Abstract
When the Jesuits began to teach mathematics, they adopted the existing European curriculum which included Sacrobosco’s Sphaera. Christoph Clavius, the most influential Jesuit mathematician, published a commentary on the Sphaera in 1570 which was widely used. Its publication also marked a change in publication policy by the Roman Jesuits. As the Jesuits prepared a uniform curriculum for the Society’s schools in the 1580s and 1590s, Clavius offered a comprehensive mathematics curriculum and urged the Society to teach more mathematics and to train more Jesuit mathematicians. But some Jesuit philosophers rejected mathematics as unscientific. The Ratio Studiorum of 1599 included the Sphaera but did not expand Jesuit mathematical education. Jesuits continued to teach the Sphaera and to use Clavius’ commentary until about 1650.
Keywords
 Sacrobosco
 Sphaera
 Christoph Clavius
 Benet Perera
 Jesuits
 Society of Jesus
 Mathematics
 Astronomy
 Natural philosophy
 Ratio studiorum
 Roman College
 Vittorino Eliano
 Giovanni Battista Eliano
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1 Introduction
Johannes de Sacrobosco’s (1195–1256) Sphaera was a major text in Jesuit mathematical education in the first century of the Society.^{Footnote 1} And Christoph Clavius (1538–1612) , the leading Jesuit mathematician, published a commentary on it that one scholar calls “the amplest synthesis of elementary astronomy available in the fifty years between 1570 and 1620.”^{Footnote 2}
The Jesuits were not the first to teach Sacrobosco’s Sphaera. Teachers and students across Europe taught or learned from it, because it was part of Renaissance mathematical and astronomical education, which were viewed as one whole discipline. Renaissance mathematics included astronomy and sometimes astrology. And the position of mathematics in the curriculum was different in the collegiate universities of northern Europe and Spain from its position in Italian law and medicine universities. A collegiate university was a university dominated by colleges, which were combination teaching and residence institutions that concentrated on teaching humanities and philosophy to young students pursuing Bachelor of Arts and Master of Arts degrees. Paris and Oxford were famous collegiate universities. Collegiate universities also taught a great deal of theology, but little law and medicine. Mathematics instruction in collegiate universities was part of the broad collection of studies leading to the Bachelor of Arts and Master of Arts degrees. Hence, many teachers taught, and practically all students learned, a little mathematics. But collegiate universities might or might not have had a professor of mathematics.
Italian universities concentrated on teaching law and medicine to older students pursuing doctorates in those disciplines. All larger Italian universities also had professors of mathematics who lectured on mathematics and astronomy at an advanced level. Galileo Galilei (1564–1642) at the University of Padua is the best known. But a limited number of students attended mathematics lectures, because they were not a prerequisite for law or medicine doctorates. Nevertheless, some medicine students attended mathematics lectures in order to learn about medical astronomy and astrology, on the belief that the movements of heavenly bodies influenced the progress of a disease and, properly understood, could tell the physician when to apply a therapy. And some students, whatever their major interest, were fascinated by the heavens. Although collegiate and Italian universities approached instruction in mathematics differently, one thing was the same. Practically every mathematics course included some use of Sacrobosco’s Sphaera or a commentary on it with additional information and speculation on the movements of heavenly bodies.
2 The Early Years of Jesuit Education
In 1548, the Jesuits opened their first school in Messina, Sicily. The Jesuits had no master plan when they began and certainly not for mathematics. Nevertheless, they moved unevenly toward a tripartite school structure. The lower school taught Latin grammar, the humanities, a little Greek, and rhetoric, based on the ancient classics. This was the Renaissance studia humanitatis curriculum. Next came an upper school teaching Aristotelian philosophy by lecturing on individual texts of Aristotle (385–323 BCE) rather than by subject matter.^{Footnote 3} For the vast majority of students, philosophy ended their Jesuit schooling, as they left for employment or university study. The few remaining students—mostly Jesuits and other clergymen—studied Scholastic theology for three or four years and were ordained priests. Scholastic theology had a wellestablished tradition, which the Jesuits adopted and altered for their purposes.
The first Jesuits were uncertain about the content and organization of philosophical instruction. Because all ten founding Jesuits, plus other key early Jesuits, had studied at the University of Paris, they looked to it for guidance. The preparation for the Bachelor of Arts degree at Paris consisted of lectures on logic, the Physics of Aristotle, metaphysics, moral philosophy, and other topics, plus lectures “on some mathematical books, especially the Sphaera of Sacrobosco” (Schurhammer 1973, 144).^{Footnote 4} This was a broad but not sharply focused program that influenced Ignatius of Loyola (1491–1556) , who had studied at Paris for seven years. In the section on universities in the Jesuit Constitutions adopted by the Society in 1558, Ignatius wrote: “Logic, physics, metaphysics, and moral philosophy should be treated, and also mathematics, with the moderation appropriate to the end which is being sought” (Constitutions 1996, pt. 4, ch. 12, 451, 180).^{Footnote 5} The view of Ignatius echoed the position of mathematics in collegiate universities. Ignatius endorsed mathematics, but provided no further guidance.
Jesuit schools in their first twenty years taught mathematics irregularly, but did teach Sacrobosco’s Sphaera at least part of the time. For example, in 1555 the University of Perugia appointed a young Jesuit to be extraordinary professor of rhetoric and Greek without stipulating what he should teach. He surprisingly lectured on Sacrobosco’s Sphaera for all or part of the academic year 1555–1556 (Springhetti 1961, 109–110).^{Footnote 6} The Jesuit school at Cologne taught the Sphaera in 1557 and 1561. So did Jesuit schools in Coimbra in 1562 and Évora in 1563 (MP, III, 530, 547, 319, 591). Of course, the Jesuits taught other texts as well. In 1548, the Messina school taught De mundi sphaera (1542) of Oronce Finé (1494–1555) (MP, I, 26).
In the 1560s and 1570s, Jesuit schools moved toward a more structured threeyear cursus philosophicus of logic, natural philosophy, and metaphysics based on Aristotelian texts. But they continued to pay limited attention to mathematics. In the late 1570s, there were twentyeight Jesuit schools in Italy, of which seven taught philosophy. Only two, the Collegio Romano (the leading Jesuit school founded in 1551, with accomplished Jesuit scholars as teachers, and the broadest curriculum) and the Milan school offered a mathematics course. The situation was similar in northern Europe (Grendler 2004, 488–499).^{Footnote 7} This was the state of mathematics when Christoph Clavius began to teach mathematics and to train future mathematics teachers.
3 Clavius: The Academy of Mathematics and Sphaera Commentary
Clavius was the most influential Jesuit mathematician from 1570 until at least 1620. He was born in the city of Bamberg, capitol of an imperial princebishopric, or near it, in 1538. His name may have been a Latinized version of Clau or Schlüssel.^{Footnote 8} Nothing more is known about his early life until February 1, 1555, when he became a Jesuit novice in Rome. Ignatius of Loyola himself accepted him. The normal next step would have been to finish his novitiate and then study philosophy and theology at the Roman College. But in the autumn of 1555, Ignatius sent him to the University of Coimbra to boost the Jesuit presence there. In 1555, the Jesuits were given control of the Colégio des Artes, the most important part of the university; it was the first time that the Jesuits secured a strong institutional position in a university. Consequently, Ignatius sent some excellent Jesuit scholars to teach and some promising students to study at Coimbra.
However, the Colégio des Artes of Coimbra lacked a mathematics teacher; whether Clavius studied with the sole mathematics professor of the university, Pedro Nuñez (1502–1578), who was hostile to the Jesuits, is unknown. Clavius wrote that he was selftaught; if he meant that literally, he taught himself extremely well. He was well acquainted with the works of all the important ancient, medieval, and Renaissance mathematicians and astronomers.
Clavius was recalled to Rome in 1560 to study theology at the Roman College. He was appointed mathematics lecturer there in 1563 and spent the rest of his life in Rome except for short trips. Clavius lectured on mathematics from 1563 to 1571, possibly in the academic year 1575–1576, certainly in 1577–1578, and possibly other years in the 1580s for which records are missing. But he stopped by 1590 (Baldini 1992, 568).^{Footnote 9} In the academic year 1564–1565, he lectured on Sacrobosco’s Sphaera at an advanced level and prepared a first draft of his commentary on the Sphaera (Baldini 2003, 51, 70). He became the key figure in the papal commission that prepared the reformed Gregorian calendar of 1582. His reputation soared.
In 1563, Clavius assumed leadership of an academy of advanced mathematical studies at the Roman College.^{Footnote 10} While it had begun in 1553 under a previous mathematics lecturer, Clavius made it into the most important center for mathematical studies in Europe. In Renaissance Italy, the word “academy” brings to mind informal associations in which working writers and dilettante nobles met periodically to discuss literature and enjoy each other’s company. Clavius’ academy was nothing of the sort. It was a group of men engaged in intense study of a range of advanced mathematical topics under Clavius’ tuition and leadership. Numbers were small, ten or fewer, most often about five. A large majority were Jesuits; a few were laymen. The primary purpose of the academy was to train the members in a broad range of mathematical skills to serve their future needs. Typical members of the academy included future Jesuit mathematics teachers, who learned at the academy what they would teach, and future Jesuit missionaries who brought European mathematics to distant lands. The most famous of the latter was Matteo Ricci (1552–1610). While studying philosophy at the Roman College from 1572 to 1577, he attended the public mathematics lecture course in 1575–1576 taught by either Clavius or another Jesuit. He was also a member of Clavius’ mathematical academy, possibly in the summer of 1576 and certainly in the academic year 1576–1577. In China, Ricci translated several of Clavius’ mathematical works into Mandarin, including his commentary on Sacrobosco’s Sphaera (Peking in 1607) (Baldini 2013, 138–147, 153–154).^{Footnote 11} Most Jesuit academy members studied for one or two years, then returned to their home provinces. However, Christoph Grienberger (Hall, Tyrol 1564–1636 Rome), who lived in Rome and often taught the public mathematics lectureship of the Roman College, was a member of the academy for about twenty years.
Clavius taught in the academy, assisted by other Jesuit academicians who served as research assistants in his later years. Clavius’ major mathematical publications were largely the products of his academy teaching and research, rather than his public lectures in the Roman College. Young members of the academy occasionally taught in the academy in order to demonstrate their mastery of a body of material, or to present the results of their research. Much of the research by members began in the academy and was finished and published years later. The academy had its own library of astronomical and mathematical texts separate from the main library of the Roman College. The academy also served as a center for the exchange of scientific information, as the academy disseminated its results, received news from abroad, and welcomed visitors.
Clavius published numerous mathematical works, including extensive commentaries on Euclid’s Elementa, and books on practical arithmetic, algebra, practical geometry, sun dials, the astrolabe, and cosmography.^{Footnote 12} The first and most often reprinted was Christophori Clavii Bambergensis, ex Societate Iesu, in sphaeram Ioannis de Sacro Bosco commentarius (Sacrobosco and Clavius 1570). It was probably the most used postmedieval book on astronomy (Baldini 1999a, 18). The Sphaera database lists twentyone subsequent European editions.^{Footnote 13}
Clavius’ book is often called a textbook. If so, it was a textbook intended for teachers, practicing astronomers, and advanced students. Like many other Renaissance authors, Clavius used the commentary format because Sacrobosco’s brief text offered a familiar Ptolomaic framework. It enabled Clavius to discuss issues that had risen over the centuries, and to add new material, including his own astronomical observations and insights. Like Sacrobosco, Clavius accepted a geocentric universe throughout his life. But so did practically everyone else at the time. And Ptolemaic astronomy supported by the latest astronomical observations provided much useful information. Clavius’ work was comprehensive, learned, and uptodate. It is not surprising that “contemporaries and modern historians have judged Clavius’ Sphaera to be the greatest of all Sphere commentaries.”^{Footnote 14}
4 Clavius’ Publisher and Jesuit Printing Policy
The publisher was a surprise. Vittorio Eliano (1528–1581)—just arrived in Rome and littleknown—published the first edition of Clavius’ commentary. Behind this development was a change in the attitude of the Roman Jesuits toward printing and publishing.
In the last one to two years of his life, Ignatius of Loyola (died July 31, 1556) keenly wanted the Jesuits of the Collegio Romano to have their own press. He wanted them to be able to print the works of the teachers at the Collegio Romano, to produce inexpensive books for students, and to publish editions of ancient authors purged of morally objectionable passages for young readers. There were some misadventures. Ignatius ordered some typeface to be cast in Venice, but upon arrival in Rome, it proved to be defective. A German printer was hired, but it was discovered that he did not read Latin. Jesuit students were pressed into service as correctors (Villoslada 1954, 44–46; Garcia Villoslada 1990, 1001–1002).^{Footnote 15}
Despite the setbacks, beginning in 1555 the words “Romae: in aedibus Societatis Iesu,” rendered into “Tipografia del Collegio Romano” by the Universal Short Title Catalogue (USTC), began to appear on the title pages of modest inhouse publications. Many were sixteenoreighteenpage booklets of theses that a student at the Roman College intended to defend in a public disputation.^{Footnote 16} The Tipografia del Collegio Romano volumes often indicated that “Blado ,” that is, the firm of Antonio Blado (1490–1567), Rome’s most prolific and important publisher at that time, had done the printing.^{Footnote 17}
Despite the urging of Ignatius of Loyola, the Jesuits were not certain that printing and selling books were an appropriate ministry for a religious order. After Ignatius’ death, the First General Congregation of the Society met from June 19 to September 10, 1558, with twentyseven senior Jesuits, including the five remaining members of the ten founders, in attendance. Its first task was to elect a new superior general, which was dispatched by electing Diego Laínez (1512–1565), who had been vicar general since the death of Ignatius. It also debated and passed 168 decrees of great and small importance.
Decree 105 After the Election read “The printing and sale of books is left to Father General’s judgment.” The official summary of the congregation’s deliberations stated the questions that were discussed, and the resolution.

Is it tolerable or even praiseworthy in the Society to print and sell books for the sake of the general good that would ensue? Or rather should it be forbidden, lest we appear to be engaging in business? It was decreed that nothing should be decided in favor of either side of the question, but rather that it should be left to the discretion of the superior general. It seemed worthy of consideration, however, so that nothing may be done that would damage the [vow of] poverty or the institute of the Society (For Matters of Greater Moment 1994, 96).
In other words, the participants at the General Congregation meeting were divided. So, they left the decision to Laínez. In practice, the Jesuits carried on as before. The Tipografia del Collegio Romano published lists of theses to be disputed and house publications, including college rules, the Constitutions of the Society, the Spiritual Exercises of Ignatius, and the Annuae litterae Societatis Iesu, the annual reports of Jesuit activities around the world distributed to Jesuit colleges. The vast majority of these publications were works of fewer than one hundred pages in octavo format. According to USTC, the Tipografia del Collegio Romano published 136 editions between 1556 and 1635, but only four after 1617.^{Footnote 18} It did not publish significant scholarly and pedagogical works written by Jesuits at the Roman College or elsewhere.
Then in 1570, Vittorio Eliano published Clavius’ commentary on the Sphaera. Eliano was a very surprising choice. A Jew born in Rome in 1528 with the first name of Yosef, he was the son of a merchant and the grandson on his mother’s side of Rabbi Elia Levita (1469–1549), a famous Hebrew grammarian, scholar, and poet. Yosef learned the printer’s trade at an early age. While living in Isny im Allgäu, a free imperial city in Württemberg, Yosef and his younger brother Elia (see below) assisted Paul Fagius (Büchelin, 1504–1549), a Protestant Hebraist and printer. Fagius collaborated with Elia Levita to print twelve editions of Latin and Hebrew works in 1541 and 1542, including texts and studies of the Old Testament in Hebrew and Latin and a HebrewGerman grammar (Clines 2020, 208 n. 31). Fagius later taught Hebrew and biblical studies at Strasbourg and the Universities of Heidelberg and Cambridge. Yosef next moved to Venice where he converted to Catholicism between 1544 and 1546 and changed his name to Vittorio Eliano. He then became the printer and collaborating publisher of some landmark Hebrew titles in Venice, Cremona, and elsewhere in northern Italy. He also censored Hebrew books in these cities (Casetti Brach 1993, 1997). He moved to Rome in 1568 or 1569 and began to publish under his own name in 1569. His first publication was an expurgated version of the poems of Horace for use in Jesuit schools (Quinctus Horatius 1569).
Eliano’s publication of the Clavius commentary on the Sphaera in 1570 carried a comprehensive papal privilege dated January 12, 1569.^{Footnote 19} It granted to Vittorio Eliano and unnamed associates the exclusive right to publish a long list of potential major and lesser works by Jesuit authors. The papacy granted to Vittorio Eliano the right to print and publish the following works (here listed in the order found in the privilege and identified or explained in English).

Francisco de Toledo, commentary on the Summa Theologica of Thomas Aquinas

Francisco de Toledo, Instructionem sacerdotis sive casus conscientiae

Francisco de Toledo’s commentary on Aristotle’s De anima

Clavius’ commentary on the Sphaera

Jesuit letters from the Indies

Selected epigrams

Selected orations

The same from Cicero, Terence, Plautus, and Horace “cleansed of all indecency”

A catena (chain or series) of (verses from the) Gospels by Doctor Emanuele of the Society of Jesus.^{Footnote 20}
The papacy granted to Eliano and his associates exclusive rights to many titles, some precisely indicated, others generic and vague. The extended list of titles was unprecedented. Otherwise, the terms were similar to those of a large majority of papal privileges issued in the sixteenth century. The privilege was for ten years. The texts were subject to religious censorship by the Inquisition or the Master of the Sacred Palace in Rome (the pope’s theologian, usually a Dominican, whose duties included prepublication book censorship in Rome). No one else was allowed to publish these works in Latin or Italian without the express permission of Eliano, nor could publication rights be transferred to others without his permission. The privilege was in force in all areas in Italy and beyond. Violators were subject to automatic excommunication and a fine of 500 gold ducats to be paid to the papal treasury. The justification for the privilege was that Eliano and his associates were printing these books “for the general and universal benefit of students” (ad communem omnium studiosorum utilitatem) and therefore deserved compensation for their expenses and labor. This was a variation on “the common good” justification frequently found in papal privileges.^{Footnote 21} In short, the terms of the privilege were unexceptionable except for the long list of potential titles.^{Footnote 22}
The expansive privilege argues that the Roman Jesuits had decided to move from a small inhouse publishing operation to working with an external commercial press for the purpose of publishing major works of scholarship, the majority prepared by Jesuits teaching in the Roman College. The obvious choice for such a publisher would have been Antonio Blado, had he not died in 1567, and the Jesuits did not make an arrangement with his heirs. Instead, they chose a publisher who had just arrived in Rome and was known for publishing Hebrew books. Why Vittorio Eliano?
Giovanni Battista Eliano (1530–1589), Vittorio’s younger brother, may have brought the Jesuits and Vittorio together. Giovanni Battista Eliano was born a Jew with the name of Elia in Rome in 1530. Elia lived in Italy, then in Isny im Allgäu where, like his brother, he assisted Paul Fagius (Clines 2020, 31–32). He next lived in Constantinople, Cairo, and elsewhere, and was intended to be a merchant like his father. Then his family sent him back to Venice to try to persuade Vittorio to return to Judaism and move to Cairo. Instead, Elia met André des Freux (ca. 1515–1556), an important early Jesuit, and also became a Catholic in 1551. Elia took the Christian name Giovanni Battista Eliano; he was also sometimes called Giovanni Battista Romano.^{Footnote 23} He immediately joined the Society of Jesus and followed des Freux to Rome, where he studied philosophy and theology at the Roman College (Ioly Zorattini 1993, 472–473; Libois 2001, 2:1233; Clines 2020, 25–42).
Literate in Hebrew, Arabic, Turkish, Latin, German, Italian, and Spanish, and intensely spiritual, Giovanni Battista Eliano became a valued member of the Jesuit community in Rome and useful to two popes. Giovanni Battista Eliano is best remembered for his yearslong religious and diplomatic missions undertaken for the papacy to Egypt and Lebanon in an effort to bring Coptic Christians into union with Rome, which was unsuccessful, and to promote closer relations with the Maronite Church, where he had considerable success.^{Footnote 24} During these missions, he put his knowledge of printing to use by translating and printing books and by working to establish a press in Rome capable of producing books in Arabic and Syriac for Maronite Christians (Clines 2020, 31–32, 122–123, 142–145, 147, 157, 171).
When in Rome, Giovanni Battista Eliano taught at the Roman College. Although still studying philosophy and theology, and not ordained a priest until 1561, he began to teach Hebrew in the Roman College in 1552 or 1553. He continued to teach Hebrew to about 1561, from 1563 to 1570, and again in the academic year 1577–1578. Pius IV (1499–1565; ruled December 25, 1559–December 9, 1565) decided to promote the knowledge of Arabic for missionary reasons and to facilitate contacts with eastern Christians, and he recruited Eliano to this cause. He ordered the Roman College to teach Arabic. So Eliano added teaching Arabic to his duties in the academic year 1563–1564, and he continued to teach Arabic there at least through the academic year 1566–1567, and probably longer.^{Footnote 25} Pius IV also asked Eliano to write an Arabic version of a short Catholic profession of faith designed to persuade eastern Christians to join Rome, and this was published in 1566 by the Tipografia del Collegio Romano (Fidei orthodoxae confessio 1566).^{Footnote 26} And he asked Eliano to write an account of the Council of Trent in Arabic, which remains in manuscript.^{Footnote 27} Pius IV also wanted a press capable of printing an Arabic New Testament, grammars, and dictionaries. After his long trips to the Middle East, Giovanni Battista Eliano returned to Rome where he died in 1589 (Ioly Zorattini 1993; Libois 2001).
In short, Giovanni Battista Eliano was trusted by popes and had the attention of his Jesuit superiors; he had considerable experience with printing; and he was multilingual. He was in a position to bring his brother’s printing expertise to the attention of the papacy and his Jesuit superiors. Finally, perhaps a common language helped Clavius and the Eliano brothers to bond. Giovanni Battista Eliano learned German as a child in Isny im Allgäu and Vittorio likely did the same, while Clavius came from Bamberg (Clines 2020, 31–32). Clavius and Giovanni Battista Eliano were probably the only German speakers teaching at the Roman College, which was filled with Italian, Spanish, and Portuguese Jesuits.
The comprehensive papal privilege granted to Vittorio Eliano meant that the Jesuits had decided to trust an external commercial press to publish scholarship emerging from the Roman College, plus some books for students. It was a delayed answer to the question that the General Congregation of 1558 left up to the general: Should the Jesuits do their own publishing? However, the external press was not far outside the Society, because it was run by the brother of a Jesuit.^{Footnote 28} It is also likely that Vittorio Eliano was chosen for his ability to publish in Hebrew and to handle complex typographical matters, such as the planetary diagrams in Clavius’ book. The decision was not a complete break with past policy, because the Tipografia del College Romano continued to publish books intended for a limited Jesuit readership.
However, Vittorio Eliano did not publish very many of the works for which he held a privilege. The 1569 privilege stated that Vittorio Eliano would publish three works of Francisco de Toledo (Córdoba 1532–1596 Rome, cardindal from 1593), a prominent Jesuit philosopher and theologian at the Roman College for many years. Eliano did not publish any of them. But it was not his fault. Toledo’s commentary on Aristotle’s De anima appeared in 1574/1575, published in Venice by Luc’ Antonio Giunta II (1540–1602) (Toledo 1575; Camerini 1962–1963, II, nos. 769, 774) (Chap. 8).^{Footnote 29} Why this happened is unknown. Eliano often could not publish a work because the author did not finish it. Toledo’s famous casuistry manual, De instructione Sacerdotum, was only published posthumously in 1599 in Milan, Cologne, and Lyon (Toledo 1599a, b, c; Sommervogel 1960, VIII, 70–71).^{Footnote 30} And his commentary on the Summa Theologica of Thomas Aquinas (1225–1274) was not published until 1869 in four volumes (Donnelly 2001, 4:3808).^{Footnote 31} Vittorio Eliano published only two of the many volumes that the papal privilege licensed him to publish.
Vittorio Eliano did publish other Jesuit scholarship, including Francisco de Toledo’s work on Aristotelian logic in 1569 and 1572 (Toledo 1569, 1572), three complete and partial editions of the Jesuit Constitutions in 1570 (Constitutiones 1570a, b, c), and a Latin grammar manual of Manuel Álvarez (1525–1583) in 1572 (Alvarez 1572). Eliano’s last publication of a Jesuit work was Juan de Polanco’s (1517–1576) Methodus ad eos aiuvandos, qui moriuntur. Roma, apud Vittorio Eliano, 1577 (Polanco 1577), which offered advice and useful texts to those comforting the dying. Polanco was a very influential Jesuit who served as secretary to Ignatius of Loyola and two subsequent superior generals, and his book went into many editions plus translations. Overall, ten of the thirty works that Vittorio Eliano published in Rome between 1569 and 1577 were Jesuit texts. In 1578, he began to collaborate with Francesco Zanetti (1530–1591); they published three editions of the Hebrew Bible (1578, 1580, and 1581), and another Jesuit work, Robert Bellarmine’s (1532–1621) Hebrew grammar. Nothing more is heard of Vittorio Eliano after 1581; he probably died in 1582 (Casetti Brach 1993, 1997).^{Footnote 32}
Domenico Basa (1500–1596), and Francesco and Luigi Zanetti (fl. 1590–1616) published the books of Clavius and other Jesuits for the rest of the century and beyond. In 1581, Domenico Basa and Francesco Zanetti published and printed a revised second edition of Clavius’ commentary on the Sphaera (Sacrobosco and Clavius 1581). In 1585, Domenico Basa published the revised third edition (Sacrobosco and Clavius 1585). According to the USTC, Domenico Basa published and/or printed 125 Roman editions between 1579 and 1596 when he died, of which ten percent (thirteen) were books written by Jesuits. Again, according to the USTC, Francesco Zanetti published 219 Roman editions of which seventeen percent (thirtyeight) were authored by Jesuits.^{Footnote 33} Luigi Zanetti published 203 Roman editions between 1591 and 1606, of which twentyfive percent (fiftyone) were authored by Jesuits.
Most of Domenico Basa’s Jesuit editions were works of Jesuit Latin scholarship including instructional manuals, which was the original purpose of publishing with Vittorio Eliano’s press. But far less than half of the Jesuit editions published by Francesco Zanetti and Luigi Zanetti consisted of works in Latin. Their most frequent Jesuit publications were Italian translations of letters from the Oriental missions (ten by Francesco and thirteen by Luigi), which were probably read by many readers. At the same time, Francesco Zanetti collaborated in the publication of the first edition of Benet Perera’s (also Benito Pereira, Pereyra, or Pererius; Valencia 1536–1610 Rome) important De communibus omnium rerum naturalium principijs & affectionibus, libri quindecim (1576) discussed below.
Overall, the initial alliance of the Jesuits with Vittorio Eliano led directly to three other Roman publishers who produced a substantial number of editions of Jesuit works. And other Roman presses also published Jesuit authors. The principle was established and put into practice that Jesuit authors would publish with external commercial presses. But after the privilege granted to Vittorio Eliano, no single publisher was favored. Hence, Roman Jesuit authors published with a variety of publishers in Rome and elsewhere. It is likely that the initiative of authors and printers, and the preferences of patrons who paid publication costs, played key roles in the choice of a publisher for the first editions of Jesuit works. The number of Jesuit books that publishers issued, and the expanding fraction of their total production that Jesuit books represented, demonstrated the commercial importance of Jesuit works to publishers.
5 Dedications and a Venetian Publisher
The 1570 edition of Clavius’ commentary on the Sphaera carried a dedication letter dated March 20, 1570, Rome, from Clavius to Prince Wilhelm Wittelsbach of Bavaria (1548–1626). In 1579, he became Wilhelm V, called “the Pious,” duke of Bavaria (abdicated in 1597). Hence, Clavius wrote a second dedication letter to him recognizing the new title dated September 18, 1581.^{Footnote 34} The 1581 dedicatory letter was more personal and informative. Clavius wrote that he had worked long into the night on the revisions, making changes and adding much new material. He stated that he was a German, and he recalled fondly the church and city of Bamberg “of which I am a fosterson.” (cuius ego alumnus sum) (Sacrobosco and Clavius 1581, sig. 3r).^{Footnote 35} Clavius paid tribute to Duke Wilhelm V and his late father Duke Albrecht V (1528–1579) (Duke from 1550) for their firm support of Catholicism and the Jesuits. This was true. One example among many was their strong political support that enabled the Jesuits to take control of the University of Ingolstadt despite opposition from the rest of the faculty (The Mercurian Project 2004, 156–160, 169, 187, 189–193, 214, 216–17, 235–243). The 1581 dedicatory letter to Wilhelm V appeared in a large majority of the subsequent editions of Clavius’ commentary on the Sphaera.
In 1611, Clavius dedicated volume three, comprising the Sphaera commentary and his Astrolabium (first published in 1593) of his opera mathematica to Johann Gottfried von Aschhausen (1575–1622), princebishop of Bamberg (ruled from 1609). Now ill and unable to teach, Clavius again mentioned his labors to revise the work, and he praised Gottfried as a good shepherd of his flock. Like Wilhelm V, Gottfried was a strong Counter Reformation ruler who helped the Jesuits found a college and school in Bamberg in 1611. As has been pointed out, Clavius’ letters to northern European rulers as Wilhelm V and PrinceBishop Gottfried helped create a stream of revenue to support his and other Jesuit publications (Baldwin 2003, 287–301).
The Venetian editions of Clavius’ Sphaera commentary were the result of the initiative of Giovanni Battista Ciotti (ca. 1561–ca. 1629). A man of broad culture, Ciotti published a very large number of editions in Venice from 1590 through 1629 in many subjects, about seventyfive percent Italian editions and twentyfive percent Latin. He published the works of wellknown Italian vernacular authors such as the poet Giambattista Marino (1569–1625) (Firpo 1981; Contò 1997). In 1591, he published Clavius’ commentary on the Sphaera, his first Jesuit work. He wrote a dedication letter dated September 1, 1591, Venice, in which he praised Clavius as the prince of mathematicians of our time.^{Footnote 36} Three more editions followed: 1596 (published by Bernardo Basa, although it was Ciotti’s edition), 1601, and 1603 (Sacrobosco and Clavius 1596, 1601, 1603) (Chap. 6).^{Footnote 37} All included the same dedicatory letter of Ciotti with a changed date of 1596.
After Clavius’ Sphaera commentary, Ciotti published many other editions of Latin and Italian works by Jesuits. According to the USTC, Ciotti published 651 editions between 1590 and 1608, of which fiftynine were written by Jesuit authors, that is, nine percent of the total.^{Footnote 38} Although Ciotti published such major works of Jesuit scholarship as Clavius’ Sphaera commentary and theological works of Robert Bellarmine in Latin, he most often published the vernacular devotional works of Luca Pinelli (1543–1607), followed by “letters from the Indies,” that is, vernacular accounts of Jesuit missionary labors in India, China, Japan, and the Philippines.^{Footnote 39} Ciotti created a Jesuit publication list that combined widely popular vernacular works, which sold well, with Latin scholarship important to university scholars. In 1606, the Jesuits were expelled from the Republic of Venice, which meant the closing of their churches and their five schools in the Republic. Ciotti continued to reprint Pinelli’s vernacular devotional works but fewer other Jesuit titles, as the exile continued. The Jesuits were not permitted to return until 1657.
6 Clavius’ Proposals for Jesuit Mathematical Education
Clavius wanted the Jesuits to teach more mathematics and astronomy. So, he tried very hard to persuade his own order to adopt a muchexpanded mathematical curriculum. But he encountered opposition from Jesuit natural philosophers and some Jesuit provinces.
The opportunity to present the case for more mathematics and astronomy instruction arose in 1581. After General Everard Mercurian (b. 1514) died on August 1, 1580, fiftynine leading Jesuits met in Rome from February 7 to April 22, 1581, for the Fourth General Congregation of the Society.^{Footnote 40} Although General Congregations normally occurred when a general died and a new one had to be elected, they were also opportunities to chart the path forward.^{Footnote 41} After electing Claudio Acquaviva (1543–1615) (General from 1581) the new superior general on February 19, the congregation passed sixtyseven decrees. The most important by far was decree thirtyone which appointed a commission of twelve Jesuits “to develop a plan of studies,” that is, to draft an educational plan for the entire Society.^{Footnote 42} The decree was part of a general move in the Society toward more uniformity and tighter organization.
Jesuit schools and universities across Europe already had developed some common features. But the texts to be taught, pedagogical practices, and rules were not codified beyond individual schools or provinces and were subject to change. Moreover, like academics in all centuries, the Jesuits wanted to create the perfect curriculum in the ideal school. Indeed, beginning in 1551 Jesuit teachers had already written many lengthy treatises toward that goal. And also, like academics everywhere, they disagreed about what the perfect curriculum should look like. Now the Society intended to create a uniform and mandatory plan of studies for all Jesuit schools.
Clavius seized the opportunity. He presented to the rector of the Roman College a multifaceted proposal that would expand mathematical education and make permanent his academy. Titled “Ordo servandis in addiscendis disciplinis mathematicis” (The Order to Follow to Attain Proficiency in the Mathematical Disciplines), it was written in 1580 or 1581.^{Footnote 43} The curriculum that Clavius described was intended for the mathematical academy. But because of the action of the Fourth General Congregation, his proposal became the focus of the discussion about mathematics in a universal plan of studies for the Society.^{Footnote 44}
Clavius’ Ordo first described a twentytwo step program of comprehensive mathematical and astronomical education to be accomplished over three years. For each step, Clavius indicated what should be taught, and the texts that teachers should use, including several of his own works. Step one in the threeyear curriculum was to teach the first four books of Euclid’s (323–285 BCE) Elements using Clavius’ commentary on the first four books published in 1574. Step two consisted of basic arithmetical operations including addition, subtraction, multiplication, division of whole numbers and fractions, the use of proportions, and finding the square roots of numbers. He promised to compose a work on this material. In the meantime, he recommended two other works.^{Footnote 45}
Step three was to teach Sacrobosco’s Sphaera: “The Sphere as briefly as possible or rather any other introduction to astronomy. The more important rules regarding ecclesiastical reckoning can be added to this. I will also put out a brief treatment. Meanwhile, my commentary on John of Holywood’s Sphere will suffice, leaving out operations on curves, the treatise on isoperimetrics, and so forth since these will be treated below.”^{Footnote 46} In later steps, Clavius included more instruction and texts concerning astronomy. Overall, Clavius’ curriculum intended to teach a thorough and uptodate Ptolemaic astronomy based on the best available works, including his own.
Step four was Euclid’s Elements, books 5 and 6, again based on Clavius’ commentary. Step five involved teaching the use of the geometer’s square, the astronomer’s quadrant, and other measuring instruments. Further steps involved teaching more Euclid, algebra, the use of the astrolabe, geography, the description and construction of sundials, some study of Archimedes (287–212 BCE), the study of some other ancient Greek mathematicians, and more.^{Footnote 47}
Clavius also included two less comprehensive alternate versions of his mathematics and astronomy curriculum. The “Ordo secundus brevior pro iis, qui non curant perfectissimam mathematicarum rerum cognitionem assequi” (A Second, Shorter Order for Those Who Are not Interested in Acquiring a Completely Thorough Understanding of Mathematics) consisted of nineteen steps over three years. It was basically the same as the first version, but with less detail. For example, Step three said simply “The Sphere and ecclesiastical calendrical reckoning in very brief fashion. John of Holywood with my commentaries.” And he offered a third version, which was a twoyear course: “Ordo tertius brevissimus et ad cursum mathematices, qui duobus annis absolvi debet, accommodatus” (A Third Order of Greatest Brevity and Adapted for a Mathematics Course that Ought to Be Finished in Two Years). The twoyear course consisted of seven steps in the first year. Step two was “The Sphere and ecclesiastical calendrical reckoning, very concisely. These can be finished off by Easter.” The second year included additional astronomical material. It is noteworthy that studying the Sphaera was a key part of all three versions. At the end of his document, Clavius made it clear that he much preferred the very comprehensive threeyear mathematics and astronomy curriculum (MP, VII, 113–115; Jesuit Pedagogy 2016, 288–291).^{Footnote 48}
7 In Defense of Mathematics
Clavius next sought to raise the prestige of mathematics teachers within the Society, and he rebuked Jesuit philosophers who underestimated the value of mathematics.
In 1582, Clavius addressed to Superior General Acquaviva a second treatise entitled “Modus quo disciplinae mathematicae in scholis Societatis possent promoveri (A Method by Which Mathematical Disciplines Could be Promoted in the Schools of the Society).^{Footnote 49} Clavius began by stating that the mathematics teacher should possess “uncommon learning and authority.” In order for the teacher “to have greater authority with the students, and for the mathematical disciplines to be more highly valued, and for the students to realize their usefulness and necessity,” the teacher had to be invited to participate in solemn acts “at which doctors are created and public disputations are held” (MP, VII, 115; Jesuit Pedagogy 2016, 291).^{Footnote 50}
Clavius referred to solemn acts, which were important academic exercises in Jesuit schools and universities. A student who had completed three years of philosophical study and three or four years of theological study with great distinction was invited to be the defendant in a disputation lasting four or five hours in which he was questioned by his theology and philosophy teachers on any aspect of theology. Solemn acts were formal academic performances before an audience of teachers, students, and guests.^{Footnote 51} They were also festive celebratory occasions, because it was expected that the student would display much learning and be applauded. A nonJesuit who did well in solemn acts might be awarded a doctorate of theology. Jesuits did not normally receive doctorates; successful completion of solemn acts was considered reward enough. Clavius wanted the Jesuit mathematics teacher to be a questioner of the candidate so as to be considered the equal of teachers of theology and philosophy.
Clavius then made a plea for the mathematical academy. “But so that the Society always has suitable professors for these sciences, twelve suitable people (i.e., Jesuits) would have to be chosen to take on this service and they would be instructed in a private academy in different mathematical matters.” He warned that the mathematical sciences will not survive very long in the Society without the academy. On the other hand, having Jesuits learned in mathematics “would be a great enhancement for the Society, (mathematics) being very frequently brought up in conversation in talks and meetings of princes when those individuals realize that ours (Jesuits) are not ignorant of mathematics.” But if Jesuits “fall silent in such meetings” there will be “considerable embarrassment and dishonor. Those to whom this has happened have often related it” (MP, VII, 115–116; Jesuit Pedagogy 2016, 291–292).^{Footnote 52}
Clavius next argued that mathematics was essential to the study of natural philosophy. Students must understand that mathematics was “useful and necessary for correctly understanding the rest of philosophy.” There was such a “mutual affinity” between mathematics and natural philosophy “that unless they aided one another, they could in no way maintain their own stature.” It will be necessary “that students of natural philosophy study mathematics at the same time.” He continued: “The experts agree that natural philosophy (physica) cannot be rightly perceived without mathematics, especially the parts that bear on the number and motion of celestial orbs; the number of intelligences; the effects of stars that depend on various conjunctions, oppositions, and the distances left among them; the infinite division of a continuous quantity; the ebb and flow of sea tides; the winds; the comets; the rainbow; the halo [around the sun and the moon] and other meteorological events; and the relationship of movements, qualities, actions, passions, and reactions, and so forth…I am leaving out innumerable examples in Aristotle, Plato (427–447 BCE), and their renowned interpreters, examples that can in no way be understood without an intermediate understanding of the mathematical sciences” (MP, VII, 116; Jesuit Pedagogy 2016, 292).^{Footnote 53} This was a sweeping claim that much of the astronomical part of mathematics instruction was absolutely necessary for the study and understanding of Aristotelian natural philosophy, which might also be called Aristotelian physical science.^{Footnote 54}
Clavius followed by criticizing Jesuit philosophy teachers for their ignorance of mathematics. “Indeed, on account of their ignorance, some professors of philosophy have very often committed many errors, and very bad ones at that; and what is worse, they have even committed them to writing. It would not be difficult to expose some of them. By the same token, instructors of philosophy ought to be proficient in the mathematical disciplines, at least to an intermediate degree, so that they do not founder on similar reefs to the great loss and dishonor of the reputation that the Society has in letters” (MP, VII, 116; Jesuit Pedagogy 2016, 292–293).^{Footnote 55}
Clavius then charged that some Jesuit philosophers ridiculed mathematics. “It will be a considerable contribution…if the instructors of philosophy stay away from those debates…[in which it is said] that the mathematical sciences are not sciences, that they do not have demonstrations, that they are distractions from metaphysics, and so forth. For experience teaches that this is a stumbling block for the students, one that is entirely unprofitable, especially because the instructors can hardly teach them without ridiculing these [mathematical] sciences (as has been gathered more than once from the reports of others).” Clavius wanted Jesuit philosophy teachers to encourage their students to study mathematics “and not…lead them away from studying them, as many have in earlier years” (author’s emphasis) (MP, VII, 116–117; Jesuit Pedagogy 2016, 293). These were strong words directed against his colleagues.
Clavius concluded by proposing additional academic procedures by which Jesuit students would win support for mathematical studies and Jesuit philosophers would come to appreciate mathematics. Every month “all the philosophers” (meaning Jesuits studying philosophy and their teachers, who normally presided over or observed student presentations) should gather together. One student should “present a brief recommendation of the mathematical disciplines.” Then with the help of another student or two “he should explain a problem in geometry or astronomy which is both interesting to the audience and useful in human affairs. “Or he should explain a mathematical passage from Aristotle or Plato, “(and passages of this kind are not scarce in their works).” Or he should introduce “new demonstrations of certain propositions of Euclid.” Clavius believed that these exercises would stimulate “a burning desire” for mathematical studies. Finally, Jesuit students who wanted to obtain a master’s degree or doctorate in philosophy or theology should be examined in mathematics as well, and a mathematician should be one of the examiners (MP, VII, 117; Jesuit Pedagogy 2016, 293–294).
8 Perera’s Dismissal of Mathematics
Although Clavius did not name any Jesuit philosophy teachers who dismissed mathematics as unscientific, one of his very prominent colleagues at the Roman College did exactly that. This was Benet Perera. Perera entered the Society of Jesus in 1551 in Valencia. A brilliant student, he was sent to Rome where he studied at the Roman College and performed well in acts and public disputations. In 1558, at the age of twentythree—quite young for a Jesuit—he began to teach the natural philosophy course at the Roman College. And he taught, wrote, and probably lived in the Roman College for the rest of his life. From 1558 through 1567, he thrice taught the threeyear cycle of logic, natural philosophy, and metaphysics, always in that order (Baldini 1992, 569–570). He next taught Scholastic theology from 1567 to 1570. After a hiatus of six years, he taught Scholastic theology, positive theology, or scripture until 1597, although not all dates in which he taught each course are known, because of gaps in the records. It is possible that he was excused from teaching so that he might study and write between 1570 and 1576, again at one time or another between 1576 and 1597, and after 1597, because he published numerous long works, especially biblical commentaries (Villoslada 1954, 29, 41, 51–52, 59, 76, 78–79, 323, 324, 325, 327, 329, 331; Solà 2001). Some fellow Jesuits at the Collegio Romano viewed him as too much a follower of Averroes. Hence, in 1578 three fellow teachers at the Roman College plus another prominent Jesuit denounced Perera as an Averroist to Pope Gregory XIII. But the pope referred the matter to Jesuit General Mercurian, who supported Perera, and exiled one denouncer to Turin.^{Footnote 56}
In 1547, Alessandro Piccolomini (1508–1579), a prominent Aristotelian natural philosopher, published Commentarium de certitudine mathematicarum disciplinarum (Piccolomini 1547). He argued that mathematical demonstrations lacked scientific certitude for two reasons. Mathematical axioms lacked the certainty of the syllogistic reasoning of logic which provided intellectually convincing proof, and mathematics presented abstractions. Hence, mathematics was not a real or universal science because it did not explain the nature of matter, as Aristotelian physics did.^{Footnote 57} This provoked a lively debate, as some strongly defended the certitude of mathematics, while Aristotelian philosophers often echoed Piccolomini’s views.^{Footnote 58}
One of them was Perera. In his 1564 treatise on the best practices in humanistic studies, he wrote that “Mathematical sciences require one kind of proof; moral explanations and elaborations demand another; and theories and arguments involving nature demand yet another” (MP, II, 680; Jesuit Pedagogy 2016, 199).
Perera returned to this topic later. In 1576, he published his major philosophical work: De communibus omnium rerum naturalium principiis & affectionibus libri quindecim (Fifteen Books on the Principles and Properties Common to all Natural Things), a folio volume of nearly 600 pages (Perera 1576).^{Footnote 59} Fourteen confirmed, and two unconfirmed editions followed between 1579 and 1618, published in Rome, Venice, Paris, Lyon, Cologne, and possibly Strasbourg, in quarto or octavo, and the octavo editions were about 900 pages long.^{Footnote 60} The number and arc of editions of Parera’s major philosophical work roughly paralleled the publication history of Clavius’ commentary on the Sphaera.
Perera’s book was a comprehensive study of the various branches of philosophy, their principles, and the relations between them. Its goal was to provide a unified approach to Aristotelian philosophy and the epistemology of scientific investigation. The book was heavily based on his lectures on logic, natural philosophy, and metaphysics.^{Footnote 61} In the course of the book, Perera weighed the claim of mathematics to be a science against Aristotle’s criteria for scientific truth in physics with its emphasis on causes and substance. He found mathematics wanting.
In book three, Chap. 4, Perera offered a particularly negative discussion about whether mathematical proof met the standard of demonstration as formulated by Aristotle in the Posterior Analytics. Perera began by posing the question, whether mathematical demonstrations can claim the first order of certitude. Perera wrote that although many accepted that they could, he completely disagreed. Although mathematics is called a science because it can produce connections and a most beautiful and admirable order, mathematical certitude does not go beyond mathematics itself. Mathematical demonstration does not address or determine causes. By contrast, a true demonstration clarifies the essence of something, how it depends on its cause, and is recognized as such. True demonstration is securely connected to matter, that is, natural things. Drawing mathematical abstractions from matter is not difficult, because they depend only on quantity; hence, the intellect can easily conceive them. They are not tied to a definite and certain material that depends on physical accidents (Perera 1579a, 118–121).^{Footnote 62} Mathematics does not require long experience and careful observation, as do the principles of physics (meaning natural philosophy) or medicine. For this reason, boys are able to escape the mathematicians, but not the natural philosophers.^{Footnote 63} He meant that students did not need to study mathematics, but must study natural philosophy in order to understand science. In other words, studying mathematics was not necessary. Whether or not Clavius had Perera in mind when he accused philosophers of ridiculing mathematics, the above comment fit his words.
It is likely that Perera made such comments in the classroom as well, because some of his book repeated wordforword material from the manuscripts of his lectures (Blum 2012, 140–141). If mathematics could not offer real demonstration of cause and effect, it was not a true science. Because mathematics was not a true science, Perera saw no reason for young people to study it. Perera’s position threatened the very existence of mathematical instruction in Jesuit schools (Romano 1999, 146).
The attacks on mathematics attracted enough attention that the Roman province discussed the matter in a meeting in 1575 or 1576. The Roman province wanted more attention to be given to mathematics lest it declines. And in the next sentence, it warned professors of philosophy not to speak publicly about trivialities.^{Footnote 64} Whether these two statements were linked, and the second was meant to rebuke Perera, is impossible to determine.
Perera was not the only philosopher at the Roman College who did not see mathematics as a true science in the years in which the place of mathematics in Jesuit education was hotly debated. Paolo Valla (1560–1622), who taught logic, natural philosophy, and metaphysics at the Roman College from 1584 to 1590, then theology from 1602 to 1605, held the same views concerning the superiority of Aristotelian physical proof over mathematical proof as Perera (Wallace 1984, 135–136).^{Footnote 65}
In short, at the very moment when Clavius was making a strong argument for much more mathematical instruction in the Jesuit curriculum, prominent Jesuit natural philosophers also teaching in the Roman College dismissed mathematics as not a true science and not worth studying. The battle was joined.
9 The Ratio Studiorum of 1599
As mentioned, the Fourth General Congregation in 1581 ordered the preparation of a Ratio Studiorum, an educational plan for the entire Society. The Jesuits labored on it for eighteen years and through several committees, and produced at least 1,800 pages of documents.^{Footnote 66} Clavius contributed his bit: Although he had already presented his views on the importance of mathematics at length, he added two more brief comments in the 1590s. In particular, he wanted his mathematical academy permanently incorporated into the Jesuit educational structure (MP, VII, 117–122; Jesuit Pedagogy 2016, 294–300). Other Jesuits argued just as strenuously for their disciplines. A committee produced a draft Ratio Studiorum of 1586 that was sent to all the twenty provinces for comments, which came in abundance. Another committee read the comments, made revisions, and drafted a second version in 1591. The Tipografia del Collegio Romano published both drafts, with Francesco Zanetti doing the printing for the 1586 draft (Ratio studiorum 1586, 1591).^{Footnote 67} The 1591 draft was also sent to the provinces to be tried out in the classroom for three years, with the provinces charged to report what needed improvement. Again, the provinces responded fully, as did many individual Jesuits. Arguments and differences of opinion were often sharp.
The provinces had mixed views about teaching mathematics and how much mathematics they should teach. The majority of provinces endorsed teaching mathematics but for only one year. The opinion of the Province of Milan was typical. Mathematics should be taught for one year to the natural philosophy students; the younger logic students should not be burdened further. And it was enough that the mathematics class should teach the first three books of Euclid, the Sphaera, the astrolabe, and arithmetic (MP, VI, 293). The Spanish provinces did not want to teach any mathematics at all. The Province of Aragon commented that some logic students were incapable of studying mathematics; hence, it did not recommend compelling any students to study mathematics. The Province of Toledo wrote that Jesuit students could hear lectures on mathematics in universities (MP, VI, 294).^{Footnote 68}
Although the provinces teaching mathematics in some of their schools were not required to report the texts studied, some did. The Province of Portugal reported that it offered one year of mathematics in which it taught the Sphaera to students who did the threeyear philosophical cycle (MP, VI, 294). The Jesuit school in Louvain had a mathematics class that taught practical arithmetic and the Sphaera of Sacrobosco (MP, VI, 296). It is likely that teachers and/or students used Clavius’ commentary in these classes.
The provinces responded negatively to the proposal of a mathematical academy in Rome to which they would send Jesuits with mathematical aptitude. They believed that young Jesuits should study mathematics and theology in their home provinces. The provinces of the Rhine and Upper Germany were more favorably inclined and praised Clavius by name. But they too were not convinced that it was necessary to send Jesuits to Rome in order to learn to be good mathematicians (MP, VI, 293–294). One reason for the reluctance to send young Jesuits out of the province was that many provinces were experiencing a teacher shortage, because the Jesuits were opening new schools as quickly as possible. In summary, the majority of the provinces approved of one year of mathematics instruction consisting of daily lectures for the natural philosophy students. They agreed that the lectures should include Euclid, the Sphaera, and arithmetic. But they opposed a Roman mathematical academy.
The Jesuits finally completed the Ratio studiorum in 1599. The first edition was published not in Rome but in Naples by the press of Tarquinio Longo (fl. 1598–1620), who published many other Jesuit works (Ratio studiorum 1599).^{Footnote 69} Other editions followed, including the first Roman edition in 1606 published by the Tipografia del Collegio Romano (Ratio studiorum 1606). Its full title was Ratio atque institutio studiorum, which is universally shortened to Ratio Studiorum. It consisted of directions, practices, and rules to be followed by all teachers and superiors responsible for the schools. The Ratio Studiorum offered great clarity about Jesuit education, albeit in a dry and utilitarian presentation. It was mandated for use in all Jesuit schools, with some discretion in implementation permitted.
The 1599 Ratio Studiorum gave mathematics a limited place in Jesuit education. A student who undertook the entire Jesuit curriculum did not study mathematics until after four to six years of Latin grammar, humanities, and rhetoric instruction in the lower school and one year of logic in the upper school. The natural philosophy students then attended a fortyfive minutes daily lecture on mathematics (RS, par. 38). That was all. And the mathematics lecture was in addition to twice daily hourlong classes in natural philosophy. After the natural philosophy year, the Ratio Studiorum did not require students to study any more mathematics. To be sure, it did not bar students not studying natural philosophy from attending mathematics lectures. How many did so is impossible to determine.
The 1599 Ratio Studiorum imposed a limited and flexible curriculum for the mathematics lecture. The teacher was to begin with Euclid’s Elements. After about two months, he should teach “Geography or the Sphere,” presumably Sacrobosco’s text, or “about those things that are generally of interest.” In addition, “Every month, or at least every other month, he [the mathematics teacher] should make sure that one of the students elucidates a famous mathematical problem at a large gathering of philosophers and theologians. Afterward, it ought to be submitted to disputation if it seems right to do so” (RS, par. 239, 240). This was something that Clavius wanted.
The Ratio Studiorum did not authorize an academy for advanced study in mathematics or in any other discipline.^{Footnote 70} Hence, it did not discriminate against mathematics. It did encourage students who attended the mathematics lecture course and had an interest in mathematics to study mathematics privately (RS, par. 38). There was one more reference to mathematics. The rules for professors of natural philosophy told them to devote the entire year to “topics in physics” followed by a list of topics that included “the different manners of proceeding in physics and in mathematics, about which Aristotle comments in Physics, book 2” (RS, par. 219).^{Footnote 71} Thus, the Ratio Studiorum pointed to passages about whose meaning Clavius and Perera sharply differed, but left it to the natural philosophy teacher—not the mathematician—to interpret them. Overall, Clavius must have been deeply disappointed with the Ratio Studiorum.
Why did the Ratio Studiorum fail to give mathematics a larger place in Jesuit education?
Perera’s attack against the scientific value of mathematics probably played a role, because he was respected by other Jesuit philosophers and widely published. But the major reason was that the provinces did not want more mathematical education. The provinces usually mentioned practical reasons. There was also an unmentioned major reason: Members of the Society of Jesus did not see mathematics contributing greatly to their fundamental purpose, which was “to help souls” in this life and to help them reach salvation in the next.^{Footnote 72} The rest of the curriculum helped souls more. The lowerschool curriculum of humanistic studies plus catechesis taught students to become morally good and eloquent individuals and citizens. Humanistic studies also gave students excellent Latin skills enabling them to earn a living or to pursue advanced education in law, medicine, or theology. Philosophy taught students how to find truth and separate it from error. Theology taught men about God and God’s plan for human beings.
Overall, the Ratio Studiorum of 1599 mandated what the majority of Jesuit provinces were already doing in mathematics, but not more, as Clavius wanted. This was not surprising, because education does not change unless teachers, students, parents, and leaders of society with power over schools demand it. This was not the case for Jesuit schools in the 1590s. On the contrary, the requests from towns and rulers for more and more Jesuit schools teaching the humanities, Aristotelian philosophy, and Scholastic theology demonstrated high satisfaction with the status quo. But the Society missed an opportunity to build on the impressive mathematical accomplishments of Clavius and the academy of mathematics.
10 Mathematics Instruction after 1599
How many Jesuit schools offered the fortyfive minutes daily lecture mandated for students enrolled in the natural philosophy course? What happened to Clavius’ academy of advanced mathematical studies and with the Sphaera? What were the practical results for mathematics and astronomy?
The answer to the first question is that only a small minority of Jesuit schools in Europe offered mathematics lectures in the first half of the seventeenth century. They were usually the one or two most important Jesuit schools in a province. And the school was sometimes part of a Jesuit university or a civicJesuit university.
The Italian assistancy presented examples.^{Footnote 73} In 1600, it included five provinces of roughly equal geographical size and number of Jesuits: Milan, Venice, Rome, Naples, and Sicily (Table 1). Each province had seven to twelve schools open to Jesuits and external students (lay boys, youths, and men). However, the vast majority of Jesuit schools were lower schools that taught one to three classes in Latin grammar and humanities; a few added a logic class. Only schools that taught logic, natural philosophy, and metaphysics, plus some theology, were likely to offer the mathematics lecture. In 1600, there were four mathematics lectureships in Italian Jesuit schools, all in schools that taught three years of philosophy plus theology.
As both the number of Jesuit schools and those that taught philosophy increased, so did the number of mathematics lectureships. There were seven mathematics lectureships in Italy in 1649 (Table 2).
In addition, the Jesuit university at Cagliari, Sardinia, had a lectureship of mathematics beginning in 1626 which continued until the suppression of 1773 (Fischer 1983, 85). However, the Sardinian Jesuits were part of the Province of Aragon and the Spanish assistancy, because Sardinia was ruled by Spain. Only in 1718 did Sardinia become part of the Duchy of PiedmontSavoy.
This was the pattern across Europe. Only a minority of Jesuit schools taught mathematics, and these were schools that taught all three philosophical courses plus theology. In some assistancies and provinces, a larger minority of schools taught mathematics. For example, in 1616 the Province of Lyon had thirteen schools of which four taught mathematics (Romano 1999, 376).^{Footnote 74} Overall, the French assistancy and German assistancy (which included the Province of Austria) taught more mathematics, while the Italian assistancy and the Province of Portugal taught less mathematics. And some of the Jesuits who taught mathematics in Lisbon were German Jesuits. The Spanish assistancy mostly ignored mathematics.^{Footnote 75}
Jesuit mathematicians in Italy, especially former academy members, commonly taught Sacrobosco’s Sphaera with the aid of the commentary of Clavius. Giovanni Giacomo Staserio (Bari 1565–1635 Naples) was a member of Clavius’ academy for two years, 1595–1597, while studying theology at the Roman College (Baldini 2003, 73, 93 n. 93). After ordination, he returned to Naples, where he taught mathematics at the Jesuit school for eighteen years, with interruptions, between 1599 and 1624. He had considerable influence on mathematical instruction in Naples and exchanged numerous letters with Clavius (Gatto 1994, 75–89, 101–113, 150–160, 277, 308–325). Upon learning that Clavius had revised his Sphaera commentary for a new edition, he wrote to Clavius in 1606 asking him to print thirty copies for the Naples college (Brevaglieri 2008, 298; Giard and Romano 2008, 110–111).
At Parma, the Jesuit mathematics lectureship was part of the civicJesuit University of Parma founded in 1601. This was a university in which lay professors taught law and medicine, and Jesuits taught theology, metaphysics, natural philosophy, logic, mathematics, and rhetoric. Basically, the Jesuit upper school was incorporated into the university. Giuseppe Biancani (Bologna 1566–1624 Parma), a member of Clavius’ academy of mathematics from 1598 to 1600 and probably the most accomplished mathematician in the Province of Venice, was the mathematics professor at the University of Parma from 1605 until his death.^{Footnote 76} The university rotulus (a list of the professors, the lecture schedule, and a brief summary of the contents of the lectures) for the academic year 1617–1618 indicated that he lectured on Euclid’s Elements, and the “sphere” (Grendler 2017, 168).
It was the same in Mantua. In 1624, with the strong support of Duke Ferdinando Gonzaga (1587–1626; ruled 1613–1616), the Jesuits expanded their small school into a complete school teaching the humanities, philosophy, and theology. And in 1625, Duke Ferdinando created the civicJesuit University of Mantua, whose structure was the same as the civicJesuit University of Parma. The Jesuit who taught mathematics at the Jesuit upper school and then the university from 1624 to 1629 was Cesare Moscatelli (Bologna ca. 1585–1644 Modena). He studied mathematics at Parma, probably with Biancani. Four of the five rotuli for the years that he taught mathematics at Mantua survive. He always taught Euclid’s Elements and the Sphaera, most likely on the basis of Clavius’ commentary, plus another mathematical topic.
Unfortunately, the University of Mantua only lasted four years. It closed as a consequence of the War of the Mantuan Succession, the plague which killed thousands in Mantua including several Jesuits, and the terrible Sack of Mantua in July 1630 (Grendler 2009, 81, 164, 169, 200–201, 252–253 et passim). Although the university did not return to its previous form, the Jesuits slowly rebuilt their school, which included a renewal of the mathematics lectureship in the middle of the 1640s.
The second question concerns mathematical academies. What happened to Clavius’ academy? Were there any academies of advanced mathematics in Italian Jesuit schools after 1599? If not, how were Jesuit mathematicians trained?
Clavius’ academy continued as before until he became ill and had to cease teaching in 1610 and died in 1612. At his death, his academy “was considered as second to no other European scientific institution” (Baldini 2003, 68). It did not formally dissolve but lived on for a while. Some Jesuits and a few nonJesuits continued to receive advanced mathematical instruction in Rome from able Jesuit mathematicians such as Christoph Grienberger until about 1615. But by the 1630s there is little or no evidence of the existence of advanced mathematical instruction in Jesuit Rome. Outside of Rome, Italian mathematical academies have not been found in the rest of the seventeenth century.
Instead, advanced mathematics was taught oneonone or in very small groups, as young Jesuits with mathematical aptitude connected with expert Jesuit mathematicians.^{Footnote 77} The best mathematician in the province usually taught in the most important Jesuit school where the majority of Jesuit scholastics in the province did their philosophical and theological studies. Hence, a young Jesuit with mathematical aptitude from somewhere else in the province went to Rome, Milan, Parma, Naples, or Palermo to study philosophy and theology, where he heard mathematics lectures as well. He might also ask his superiors to permit him to remain in Rome, Milan, et al., for another year or two in order to study with a master mathematician. Superiors were more likely to grant such requests than earlier, because the teacher shortage had eased, thanks to a wave of young men who joined the Society in the first quarter of the seventeenth century. Private instruction may or may not have been as productive as attending a mathematical academy, but it was a way to learn.
What happened at Bologna suggests one pathway to advanced mathematical study. The Society founded a day school in Bologna in 1551; it added a boarding school for noble boys in 1634, and a boarding school for citizen boys in 1645.^{Footnote 78} The noble and citizen boarders lived supervised lives in separate buildings, but attended classes together in the Jesuit day school. The University of Bologna was very concerned about competition from the Jesuit school, so it tried to prevent the Jesuits from teaching subjects, including mathematics, that the university taught. A compromise was reached: The Jesuit school was permitted to teach theology, philosophy, and mathematics to fellow Jesuits and to boarding school students only. They were not permitted to teach these classes to day students, that is, lay boys and youths from the town, who comprised ninetyfive percent or more of the student body in Jesuit schools. Hence, the Bologna Jesuit mathematics class had very few students; in 1646, it had only five students, all of them Jesuits.^{Footnote 79} Who the Jesuit mathematics students were is unknown; they might have been philosophy students, theology students, or older Jesuits with an interest in mathematics. In any case, there were five Jesuits interested in mathematics, ideal conditions for transforming the class into a de facto academy of advanced mathematics.
This may have happened. In 1672, students and professors from the University of Bologna complained that the Jesuit school was teaching the same advanced mathematics that university professors taught. Even worse, the mathematics students at the Jesuit school were posting their mathematical conclusions in the courtyard of the Archiginnasio, the university building in the center of the city (Grendler 2017, 309–310). That some advanced mathematics was taught at the Bologna Jesuit school is not surprising, because the Jesuit mathematics teacher at that time was Giuseppe Ferroni (Pistoia 1628–1709 Siena). He was a very able mathematician who had studied mathematics with one of the best Jesuit mathematicians in the Province of Venice and with two nonJesuit followers of Galileo Galilei. Ferroni then taught mathematics in the Roman College from 1657 to 1660, at the Jesuit school in Mantua from 1660 to 1666, at Bologna from 1667 to 1686, and at the University of Siena and the Jesuit school in Siena from 1686 until his death. He had the knowledge to teach advanced mathematics in Bologna (Torrini 1973; Zanfredini 2001; Baldini 2002, 312; Grendler 2017, 310–311, 387, 389–390).
In their public instruction, Jesuits followed the papal decree of 1616 forbidding the teaching of heliocentrism as physical reality. As astronomers and mathematicians, they might—or might not—accept the concept of and evidence for heliocentrism as physically true. But as Jesuits, they were obliged to interpret the new data in light of the papal decree (Baldini 2003, 69). On the other hand, some Jesuits found ways to express their dissent. Again, Bologna and Ferroni offered an example.
Ferroni accepted the heliocentric position of Copernicus (1473–1543) and Galilei, but did not publish his views because of Jesuit censorship. But he did not completely hide them either. In 1680, an anonymous dialogue appeared in Bologna: Dialogo fisico astronomico contro il sistema copernicano tenuto fra due interlocutori, Sig. Francesco Bianchini veronese sotto il nome di Adimanto, Sig. Ignatio Rocca piacentino sotto il nome di Silvio, convittori del Collegio del Beato Luigi Gonzaga della Compagnia di Gesù in Bologna (A Physical and Astronomical Dialogue Against the Copernican System Between Two Interlocutors, Signore Francesco Bianchini From Verona Under the Name of Adimanto, Signore Ignatio Rocca of Piacenza Under the Name of Silvio, Boarding Students of the College of Blessed Luigi Gonzaga of the Society of Jesus in Bologna), per Giuseppe Longhi, Bologna 1680.^{Footnote 80}
The title was inaccurate and Bianchini and Rocca were fictitious characters. The dialogue supported Copernicus, who was presented positively. The arguments supporting Copernicus were mathematical and physical, while the arguments favoring the Ptolemaic system were scriptural and miraculous. The dialogue also criticized the Holy Office prohibition against heliocentrism. The anonymous author was Ferroni. Setting a proCopernicus and antiPtolemy dialogue in a Jesuit boarding school (The College of Blessed Luigi Gonzaga was the Jesuit citizen school in Bologna) was a way to criticize Jesuit adherence to the papal prohibition barring Jesuit mathematicians from teaching heliocentrism as physical reality. The dialogue never mentioned the Sphaera of Sacrobosco, and it is unlikely that Ferroni taught it or Clavius’ commentary in his classes.
By the late seventeenth century, the sharp separation between Jesuit Aristotelian philosophy and Jesuit mathematics had diminished greatly. Mathematicians developed an experimental methodology enabling them to describe physical reality in mathematical terms. And philosophers loosened or abandoned strict Aristotelian definitions of scientific proof. Mathematicians investigated philosophical issues and natural philosophers included mathematical evidence. They sought common ground. An institutional sign was that some Jesuits moved back and forth between the mathematics professorship and the natural philosophy professorship at the Roman College in the second half of the seventeenth century (Baldini 1999b, 269–270, 272–278; Udías 2015, 43–47; Raphael 2015). This would have been unimaginable in the time of Clavius and Perera.
Such developments meant the disappearance of the Sphaera from Jesuit mathematics instruction. Negative evidence from the Roman College supports this conclusion. The rotulus for the Roman College for the academic year 1696–1697 promised that the mathematics lectureship would teach geometry, the Elements (of Euclid), speculative and practical arithmetic, and general mathematical problems and theorems.^{Footnote 81} Noticeably absent was any reference to Sacrobosco or sphaera. The long pedagogical lives of Sacrobosco’s Sphaera and Clavius’ commentary had ended. Jesuit mathematics had entered a new era.
In 1730, the Society of Jesus finally decreed a formal cease fire between mathematics and Aristotelian natural philosophy, Clavius and Perera. The Sixteenth General Congregation meeting from November 15, 1730, to February 13, 1731, stated that they were both valid. It affirmed the Society’s loyalty to Aristotelian philosophy including its philosophy of nature. It also endorsed mathematics and experimental physics.

There is no opposition between the Aristotelian philosophy and the more attractive style of learning in physics, and especially in its more particularized branches, with which the more notable natural phenomena are explained and illustrated by mathematical principles and the experimentation of scholars; instead, there is complete agreement between them (For Matters of Greater Moment, 1994, 384, decree 36).
Although the contest had ended some time ago, the Congregation made it official. The eighteenth century witnessed a burst of Jesuit creativity in numerous scientific fields, including mathematics and astronomy.
11 Conclusion
The last phase of the pedagogical career of Sacrobosco’s Sphaera was entwined with Jesuit mathematics instruction. Christoph Clavius, the most influential Jesuit mathematician, was the key figure. He wrote a commentary on the Sphaera that was widely reprinted and used. The first edition printed in Rome 1570 also marked a change in Jesuit policy concerning the publication of Jesuit works. With Clavius’ book, the Roman Jesuits decided to entrust the printing and publication of major works of Jesuit scholarship to external commercial presses beginning with Vittorio Eliano, the brother of a Jesuit. Many other presses followed by publishing the books of Clavius and other Jesuits as part of their production.
Clavius believed that both mathematics and Aristotelian physical science offered scientific certitude, a view not shared by Benet Perera and some other Jesuit philosophers. Clavius fought to expand the mathematics curriculum of Jesuit schools and to make his mathematical academy a permanent part of Jesuit education. He was unsuccessful. The Ratio Studiorum of 1599 listed only a single class of mathematics in the standard Jesuit curriculum, and it did not make permanent his academy. Nevertheless, Jesuit schools did teach mathematics, and they used his commentary on the Sphaera until mathematical research and instruction changed in the middle of the seventeenth century. While it lasted, the alliance between a medieval astronomical text, its most important Renaissance commentary, and the preeminent Catholic teaching order was remarkable.
Notes
 1.
I am grateful to Mordechai Feingold for reading an early draft of this paper, and Nelson Minnich for help with a Latin passage. I am grateful to members of the seminar for their comments and especially to Christoph Sander and to Andrea Ottone, who also carefully edited my article. The remaining mistakes are mine.
 2.
“il commento alla Sphaera di Sacrobosco fu la più ampia sintesi di astronomia elementare disponibile nei cinquanta anni dal 1570 al 1620” (Baldini 1992, 135).
 3.
 4.
Only the necessary minimum of secondary sources are given in order to hold the paper to an appropriate length.
 5.
Ignatius wrote this section of the Constitutions in late 1553 and early 1554, when there were still only a few Jesuit schools.
 6.
See (Grendler 2017, 348–351), for the context.
 7.
 8.
 9.
The information in (Villoslada 1954, 335) is incomplete.
 10.
All studies of Clavius mention his academy. The best is (Baldini 2003).
 11.
The Mandarin translation of Clavius’ commentary on the Sphaera is number 31 in (Sommervogel 1960, VI, 1794).
 12.
For the list, see (Baldini 2003, 74–76). Clavius also composed sacred music. Whether it was performed during his life is unknown. Amazon.com does not list any recordings.
 13.
See Ian Maclean’s article (Chap. 6) in this volume for comments on many of the editions.
 14.
 15.
See also (Sachet 2020, 200–206) for additional information. This book arrived too late to be fully used.
 16.
 17.
 18.
See also (Ascarelli 1972, 13, 354), for booklets of theses published in 1554 and 1555 by Blado and the Tipografia del Collegio Romano.
 19.
The privilege, “Pius Papa V. Motu Proprio &c” is found on the recto and verso of the second leaf of (Sacrobosco and Clavius 1570). It concludes “Datum Romae apud Sanctum Petrum Quarto Idus Ianuarij, Anno Quarto.” The IV Ides was January 12. Because Pius V was elected on January 7, 1566, the fourth year of his pontificate began on January 7, 1569, and ended on January 6, 1570. Hence, the date of the privilege was January 12, 1569.
 20.
“Nonnulla opera, scilicet, Commentaria doctoris Francisci Toledi Societatis IESU in summam Theologicam S. Thomae, eiusdem Instructionem Sacerdotis sive casus conscientiae, Eiusdem commentaria in libros Aristotelis de anima, Magistri Christophori Clavij in sphaeram Sacroboschi, literas Indicas patrum Societatis IESU, Epigrammatica selecta, orationes selectas, Synonyma exCicerone, Terentium, Plautum, Horatium ab omni obscoenitate purgatos, Catenam in Evangelia doctoris Emanuelis Societatis IESU…” (Recto of the second leaf of (Sacrobosco and Clavius 1570), no signature).
 21.
The indispensable study of papal privileges is (Ginsburg 2019), especially pages 115–139.
 22.
None of the approximately 430 papal privileges listed in (Ginsburg 2019, 141–284) gave permission to print so many potential titles.
 23.
In 1586, he published under the name Giovanni Battista Romano a catechism with twentyseven illustrations showing good and sinful actions; it had at least four editions. The 1591 edition and its title is cited: Dottrina christiana nella quale si contengono i principali misteri della nostra fede rappresentati con figure per istruttione de gl’idioti & di quelli che non sanno leggere…Composta dal p. Giovanni Battista Romano della Compagnia di Giesu (Dottrina christiana 1591). For the 1586 edition see (Eliano 1586). For editions of 1587 and 1608 and some illustrations from the work see (Grendler 1989, 354–356, 427).
 24.
Most of (Clines 2020) is a detailed study of those missions and how Eliano viewed his identity as a converted Jew.
 25.
This incomplete summary of Eliano’s teaching at the Roman College has been pieced together from various sources. The summary of his teaching in (Villoslada 1954, 326), omits his Arabic teaching and does not accurately indicate the years in which he taught Hebrew.
 26.
 27.
Undated (but late 1565 or early 1566) annual letter of Juan Alfonso de Polanco S. J., Rome, in (Polanci Complementa, 1969, I, 560–561). For other references to Eliano see (Polanci Complementa 1969, I, 284, 422, 611; II, 628, 664. Pier Ioly Zorattini states that Eliano’s Arabic manuscript on Trent is in the Biblioteca Nazionale Vittorio Emanuele II, Roma (Ioly Zorattini 1993, 475).
 28.
Vittorio Eliano’s press was another link, not previously noticed, between conversos and the Society of Jesus in its first halfcentury. Scholars have noted that several prominent early Jesuits came from converso backgrounds, albeit sometimes several generations distant. The connection was brutally severed in 1593 when the Fifth General Congregation decreed that men of Jewish and “Saracen” background, meaning converts or descendants of converts from Judaism and Islam, would not be admitted into the Society of Jesus in the future. This rule was not completely abrogated until 1946. The reasons for this bitterly contested decision were complex; see (Maryks 2010) for the story.
 29.
Some copies are dated 1574, others 1575. The edition carries the words Cum Privilegio but there is no further information. See also (Sommervogel 1960, VIII, 68–69).
 30.
Plus many more editions.
 31.
Another possible example of a work for which Eliano had a printing privilege that was not published until after the author had died was the catena of passages from the Gospels by “Doctor Emanuele.” This might have been Notationes in totam scripturam sacram…brevissime explicantur of Manuel de Sá (ca. 1528–1596), a biblical scholar who taught theology at the Roman College. It was first printed in 1598 by the Plantin Press of Antwerp (Sa 1598). On Sà see (Leite 2001).
 32.
For Bellarmine’s Hebrew grammar see (Sommervogel 1960, I, 1151–1153).
 33.
In these calculations, a small number of editions listed as published by the Tipografia Apostolica Vaticana and the Tipografia del Collegio Romano, but printed by Domenico Basa or Francesco Zanetti, are omitted. Further, the three editions of Clavius’ commentary on the Sphaera are counted as a Basa publication, even though Basa and Francesco Zanetti collaborated on them. For Basa, see (Menato 1997a). The smaller number of editions listed by (Ascarelli 1972), included about the same percentage of Jesuitauthored editions. For example (Ascarelli 1972, 356–358), lists 163 editions published by Francesco Zanetti, of which nineteen percent (thirtyone) were Jesuit works.
 34.
In the 1581 edition, the year of the letter is omitted. The letter is reprinted in (Sacrobosco and Clavius 1585), with the date 1581.
 35.
Although the normal translation of alumnus is “fosterson,” in Jesuit pedagogical documents it sometimes meant a student who was in some way unusual, such as a scholarship student in a school full of feepaying students.
 36.
“Christophorus Clavius nostrae tempestatis mathematicorum Princeps” (Sacrobosco and Clavius 1591, Sig. †2v).
 37.
Bernardo Basa, nephew of Domenico Basa, was active as a publisher in Venice from 1582 to 1596 (Bruni 1997).
 38.
This is based on a survey of Ciotti editions in USTC. Because the short titles in USTC often do not identify authors as Jesuits, a few Jesuit editions may have been missed.
 39.
 40.
All the provinces were European at this date, and they oversaw the overseas missionary outposts.
 41.
The Society continues to follow this practice today with a significant modification. The last two superior generals did not die in office. Instead, they announced their impending retirements about two years in advance, which allowed for lengthy preparation for the general congregations that followed.
 42.
Quote in (For Matters of Greater Moment 1994, 176).
 43.
The Latin text is found in (MP, VII, 109–115), and an English translation in (Jesuit Pedagogy 2016, 281–291). Although the Archivum Romanum Societatis Iesu (hereafter ARSI) manuscript lacks a date, Lukács, the editor, gives the date as not later than 1581 and ca. 1581 (MP, VII, 109), which (Jesuit Pedagogy 2016, 283) follows. Ugo Baldini believes that the date was “almost certainly” 1580 (Baldini 2000, 56); he also prints the first section with the threeyear mathematical program (Baldini 1992, 172–175). All three editions include notes. Baldini’s edition provides the most extensive notes and adds the most detailed identifications of the texts named on pp. 179–182.
 44.
Several scholars have briefly analyzed or mentioned Clavius’ plan for mathematical education. The following pages are a partial account that focuses on the position of his commentary on the Sphaera.
 45.
 46.
 47.
Because this study focuses on the Sphaera, the rest of the threeyear mathematics curriculum is omitted.
 48.
Quotes on (Jesuit Pedagogy 2016, 288, 289, and 290).
 49.
The text is found in (MP, VII, 115–117); English translation in (Jesuit Pedagogy, 2016, 291–294).
 50.
I have slightly altered the translation of “actus solemniores” and “doctores creantur” to convey better the academic meaning.
 51.
The Ratio Studiorum of 1599 called them “general acts” (actus generales) or “theological acts” (RS, 105–107).
 52.
Again, I have very slightly modified the English translation.
 53.
The only change made to the English translation is translating physica as natural philosophy (Jesuit Pedagogy 2016) translates physica as “natural sciences” which is not precise enough in this case. In Jesuit curriculum discussions at this time physica meant natural philosophy, because the fundamental text studied in the natural philosophy course was Aristotle’s Physics.
 54.
 55.
In this passage, Clavius uses “praeceptores philosophorum,” meaning all teachers of philosophy, not just teachers of natural philosophy.
 56.
 57.
 58.
 59.
There is a fuller bibliographical description in (Tinto 1968, item 244).
 60.
The subsequent editions are Paris, apud Michel Sonnius, 1579 or Thomas Brumen, 1579 (Perera 1579a, b). It is the same edition, because the royal privilege was granted to them jointly. See the last page of the Michel Sonnius edition. Other editions are Rome 1585 (Perera 1585a); Paris 1585 (Perera 1585b); Lyon 1585 (Perera 1585c); Venezia 1586 (Perera 1586); Paris, Michel Sonnius, 1586 (Sommervogel 1960, VI, 499); Lyon 1588 (Perera 1588); Paris 1589 (Perera 1589); Venezia 1591 (Perera 1591); Köln 1595 (Perera 1595); Strasbourg, no further information, 1595 (Sommervogel 1960, VI 500); Köln 1603 (Perera 1603), Köln 1609 (Perera 1609a); Venezia 1609 (Perera 1609b), Venezia 1618 (Perera 1618), Köln 1618 (Perera 1618a, b). (Sommervogel 1960, VI, 499) also lists a first edition of Rome 1562. Almost all scholars dismiss this as a ghost, because no copy has been located. And Perera was only twentyseven at the time and had been teaching for only four years. Jesuits did not publish large controversial works at such a young age.
 61.
 62.
There are many other passages rejecting the scientific validity of mathematics in the book. (Romano 1999, 142–145; Lamanna 2014, 69–80) quote and analyze some of them. The epistemic structure of Aristotelian physics made it very difficult for Aristotelians such as Perera to accept mathematical proof as scientifically valid (Baldini 1999b, 263–264).
 63.
“Praeterea, principia Mathematicae non exigunt longam experientiam & diligentem observationem, quaemadmodum principia Physicae vel Medicinae…propter quam pueri possunt evadere Mathematici, non autem Physici…” (Perera 1579a, 121).
 64.
“25. Curandum videretur ut maior adhibeatur diligentia circa disciplinas mathematicas, ne brevi contingat nullum reperiri qui eas praelegat. Simul et cavendum ne philosophiae professores eas publice coram auditoribus flocci faciant” (MP, IV, 254). This is a document that issued a number of admonitions about education in the province, most often concerning the Roman College and Roman Seminary. If the two sentences are not linked, it is possible that the warning to the philosophy teachers concerned the strife in the Roman College about whether Perera was an Averroist, which came to a head in 1578.
 65.
Valla’s major work on logic, which expressed his views, was published posthumously in 1622. For a translated quote from that work stating that mathematics did not deal with substances as Aristotelian physics did, see (Baldini 2000, 253 n. 42). For a brief biography of Valla, see (Pignatelli 2001). However, Valla began to teach natural philosophy at the Roman College in the academic year 1584–1585, rather than 1587 as Pignatelli states (Baldini 1992, 570).
 66.
See (MP, 5–7). These are the documents, almost all of them from ARSI, that Lukács edited and printed. Other repositories may have more documents. There is no comprehensive study of the drafting of the Ratio Studiorum for the obvious reason that it would be an immense task. However, Ladislaus Lukács in (MP, V, 1*34*; Lukács 1999, 2000) provides good short accounts.
 67.
For illustrations of the title pages see (MP, V, 41, 229).
 68.
For more comments from the provinces, see (MP, VII, 136, 147, 165, 175, 235).
 69.
For a reproduction of the title page, see (MP, V, 355). For the Jesuit editions published by Longo, see USTC. Why a Neapolitan publisher rather than a Roman publisher was chosen is unknown.
 70.
The 1599 Ratio Studiorum did mandate the establishment of academies of Greek and Hebrew, meaning Jesuits who would meet for two or three times a week to practice these skills. It also mandated teachertraining academies in which an “expert teacher” would guide young Jesuits about to begin teaching Latin grammar and the humanities in “giving lessons, dictating, writing, correcting, and performing the other duties of a good teacher” (RS, par. 81, 83) (quote). These were not academies of advanced study.
 71.
The relevant passages in the Physics are in II.ii.193b–194a.
 72.
See the explanation of “to help souls” in (O’Malley 1993, 18–19).
 73.
Assistancies were part of the structure of the Society. In 1609, there were five geographical assistancies: Italy, France, Germany, Portugal, and Spain. Each assistancy included several provinces. The Asia missions were part of the Portuguese assistancy.
 74.
 75.
 76.
For his participation in Clavius’ academy, see (Baldini 2003, 73). There is a large bibliography on Biancani.
 77.
The rest of this paragraph is speculative but likely. Much research needs to be done.
 78.
In some Italian cities, “citizen” was a legal class lower than the nobility but above commoners. Certain governmental offices were reserved for citizens, while citizen merchants enjoyed tax concessions.
 79.
For the enrollment in the mathematics class, see ARSI, Veneta 125, f. 3r, “Stato dei Studij del Colleggio di Bologna.” For details about the Bologna Jesuit schools and the struggle between the Jesuits and the university, see (Grendler 2017, 297–316).
 80.
The dialogue is printed with explanatory notes in (La scienza dissimulata 2005, 107–140).
 81.
“EX MATHEMATICIS. Praeter Geometriae, atque Arithmeticae speculativae, & practicae Elementa, traduntur ex universa Mathesi, Problemata, & Theoremata.” Archivio di Stato di Roma, Università 195, folio 23, which is the printed rotulus for the academic year 1696–1697. The descriptions of the mathematics course in the rotuli for the academic years 1697–1698, 1698–1699, and 1699–1700 are the same. ASR, Università 195, folios 23, 104, 185, 384. For photographic reproductions of those of 1696–1697 and 1699–1700, see (Grendler 2017, 328–329, 336–337). Only these four rotuli have been located.
Abbreviations
 Sphaera CorpusTracer:

Max Planck Institute for the History of Science. https://db.sphaera.mpiwgberlin.mpg.de/resource/Start. Accessed 07 June 2021
 USTC:

Universal Short Title Catalogue. University of St. Andrews. https://www.ustc.ac.uk/. Accessed 07 June 2021
 ARSI:

Archivum Romanum Societatis Iesu
 ASR:

Archivio di Stato di Roma
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Grendler, P.F. (2022). The Sphaera in Jesuit Education. In: Valleriani, M., Ottone, A. (eds) Publishing Sacrobosco’s De sphaera in Early Modern Europe. Springer, Cham. https://doi.org/10.1007/9783030866006_11
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