Mario Bettinus

Mario Bettinus studied mathematics under the Belgian Jean Verviers and Giuseppe Biancani at the Jesuit College of S. Rocco, in Parma. When Biancani died in 1624, the chair of mathematics went to Bettini, who taught military art, stereometry, and conics theory.{{sfn|Aricò|1996|p=209}} He was also responsible for teaching military architecture during the period 1624–1630. Among the students attending his classes were the two sons of Duke Ranuccio, Ottavio and Odoardo. Besides being Ottavio's teacher of military mathematics, Bettinus also served as military consultant to the courts of Parma (1612–1613), Modena (1617–1618) and again Parma (1626–1627), and as a military architect at Novellara (1618–1619), seat of the novitiate of the Jesuit ‘Provincia Veneta’.{{Cite book|first=Denis|last=De Lucca|title=Jesuits and Fortifications: The Contribution of the Jesuits to Military Architecture in the Baroque Age|publisher=Brill Publishers|year=2012|page=90|isbn=9789004216518}}

Bettinus was primarily a mathematician and mathematical physicist. He labeled himself a philosophus mathematicus, meaning a scholar who relies on mathematics to study natural philosophy.{{cite book |last=Carolino |first=Luís Miguel |title=The Oxford Handbook of the Jesuits |date=2019 |publisher=Oxford University Press |isbn=9780190639655 |editor=Ines G. Županov |location=Oxford |page=671 |contribution=Astronomy, Cosmology and Jesuit Discipline, 1540-1758}} Bettinus was somewhat ambivalent towards Galileo's Copernicanism and his new astronomical observations. Although generally recognizing the importance of Galileo's discoveries, he disagreed with some of the conclusions expounded in Sidereus Nuncius especially over the height of the mountains on the moon.{{cite book |last1=Piccolino |first2=Nicholas J. |first1=Marco |title=Galileo's Visions. Piercing the Spheres of the Heavens by Eye and Mind |last2=Wade |publisher=Oxford University Press |year=2014 |location=Oxford |page=89}} According to Bettini, if there were very high mountains on the Moon, the lunar disk observed with the telescope would appear irregular and jagged, while on the contrary, it looked perfectly round.Denise Aricò, ""In Doctrinis Glorificate Dominum': Alcuni aspetti della ricezione di Clavio nella produzione scientifica di Mario Bettini," in Christoph Clavius e l'attività scientifica dei Gesuiti nelletà di Galileo, Ugo Baldini, ed. (Rome: Bulzoni: 1995), 189-207, especially 191-196. Bettini's objections echoed the doubts raised in Johannes Kepler's Dissertatio cum Nuntio Sidereo.See Kepler, J. Conversation with Galileo's Sidereal Messenger, with an introduction and notes by E. Rosen (New York, 1965). pp. 28-9. Giovanni Riccioli, who heard Bettinus lecture at Parma, mentions his attempts to measure the heights of lunar mountains.

Besides being the mentor of Guarino Guarini (1624–1683) and a friend of Christoph Grienberger,On Bettini, his place among the Jesuits and his relationship with Christoph Grienberger, see {{citation |last=Gorman |first=Michael John |title=The New Science and Jesuit Science: Seventeenth Century Perspectives |date=2003 |volume=6 |pages=4–7 |editor-last=Feingold |editor-first=Mordechai |url=http://www.stanford.edu/group/shl/Eyes/modesty/index.htm |archive-url=https://web.archive.org/web/20050313041653/http://www.stanford.edu/group/shl/Eyes/modesty/index.htm |archive-date=March 13, 2005 |url-status=dead |series=Archimedes |contribution=Mathematics and modesty in the Society of Jesus: The Problems of Christoph Grienberger (1564–1636) |location=Dordrecht |publisher=Kluwer}}. Bettinus was also a close friend of Prince Raimondo Montecuccoli (1609–1680)—the latter had even sent him a copy of his work on fortifications from Hohenegg on 15 July 1652.{{sfn|Aricò|1996|p=69}} He opposed Bonaventura Cavalieri's method of indivisibles and the theory of the infinitesimal quantities.{{sfn|Gatto|2019|page=646}}

Bettinus privileged mathematics, intended as the only discipline abstract enough to allow intellect to approach theology. The Jesuit mathematician held the belief that, precisely because of their abstraction, mathematical theorems and demonstrations lead one away from the mundane and toward the divine. On the contrary, he considered a research based on sense as too bound to human limitations (and, therefore, unreliable). Yet, Bettinus was a skilled astronomer; and clues of experimental knowledge are all but invisible in his work.{{cite journal|title=Description, analogy, symbolism, faith. Jesuit science and iconography in the early modern debate on the origin of springs|first=Francesco|last=Luzzini|doi=10.7343/as-2016-223|volume=5|issue=2|year=2016|journal=Acque Sotterranee - Italian Journal of Groundwater|page=66|doi-access=free|hdl=10278/3743272|hdl-access=free}}

His best-known work is Apiaria Universae Philosophiae Mathematicae 'Beehives of all mathematical philosophy' (1645), an encyclopedic collection of mathematical curiosities.{{citation|title=The Geometry of an Art: The History of the Mathematical Theory of Perspective from Alberti to Monge|series=Sources and Studies in the History of Mathematics and Physical Sciences|first=Kirsti|last=Andersen|publisher=Springer|date=2008|isbn=9780387489469|page=[https://books.google.com/books?id=8B_JeMxNUIkC&pg=PA374 374]|title-link=The Geometry of an Art}}. This book, reflecting his many interests, is a collection of scientific mysteries embracing everything from geometrical demonstrations to illusionistic stage sets, perpetual motion machines, anamorphoses and sundials.Bettinus penned a method for laying out a sundial which was posthumously published in the book Recreationum Mathematicarum Apiaria Novissima 1660. The second volume has a section on music and acoustics. According to Bettinus, the natural world abounds in mathematical delights such as spider webs and the honeycombs of bees. From these creations of nature can be drawn geometrical principles useful for mechanical, optical, and artistic designs.{{cite book|title=The Age of the marvelous|page=436|publisher=Hood Museum of Art|year=1991|isbn=9780944722107}} The Apiaria surveys a staggering array of instruments, machines, and other tangible applications of mathematical principles. It is illustrated with beautiful engravings of these machines, which – Bettini points out – are rough imitations of the great and perfect mechanisms provided by nature. The work included a commentary on the first six books of Euclid, a traditional part of Jesuit mathematical curriculum and a form followed by Clavius a half century earlier.{{cite journal |last=Baldwin |first=Martha |year=2003 |editor-last=Feingold |editor-first=Mordechai |title=Pious Ambition: Natural Philosophy and the Jesuit Quest for the Patronage of Printed Books in the Seventeenth Century |journal=Jesuit Science and the Republic of Letters |publisher=MIT Press |page=298 |isbn=0262062348}}

In his Apiaria military technologies featured prominently. His machines of war were mentioned by Montecuccoli, by the famous Jesuit mathematicians Athanasius Kircher and Jacques Ozanam and by the Polish master of artillery, Casimir Semenowycz. The book was a huge success throughout Europe. It was read by John Collins and Isaac Barrow{{cite journal|last = Beeley|first=Philip|title=Mathematical Businesses: Seventeenth-Century Practitioners and their Academic Friends|journal=Beyond the Learned Academy: The Practice of Mathematics, 1600-1850|location=Oxford|year=2024|doi=10.1093/oso/9780198863953.003.0011|pages=294–295|publisher=Oxford University Press}} and a copy of it can be found in the library of the English physician and philosopher Sir Thomas Browne.{{cite book | editor-last = Finch | editor-first = Jeremiah S. | date = 2023 | title = A Catalogue of the Libraries of Sir Thomas Browne and Dr. Edward Browne, His Son: A Facsimile Reproduction with an Introduction, Notes, and Index | url = | location = | publisher = Brill Publishers | pages = 109–110 | isbn = 978-9004617612}}

File:Bettinus crater 4154 h3.jpg named after Bettinus]]

• Apiaria Universae Philosophiae Mathematicae, in quibus Paradoxa, et nova pleraque machinamenta ad usus eximios traducta et facillimis demonstrationibus confirmata exhibentur, 3 vols. Bologna: Typis Io. Baptistae Ferronij, Venice: Apud Paulum Baleonium, 1642–55. The 'paradoxes' are of many different kinds—scientific ideas contrary to general opinion, logical and mathematical paradoxes, geometrical problems which had not yielded to solution, curious machines and engines, illusions, games, and tricks. Bettinus tackled the 'learned hallucinations' constellated about the quadrature problem, and about asymptotic lines which go de infinito infinito, as well as those that result from deformation of the rules of perspective. Archimedes' screw (which raised by lowering itself), wedges, levers all make their appearance, magnificently illustrated.{{cite book|isbn=9780691650487|pages=305–6|title=Paradoxia Epidemica: The Renaissance Tradition of Paradox|author-link=Rosalie Littell Colie|first=Rosalie Littell|last=Colie|year=1966|publisher=Princeton University Press}}
• {{Cite book|title=Aerarium philosophiae mathematicae|volume=1|publisher=Giovanni Battista Ferroni|location=Bologna|year=1647|language=la|url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=825639}}
• {{Cite book|title=Aerarium philosophiae mathematicae|volume=2|publisher=Giovanni Battista Ferroni|location=Bologna|year=1648|language=la|url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=47338}}
• {{Cite book|title=Aerarium philosophiae mathematicae|volume=3|publisher=Giovanni Battista Ferroni|location=Bologna|year=1648|language=la|url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=1217105}}

• List of Jesuit scientists
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{{Reflist}}

• {{Cite book |last=Aricò |first=Denise |title=Scienza, teatro e spiritualità barocca: il gesuita Mario Bettini |publisher=CLUEB |year=1996 |location=Bologna |isbn=9788880913177}}
• {{cite book

| last = Aricò

| first = Denise

| date = 2002

| chapter = Politica e istruzione alla corte di Ranuccio Farnese: i gesuiti Mario Bettini e Jean Verviers

| publisher = CLUEB

| title = Gesuiti e università in Europa (secoli XVI-XVIII) Atti del Convegno di studi. Parma, 13-15 dicembre 2001

| location = Bologna

| pages = 213-242

| editor1 = Gian Paolo Brizzi

| editor2 = Roberto Greci

| doi = 10.1400/35003

}}

• {{cite journal|first=Denise|last=Aricò|title=Una corrispondenza fra il gesuita bolognese Mario Bettini e Raimondo Montecuccoli|journal=Filologia e Critica|volume=XXXI|year=2006|issue=2 |pages=288–312|doi=10.1400/81069}}
• {{cite book

| last = Gatto

| first = Romano

| contribution = Jesuit mathematics

| date = 2019

| title = The Oxford Handbook of the Jesuits

| editor = Ines G. Županov

| location = Oxford

| publisher = Oxford University Press

| page = 637-669

| isbn = 9780190639655

}}

• {{cite book |last1=Cocks |first1=Elijah E. |last2=Cocks |first2=Josiah C. |year=1995 |title=Who's Who on the Moon: A Biographical Dictionary of Lunar Nomenclature |publisher=Tudor Publishers |isbn=9780936389271 |url=https://archive.org/details/isbn_9780936389271}}

{{Commons}}

• Bettinus' (1642, 2 vol.) [https://catalog.lindahall.org/discovery/delivery/01LINDAHALL_INST:LHL/1289476080005961 Apiaria universae philosophiae mathematicae] - Linda Hall Library
• {{cite journal

| last = Briatore

| first = Samuele

| date = 2015

| title = Suono e acustica nella trattatistica gesuitica del Seicento. Il caso di Mario Bettini

| url =

| journal = Forum Italicum: A Journal of Italian Studies

| volume = 49

| issue = 2

| pages = 322–337

| doi = 10.1177/0014585815583287

| access-date =

}}

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