Even as a newly enrolled student, Galileo showed a certain contempt for academic life which was to continue and which intensified when he became a teacher himself. This attitude was to inspire the biting Capitolo contro il portar la toga [Against wearing t he Gown] (1590), in which his reaction against the requirement to dress as befits a 'doctor' (that is, to wear a gown) is a vehicle for a none-too-veiled criticism of the working method of those

 

who go searching for the highest good

but for ever fail to find it,

since it is not where they are seeking.

 

His judgment of a certain type of scholar, not merely of his dress, was severe. Against a concept of knowledge that he saw as the unthinking repetition of a tradition, Galileo advanced an opposing view:

 

h e who seeks to find a thing

must use his imagination,

and play with invention, and guess.

 

Galileo indeed had been gifted with imagination since boyhood. According to Vincenzo Viviani, a young pupil of his and later his [a1] biographer, Galileo in 1583, while observing in the Cathedral of Pisa the oscillation of a lamp, now conserved in the Camposanto, had asked 'whether the times of oscillation between two points, for large, medium and small arcs, were the same.' He had in fact deduced the constant period of a pendulum, which he established by measuring the oscillations against the beating of his own pulse, employing the sense of rhythm he had developed in studying music. This story may be a product of Viviani's eulogistic frame of mind. What is certain is that Galileo anticipated the application of the pendulum in medicine (to establish a patient's pulse rate as a sign of changes in bodily temperature), but then utilised it - an indispensable instrument, thanks to the precision of its measurements - to determine the laws of motion.

Moreover, Galileo's curiosity was not satisfied by the teaching of medicine and philosophy provided at the university by such professors as Andrea Cesalpino, Girolamo Borro, Francesco de' Vieri (known as Verino Secondo) and Francesco Buonamici, tied as they all were, notwithstanding their different views and abilities, to the Aristotelian tradition or, in the case of followers of an enervated Platonism by then reduced to sterile dispute, obliged to conform to that tradition by the Statutes of Cosimo I. According to Vincenzo Viviani's account, which was not entirely detached or objective, Galileo's mind was not one that could 'easily assent to mere maxims and opinions of ancient or modern writers, when he could, through discussion, reason and experiment, satisfy himself.' Consequently, in his refusal to submit to a dogmatic, non-critical concept of science, he attracted the hostility of many 'fierce defenders' of Aristotelianism. Here was a beardless young student taking a stand in opposition to the age-old, rock-hard certainties of the Doctors.

Bored with arid Aristotelian studies, the young Galileo soon turned to geometry, in which he saw the basis for the laws of music and perspective. This move was against the will of his father, who had counted on his son becoming a physician and being able to support the family. Galileo's first teacher of geometry was Ostilio Ricci, court mathematician and tutor to the Grand Duke's pages, under whose guidance he read the entire volume of Euclid's Elements, 'keeping texts of the followers of Hippocrates and Galen close at hand ... so as quickly to cover the copy of Euclid with them when his father approached.' Galileo was also absorbed in reading Archimedes. His medical studies were neglected and subsequently, with his father's reluctant agreement, abandoned.

Thus in 1585 Galileo returned to Florence, equipped with his newly acquired knowledge of geometry, leaving university without having taken a degree although in a position to have done so. The precise reason for this is unknown but, given the circumstances, the decision is unsurprising.

Dating from this second Florentine phase is The Little Balance, a fruit of Galileo's studies of Archimedes that was never published but that has survived in the autograph manuscript. Starting from the description, handed down by Vitruvius, of the trick played on the tyrant Hiero by a goldsmith who replaced some of the gold in his crown with silver (a deception unmasked by Archimedes 'using the medium of water'), Galileo realised that the way to 'determine the mixture of two metals precisely' was to use 'the medium of a balance.' The balance could be employed to measure the weight of the substances first in air, then in water -that is, in media of unequal density - thus making it possible to determine their different specific weights, in accordance with Archimedes' laws of hydrostatics.

A development of the thought of Archimedes, who had considered the centre of gravity of planes, is also found in the Theorems concerning the Centre of Gravity of Solids, probably dating from this period, although published only in 1638 as a part of the Discorsi e dimostrazioni matematiche intorno a due nuove scienze [Discourses and Mathemati cal Demonstrations concerning Two New Sciences]. His studies on the centre of gravity of solids, considered simply as points and thus geometric elements, demonstrate not only the young Galileo's already high level of mathematical knowledge but also his remarkably youthful deviation from Aristotelian physics, which was centred on the 'quality' of bodies and indifferent to their 'quantity.' It was indeed in the work of Archimedes that Galileo, like many of his contemporaries, found the basis for this application of mathematics to physics, which was soon to engage him in vigorous opposition to the old methods of the scholastic tradition.

In 1589 Galileo left Florence, to return for good only after many years of university teaching, first in Pisa, then in Padua.