**Stephano Angeli** was an Italian mathematician who worked on infinitesimals and used them to study spirals, parabolas and hyperbolas.

- Since the Order had a major influence on Angeli's life and mathematics, we should say a little about it.
- What would Angeli have worn as a Jesuati?
- It was a good move in terms of Angeli's health, and also a good move for mathematics since in Bologna he came under the influence of Cavalieri.
- After leaving Bologna, Angeli continued his contacts with Cavalieri by correspondence, and was entrusted to publish Cavalieri's final work, Exercitationes geometricae sex Ⓣ(Six geometric exercises), since by 1647 Cavalieri's health had deteriorated to such an extent that he was unable to carry out the work himself.
- Angeli also corresponded with a number of other mathematicians including Torricelli and Viviani.
- After Cavalieri's death, later in 1647, Angeli was offered his chair of mathematics at the University of Bologna but he was still too modest about his own mathematical achievements to accept the position.
- Angeli was Rector of a Jesuati Order religious establishment in Rome from 1647 to 1652.
- James Gregory studied with Angeli in Padua from 1664 to 1668 and learnt from him about series expansions of functions.
- The Jesuati Order was suppressed in 1668 by Pope Clement IX who believed that abuses had crept in over the years, but Angeli continued in the priesthood while holding the chair of mathematics at Padua.
- Angeli's many mathematical works were on infinitesimals and he used them to study spirals, parabolas and hyperbolas.
- The approach followed by Angeli in all these works is that of his teacher Cavalieri and of Torricelli, so when Guldin and Tacquet attacked these methods and defended the approach of the ancient Greeks, Angeli disputed with them over indivisibles.
- One has to see both sides in this argument for although Angeli's methods were much more powerful, they were less rigorous than the method of exhaustion adopted by Archimedes.
- Angeli examined fluid statics based on Archimedes' principle and Torricelli's experiments.
- Of course Angeli held the chair at Padua which had been held earlier by Galileo and his work shows strong influences from his predecessor.
- For example Angeli often refers to Galileo in his writings on physics, showing clearly how he has been influenced, particularly in terms of ways of approaching problems via the experimental method.
- Also clearly influenced by Galileo is Angeli's writings on the two systems of Ptolemy and Copernicus which he writes in Galileo's dialogue style.

Born 21 September 1623, Venice, Venetian States (now Italy). Died 11 October 1697, Venice, Venetian States (now Italy).

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Analysis, Origin Italy

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive