Weeellll.

Maffeo Cardinal Barberini was Pope Urban VIII, from 1623 - 1644. As you say, he was a friend of Galileo's before becoming Pope; his opinion was that Galileo's system could well be published as long as he treated his results as hypotheses. He was not in favour of Galileo's sentencing, but went along with it when it happened (you might wonder why he kept a low profile even though he was Pope, and therefore, in command; but Bellarmin was one formidable inquisitore, and one didn't tell him how to run his office, even if you were Pope).

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