Stefano Angeli

Stefano degli Angeli (Venice, September 23, 1623 – Padova, October 11, 1697) was an Italian mathematician, philosopher, and Jesuat.

He was member of the Catholic Order of the Jesuats (Jesuati). In 1668 the order was suppressed by Pope Clement IX. Angeli was a student of Bonaventura Cavalieri. From 1662 until his death he taught at the University of Padua.

From 1654 to 1667 he devoted himself to the study of geometry, continuing the research of Cavalieri and Evangelista Torricelli based on the method of Indivisibles. He then moved on to mechanics, where he often found himself in conflict with Giovanni Alfonso Borelli and Giovanni Riccioli. James Gregory studied under Angeli from 1664 until 1668 in Padua. Jean-Étienne Montucla in his monumental Histoire des mathématiques (Paris, 1758), lavishes praise on Angeli (II, p. 69).

Angeli moved from Rome to his native city of Venice in 1652 and began publishing on the method of indivisibles. The method had been under attack by Jesuits Paul Guldin, Mario Bettini, and André Tacquet. Angeli's first response appeared in an "Appendix pro indibisibilibus," attached to his 1658 book Problemata geometrica sexaginta, and was aimed at Bettini. Alexander (2014) shows how indivisibles and infinitesimals were perceived as a theological threat and opposed on doctrinal grounds in the 17th century. The opposition was spearheaded by clerics and more specifically by the Jesuits. In 1632 (the year Galileo was summoned to stand trial over heliocentrism) the Society's Revisors General led by father Jacob Bidermann banned teaching indivisibles in their schools (Alexander p. 17). Cavalieri's indivisibles and Galileo Galilei's heliocentrism were systematically opposed by the Jesuits and attacked through a spectrum of means, be it mathematical, academic, political, or religious (Alexander, Part I). Bettini called the method of indivisibles "counterfeit philosophizing" and sought to discredit it through a discussion of a paradox presented in Galileo's Discorsi. Angeli analyzes Bettini's position and proves it untenable (Alexander, p. 168).

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