After the disappointing time in Pisa, the eighteen years that Galileo spent in Padua represented a significant change for him both professionally and privately, although his financial problems were not solved and indeed worsened when the death of his father in 1591 increased the burden of supporting his family. He had been appointed to the Chair of Mathematics at the University of Pisa, again thanks to Guidobaldo del Monte's circle, and was giving much time to private teaching as well, forming a group of pupils many of whom were to remain lifelong friends. The universities of Pisa and Padua were of more or less equal status and the professors were often the same in each; they migrated from one centre to the other, laden with their baggage of peripatetic physics which, both in Tuscany and in the Veneto, it was difficult to free from the mindset of metaphysics. Outside the walls of the academic world, the cultural ferment and the presence of important intellectual figures made Padua a centre of study and exchange of ideas totally unlike suffocating, provincial Pisa. Galileo was an active member of academies and cultural circles, not only in Padua but also in Venice, where he was in contact with prominent scientists and men of letters such as Paolo Sarpi and Giovanfrancesco Sagredo. Galileo's bond with Sagredo was such that he subsequently immortalised him as one of the interlocutors in the Dialogo sopra i due massimi sistemi del mondo [Dialogue concerning the Two Chief World Systems] and in the Discourses and M athematical Demonstrations concerning Two New Sciences. Galileo also entered into a relationship with Marina Gamba, a Venetian woman by whom he had three children, Virginia, Livia and Vincenzo, without however marrying her.

Occasional requests for opinions on applied mechanics inevitably led him to study the theoretical aspects of this discipline, which he then made the subject of a university course on the Quaestiones mechanicae [Questions of Mechanics] of the pseudo-Aristotle. Galileo gathered together the fruits of his studies, broadening the knowledge acquired during his years in Pisa, in Le mecaniche [Mechanics], a treatise written in various versions, presumably between 1593 to 1602, but circulated only in manuscript form until its posthumous publication in 1649. Basing himself on the working of machines such as the pulley, the winch, the lever scales and the lever, he formulated the definitions of gravity, the momentum of falling bodies and the centre of gravity, thus establishing the foundations of his physics as applied to mechanical work. While Aristotle was the subject of his public lectures, his private teaching centred on the Mechanics, together with the art of warfare, as attested by the Breve instruzione all' architettura militare [Brief In troduction to Military Architecture] and the Trattato di fortificazione [A Treatise on Fortification]. Apart from the subjects he taught, the phenomena of motion continued to occupy the centre of his interests. Although he had abandoned his previously announced idea of writing a treatise, Galileo had made progress towards formulating not only the law of the constant period of the oscillations of the pendulum, but more importantly, the law of falling bodies, using instruments he constructed himself, such as the inclined plane. His studies during this period provided precious groundwork for the future, when in old age he attempted a systematic explanation of the knowledge he had acquired on so-called local motion. But already in these earlier years his work, although in embryonic form, dangerously threatened the concept of an Earth positioned at the centre of the universe, to which all falling bodies are attracted.

His teaching duties obliged him to hold courses in cosmography based on the Ptolemaic system. Evidence of this is his Trattato della sfera ovvero cosmografia [Treatise on the Sphere, or Cosmography] (also published posthumously in 1656), which was the text he used to teach this subject. And yet two letters, one to Iacopo Mazzoni and one to Kepler, both dating from 1597, unequivocally attest to how Galileo already considered 'the opinion of the Pythagoreans and of Copernicus... much more probable than that of Aristotle and Ptolemy', openly stating this in correspondence with his European colleagues although not yet publicly proclaiming it. Probably the discussion in the cultural circles of the Veneto, an avant-garde milieu, had contributed to definitively formulating a hypothesis already present in embryonic form in his research on motion, which hinted at the idea that falling bodies fell toward a centre of the Earth that was not necessarily the Aristotelian centre of the universe but one of the many possible centres, in accordance with the Copernican hypothesis.

When a supernova appeared a few years later, in 1604, Galileo considered it to be a transitory 'splendour', but not, in spite of this aspect, 'a star like the rest.' This phenomenon gave him the opportunity to study more deeply the rationale of the Copernican system as against the Aristotelian concept of the incorruptibility of the heavens, according to which it was inconceivable that 'most of the comets and all such similar stars were generated in the starry skies.' The appearance of the supernova gave rise to lively debate, and, in the Dialogo d e Cecco di Ronchitti da Bruzene in perpuosito della stella nuova [Dialogue concerning the New Star by Cecco di Ronchitti of Brugine], written under a pseudonym by the Benedictine monk, Girolamo Spinelli, there is also presumably the hand of Galileo. The heated polemic on the nature of the nova gave him a first taste of that 'animosity in detracting, cheating and vilifying' which was to plague him all his life, and he would soon have to confront intrigues and deceitful manoeuvres, unyielding in the face of 'false pretences ... fraudulent tricks and ... bold appropriation of ideas.'

Teaching was not Galileo's only activity in Padua. He continued to pursue his theoretical studies and worked tirelessly on their practical application, even setting up a workshop at his home, entrusted to the mechanic Marcantonio Mazzoleni. Here, in this home laboratory, instruments of various kinds were tried out. More than once, similar devices made their appearance in the laboratories of other scientists (or would-be scientists), arousing the anger of Galileo, who considered them his own inventions. Such was the case of the thermoscope (a rudimentary thermometer), constructed by Santorre Santorio, an Istrian doctor who had moved to Padua, and, even worse, that of the geometric and military compass, claimed as his own by Baldassarre Capra (a sinister figure whose dishonesty had already been made plain on the appearance of the nova in 1604) in his Usus et fabrica circini cuiusdam proportionis [Use and Construction of the Proportiona l Compass], which was no more than a plagiarism in Latin (filled, moreover, with errors) of Galileo's Operazioni del compasso geometrico e militare [Operations of the Geometric and Military Compass], published in 1606. A furious Galileo, 'overcome by amazement, indignation and distress', was obliged to appeal to the Riformatori of the University of Padua, who enjoined Capra to destroy every copy of his book and, since some copies, dispersed abroad, could not be found and had remained in circulation, to print and disseminate a Difesa contro alle calunnie et imposture di Baldesar Capra [Defence against the Calumnies and Impostures of Baldassare Capra].

'The best eighteen years of my life': thus was Galileo to remember his time in Padua. There he had sown the seeds of everything he was to harvest in the future, ranging from statics to dynamics, to mechanics, to cosmology, facilitated by that 'splendid and generous … Republic' which, while obliging him to 'give public service' - that is, to teach in order 'to ensure the good use of public money' - nonetheless left him free to investigate whatever field most appealed to him. It was the Venetian Republic that disentangled him from his first difficulties of a legal nature, preventing any credence being given or follow-up made to the accusations of a former employee who, having 'seen Galileo in his room drawing up various horoscopes for various people', denounced him to the local Inquisition for involvement in astrological practices.

Despite his new close ties in the Veneto, Galileo had always remained in contact with Florence, where his mother, now a widow, had continued to live, probably with her sister Virginia and the latter's husband, Benedetto Landucci, in the neighbourhood of the Church of the Carmine, where in time she would be buried. Every summer Galileo returned to Tuscany, and in 1605, at the wish of the Grand Duchess Christine of Lorraine, he began to teach mathematics to Prince Cosimo de' Medici. Galileo was a guest of the Court at the Villa of Pratolino in 1605, (a stay which saw him 'confined to his bed by a tertian fever') and at the Villa of Artimino in 1608. His regular correspondence with such prominent figures as Belisario Vinta, Secretary of State of the Grand Duchy of Tuscany, shows that his contacts with the Court were far from sporadic. The time was now ripe for a definitive return home.