Are infinitesimals dangerous?

I believe this has to do with Jesuit opposition to atomism, rather than their position on infinitesimals. Of course, the two are linked and evolved together in the early 17th century. Today we consider atomism a physical theory, but at the time there was no distinction between a mathematical continuum and the physical continuum, just as there was no distinction between Euclidean geometry and the geometry of the space around us.

Aristotelian physics maintained that time, space, and matter were infinitely divisible, and the Jesuits had sided with this idea. They kept records over various ideas which they had debated and found to be flawed, and atomistic ideas appear here several times throughout the first half of the 17th century.

The idea that the continuum consisted of finitely many indivisible particles, each with some physical extension, was considered to be contrary to dogmas about the Holy Communion, and hence particularly offensive. It could be taken to imply that Christ was present in the bread and wine only to a limited degree, corresponding to the number of indivisibles present. This idea was explicitly forbidden in 1608, and in the following years the Jesuit doctrine was refined to forbid atomism also in the case when there were considered to be infinitely many indivisibles.

Galileo used some atomistic ideas to explain his new physics. When his Dialogue was published in February 1632, it would be natural to examine these ideas again, and presumably this is what happened in the meeting in August 1632 mentioned by Alexander.

(For some more details, see the chapter by Palmerino in The New Science and Jesuit Science: Seventeenth Century Perspectives. She does not mention the meeting in 1632, though.)

I got the book. An interesting read. It is historical, not a novel.

The "prohibition" mentioned was a prohibition by the Jesuits of what could be taught at Jesuit schools and colleges. Their educational system, probably the best in the world at that time, was based on a unified curriculum. The idea of "indivisibles" was banned, being contrary to Aristotle. "Indivisibles" was the early form of what became the integral calculus years later.

Amir concentrates on two places the contest of whether "indivisibles" should be allowed in mathematics was played out. In Italy, where the two sides were the Jesuits and Galileo's followers. And in England, where the two sides were Hobbes and Wallis. The book contains a lot of interesting background material on those protagonists (the Jesuits, Thomas Hobbes, John Wallis).

A belated addition: from various reading, which I cannot recall precisely, the Jesuits were unhappy far more about "atomism" than heliocentrism, because "atomism" would seem to strongly indicate that "transubstantiation" (the alleged conversion of wine into Jesus' blood, or whatever) was impossible.