I love and admire Galileo, not only for his rare learning and invention, but also for the old friendship that I had with him in Padua, where I was overcome by his courtesy and affection, which bound me to him.It is also worth recounting the tensions in Padua during the years that Biancani studied there. The Jesuit College, established in Padua in 1542, had become an important educational establishment by 1590 offering a three-year philosophy degree; logic was taught in year one, natural philosophy and physical science in year two, and metaphysics and natural philosophy in year three. However, the university students objected to the Jesuit College and the Venetian Senate became involved in the argument in December 1591. The Jesuit College was accused of being a rival university to the University of Padua, something which was illegal by Venetian law. As a result of the dispute, it was forbidden from teaching students other than Jesuits. Much of the argument, which continued during the years that Biancani studied there, was centred around the teachings of Aristotle; the Jesuit teachers were accused of not teaching directly from Aristotle but rather using modern texts. Clearly this influenced Biancani who, a few years later in 1615, published a text Aristotelis loca mathematica ex universis ipsius operibus collecta et explicata in which he treated the mathematical parts of Aristotle's writings. Biancani explained why he wrote the text:-
I, too, began devoting myself to Aristotle's writings, so that the passages which concern mathematics that are scattered throughout his work have been collected and explained by me, to make them useful, above all, to those students of philosophy who, having renounced the ancient custom without a knowledge of mathematics, dedicate themselves to philosophy to the detriment of their studies.In the early 1600s Biancani, having completed the long training period for the Jesuit order, went to the Jesuit College in Parma where he taught mathematics for his whole career. He also taught at the University of Parma; Paul Grendler in  lists the professors teaching at the university in session 1617-18 which includes 'Giuseppe Biancani of Bologna' lecturing in the afternoon on mathematics as part of "Arts and Theology". In this course he taught Euclid's Elements and astronomy.
We have quoted above from Biancani concerning his high regard for Galileo. However, he did not always agree with Galileo's views. The first disagreement came in 1611 and concerned the mountains on the moon. Galileo had observed the surface of the moon through a telescope in 1609 and had used certain mathematical techniques to prove that there were lunar mountains. His claim appeared in Sidereus Nuncius published in May 1610. In May 1611 a group of scientists, mostly Jesuits, was brought together by cardinal Ferdinando Gonzaga in Mantua to discuss Galileo's claims. One of the major points discussed was Galileo's proof that there were mountains on the moon, and the report from the group came down firmly in favour of the traditional belief that the moon was perfectly smooth. Galileo suspected that Biancani was the author of the report and letters were exchanged in which Biancani dissociated himself from any insult towards Galileo saying that he was sorry if he had been offended but, nevertheless, pointing out that he did believe that the moon was perfectly smooth. He also disagreed with Galileo in 1613 when a dispute broke out between Galileo and Christoph Scheiner over sunspots. Galileo unfairly accused Scheiner of plagiarism but, although Scheiner's discovery of sunspots was certainly independent of any work by Galileo, his explanation was quite wrong. Biancani, however, defended his fellow Jesuit Scheiner.
We noted above that Biancani published Aristotelis loca mathematica in 1615. In fact he tried to publish the work in the previous year but, like all publications by Jesuits at this time, it had to be first approved. Giovanni Camerota read the work to see if it was suitable for publication and wrote:-
It does not seem to be either proper or useful for the books of our members to contain the ideas of Galileo, especially when they are contrary to Aristotle.Before the work could be published, Biancani had to remove the description of Galileo's work on floating bodies, and replace it with a simple reference indicating where Galileo's theory could be found. Francesco Paolo de Ceglia writes about the contents of Aristotelis loca mathematica :-
... the dedication is followed by an address to the reader wherein Biancani, in a rhetorical tirade, bemoans the wretched state to which mathematics has sunk and calls for its revitalisation. Under sixteen headings, he announces "Some of the most important things, either new or restored, treated in this exposition.Biancani attached to this work his mathematical chronology De Mathematicarum natura dissertatio una cum clarorum mathematicorum chronologia. This work, which is unfortunately full of errors, is discussed in  in which Giulio Cesare Giacobbe shows that:-
Giuseppe Biancani's treatise, 'De mathematicarum natura disertatio' (Bologna, 1615) ... tried ... to assert the inclusion of mathematics into the formal structure of Aristotelian syllogistics ...As to the chronology errors, let us give some examples: Thabit ibn Qurra (836-901) who Biancani gives as a 13th century scholar, Roger Bacon (1214-1292) who is given as a 14th century scholar, and Leonardo Pisano (Fibonacci) (1170-1250) who is put in the 15th century.
It is not entirely clear where Biancani stood on the question of a geocentric or heliocentric system. He held Galileo in the highest esteem yet he believed in a stationary earth. Whether this was on scientific grounds, or whether he felt that he had to present this view to stay on the right side of the Church is a little hard to determine. His second major publication Sphaera mundi, seu cosmographia demonstrativa, ac facili methodo tradita was completed in 1615. In it Biancani presented details of the work of Nicolaus Copernicus, Tycho Brahe, Johannes Kepler, and Galileo. It also recorded his own observations with a telescope. However, the book again had difficulties with the censor and it was 1620 before it was finally published. Let us present here what Biancani writes about the geocentric/heliocentric controversy and let the reader judge his real beliefs:-
This ancient [heliocentric] belief was brought back to life again in the past century by Nicolaus Copernicus, a man of sharp mind and a great restorer of the science of astronomy. He even defended it against the argument of other men, so that today some mathematicians of high repute, as for example Johannes Kepler, William Gilbert (author of 'De magnetica philosophia'), and others, support the same unfortunate view. Other mathematicians reject this view as absurd. Copernicus actually added that not only is the earth moved in the ecliptic, but together with the earth, the water and the air and all the 'interlunary' sphere, in just the same proportion as the earth moves, by which hypothesis not only do Copernicus and his followers seek to save appearances but also believe they easily escape the counter-arguments of their opponents. For all that, however, this opinion is false and must be rejected (even if supported by better proofs and arguments), as is manifest by reasons given formerly and by many opinions of authorities; all the more because it has been forbidden by the ecclesiastical authorities as contrary to Holy Writ.Here is Biancani's description of Jupiter's four moons:-
It is a remarkable and happy discovery, which has been found by the power of the telescope, that Jupiter is accompanied. And indeed there are always four tiny stars or planets about him, running courses round him ... It is thus that we see them on a clear night through the telescope pointed at Jupiter, and, as we look, we see near to the planet, sometimes one, sometimes two or three, at times even four, of these little stars keeping the planet company, which would be impossible if they were fixed and not moving stars. Sometimes too they appear nearer and sometimes further from the planet, which is only possible if we suppose that they trace circles about Jupiter, just as Mercury and Venus revolve about the sun. ...Sphaera mundi was republished in 1630, 1635 and 1653. The last two of these have a posthumous publication of Biancani's attached, namely Novum instrumentum ad horologia describenda. This describes his method for constructing a sundial.
During his final four years teaching at Parma, from 1620 to 1624, Biancani taught Giovanni Battista Riccioli who was one of his students. Riccioli makes it clear what a strong positive influence Biancani had on him. Finally, we note that Biancani's writings on history, poetry and classical Greek and Latin have not survived. Let us end by recording, from Mathematicarum natura dissertatio, Biancani's view of mathematics:-
It absolutely follows that mathematics is superior to all other sciences, in the same way that truth is superior to all opinions.
Article by: J J O'Connor and E F Robertson