum adhortata est, prima in acie, ipsa prima consistat”, De ijs quae vehuntur in aquis, APUG Fondo Curia 2052 VIII 47r-54r (Appendix XV), on f. 47r.

[118] Francisci Aguilonii e societate Iesu Opticorum libri sex. Philosophis iuxta ac Mathematicis utiles. Antverpiae, ex officina Plantiniana: Apud Viduam et Filios Io. Moreti; 1613.

[119] On Rubens’ illustrations see August Ziggelaar, François de Auguilón S.J. (1567-1617). Scientist and Architect. Bibliotheca Instituti Historici S.I., Vol. 44. Rome: Institutum Historicum S.I.; 1983. On his relationship to the Jesuit emblem-book tradition through his master Otto Vaenius, see Charles Parkhurst, Aguilonius' Optics and Rubens' Color. Nederlands Kunsthistorisch Jaarboek. 1961; 12: 35-49. Anatomical texts using putti may also have provided Rubens with a model. On the Jesuit emblem book tradition in general see Karl Josef Höltgen, Emblem and meditation: Some English emblem books and their Jesuit models. Explorations in Renaissance Culture. 1992; 18: 55-91, Loretta Innocenti, Vis eloquentiae: Emblematica e persuasione. Palermo: Sellerio; 1983 and Mario Praz, Studi sul Concettismo. Milano: Soc. Editrice "La Cultura"; 1934, especially ch. 4, pp. 134-164 (English translation: Studies in seventeenth century imagery. Rome: Edizioni di Storia e Letteratura; 1964). The author of this study points out that the Jesuits transformed eros into amor divinus, turning profane love emblems into instruments of religious propaganda.

[120] For a contextualised appraisal of the Jesuit rhetorical tradition, the most comprehensive study remains Marc Fumaroli, L'âge de l'éloquence: Rhétorique et res literaria de la Renaissance au seuil de l'époque classique. Geneva: Librairie Droz; 1980.

[121] Jeronimo Nadal, Evangelicae historiae imagines, Antwerp: Martin Nutius, 1593. On this work see Pierre-Antoine Fabre, Ignace de Loyola: Le lieu de l’image, Paris: Vrin, 1992, and the Spanish critical edition, Jeronimo Nadal, Imagenes de la Historia Evangelica, con un estudio introductorio por Alfonso Rodriguez G. de Ceballos, Barcelona: Ediciones El Albir, 1975.

[122] Galileo Galilei, Discorso … intorno alle cose, che Stanno in sù l’acqua, ò che in quella si muovono, Firenze: Cosimo Giunti, 1612, in OG IV pp. 57-141, on p. 65: “La principale è stato il cenno dell’A.V., avendomi lodato lo scrivere come singolar mezzo per far conoscere il vero dal falso, le reali dall’apparenti ragioni, assai migliore che ’l disputare in voce, dove o l’uno o l’altro, e bene spesso amendue che disputano, riscaldandosi di soverchio o di soverchio alzando la voce, o non si lasciano intendere, o traportati dall’ostinazione di non si ceder l’un l’altro lontani dal primo proponimento, con la novità delle varie proposte confondono lor medesimi e gli uditori insieme”.

[123] “Sunt res aliae alijs graviores, leviores aliae, et quaedam eiiusdem gravitatis. sunt etiam bilances, trutinae, et staterae, quibus passim pondera ponderibus conferuntur vulgaria ille quidem sed a quibus neqe Philosophia neque mathematica abhorreat”, Anon. [Christoph Grienberger], De ijs quae vehuntur in aquis, loc. cit.

[124]Gravitas cylindri secundum meam observationem in aere quidem est Lib: 1. Un. 11. 1/4.1/8.1/128 in aqua vero est lib. 1. Unc. 8 1/8.1/16.1/64. vel in partibus 128 Unciae in aere partium 2993 in aqua partium 2586 et quia diff[erenti]a sunt partes 407 ideo cylindrus aquae cylindro stanni aequalis erit partium 407 atque ideo proportio gravitatis stanni ad gravitatem aquae erit ut 2993 ad 407”, APUG FC 2052 VIII f.130r. A series of experimental notes in Grienberger’s hand can be found in APUG FC 2052 VIII f.130r-132v. On Ghetaldi and Villalpando’s investigations of specific gravities, see P.D. Napolitani, La Geometrizzazione della realtà fisica: il peso specifico in Ghetaldi e in Galileo. Bolletino di Storia delle Scienze Mathematiche. 1988; VIII: pp.139-237.

[125] “[I]mmo ne cylindri quidem figura necessaria est, sed prorsus arbitraria ut vel hinc iterum constet, in similibus experimentis figurae resistentiaeque medij nullam prorsus rationem habendam esse”, De ijs quae vehuntur in aquis, cit.,  f. 51r.

[126] Bardi to Galileo, Rome, 2 July 1614, OG XII, pp. 79-80.

[127] Cesi to Galileo, Rome, 16 August 1614, OG XII, pp. 95-96.

[128] Stelluti to Galileo, Rome, 2 August 1614, OG XII, pp. 90-91

[129] Bardi to Galileo, Rome, 2 July 1614, OG XII, pp. 79-80.

[130] G. Bardi, Eorum quae vehuntur in aquis experimenta a Ioanne Bardio Florentino ad Archimedis trutinam examinata, IX. Kalend. Iul. Anno Domini M.DC. XIV. Romae, ex Typographia Bartholomaei Zannetti. M.DC. XIV. Even the title of the book, while giving the date of the original recital, avoided mentioning that it took place in the Collegio Romano.

[131] “Experientiam de Voce adferam (nam, ut video, subtilitatum haec arena est) quam nuper semotus gravioribus studijs praeclaram, distinctam & eloquentem infudi statuae,  non quidem ex aere, aut marmore solidae, sed gypsatae, quâ Vocis tortuosa receptacula, velut alveo inclusa, sonorum percussiones acciperent, redderentque felicius. Verba itaque immisi in hunc Vocis ductum per respirationum interpuncta, mox alia & alia post similia intervalla spiritali machinae infudi; tum vocis aditum fortiter occlusi, tandemque post diverticula, inflexiones varias, atque impedimenta quasi iuvantia, ad ipsum caput & ora Statuae pervenit oratio; verborum quippe vis acuta, successioque spirituum, fauces quam expeditissime, linguamque mobilem, ad syllabarum varietates movebant. At quantum mihi videor defecisse a meis! qui sideribus coaequales, subrident forte suum Grenibergium e gypatis lateribus studiose formantem voces”, George Fortescue, Feriae Academicae. Auctore Georgio de Forti Scuti Nobili Anglo. Duaci: Officina Marci Wyon sub signo Phoenicis; 1630, pp. 140-145.

[132] See G. de Sepi, Romani Collegii Societatis Iesu Musaeum Celeberrimum, Amsterdam: Jannson-van Waesberghe; 1678 p. 60 and Kircher, Phonurgia nova, Campidoniae: Dreherr, 1673, pp. 112-113.