iangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth.
Pope Urban VIII invited Galileo to papal audiences on six occasions and led Galileo to believe that the Catholic Church would not make an issue of the Copernican theory. Galileo, therefore, decided to publish his views believing that he could do so without serious consequences from the Church. However by this stage in his life Galileos health was poor with frequent bouts of severe illness and so even though he began to write his famous Dialogue in 1624 it took him six years to complete the work.
Galileo attempted to obtain permission from Rome to publish the Dialogue in 1630 but this did not prove easy. Eventually he received permission from Florence, and not Rome. In February 1632 Galileo published Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican. It takes the form of a dialogue between Salviati, who argues for the Copernican system, and Simplicio who is an Aristotelian philosopher. The climax of the book is an argument by Salviati that the Earth moves which was based on Galileos theory of the tides. Galileos theory of the tides was entirely false despite being postulated after Kepler had already put forward the correct explanation. It was unfortunate, given the remarkable truths the Dialogue supported, that the argument which Galileo thought to give the strongest proof of Copernicuss theory should be incorrect.
Shortly after publication of Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican the Inquisition banned its sale and ordered Galileo to appear in Rome before them. Illness prevented him from travelling to Rome until 1633. Galileos accusation at the trial which followed was that he had breached the conditions laid down by the Inquisition in 1616. However a different version of this decision was produced at the trial rather than the one Galileo had been given at the time. The truth of the Copernican theory was not an issue therefore; it was taken as a fact at the trial that this theory was false. This was logical, of course, since the judgement of 1616 had declared it totally false.
Found guilty, Galileo was condemned to lifelong imprisonment, but the sentence was carried out somewhat sympathetically and it amounted to house arrest rather than a prison sentence. He was able to live first with the Archbishop of Siena, then later to return to his home in Arcetri, near Florence, but had to spend the rest of his life watched over by officers from the Inquisition. In 1634 he suffered a severe blow when his daughter Virginia, Sister Maria Celeste, died. She had been a great support to her father through his illnesses and Galileo was shattered and could not work for many months. When he did manage to restart work, he began to write Discourses and mathematical demonstrations concerning the two new sciences.
After Galileo had completed work on the Discourses it was smuggled out of Italy, and taken to Leyden in Holland where it was published. It was his most rigorous mathematical work which treated problems on impetus, moments, and centres of gravity. Much of this work went back to the unpublished ideas in De Motu from around 1590 and the improvements which he had worked out during 1602-1604. In the Discourses he developed his ideas of the inclined plane writing:-
I assume that the speed acquired by the same movable object over different inclinations of the plane are equal whenever the heights of those planes are equal.
He then described an experiment using a pendulum to verify his property of inclined planes and used these ideas to give a theorem on acceleration of bodies in free fall:-
The time in which a certain distance is traversed by an object moving under uniform acceleration from rest is equal to the time in which the same distance would be traversed by the same movable object moving at a uniform speed of one half the maximum and final speed of the previous uniformly accelerated motion.
After giving further results of this type he gives his famous result that the distance that a body moves from rest under uniform acceleration is proportional to the square of the time taken.
One would expect that Galileos understanding of the pendulum, which he had since he was a young man, would have led him to design a pendulum clock. In fact he only seems to have thought of this possibility near the end of his life and around 1640 he did design the first pendulum clock. Galileo died in early 1642 but the significance of his clock design was certainly realised by his son Vincenzo who tried to make a clock to Galileos plan, but failed.
It was a sad end for so great a man to die condemned of heresy. His will indicated that he wished to be buried beside his father in the family tomb in the Basilica of Santa Croce but his relatives feared, quite rightly, that this would provoke opposition from the Church. His body was concealed and only placed in a fine tomb in the church in 1737 by the civil authorities against the wishes of many in the Church. On 31 October 1992, 350 years after Galileos death, Pope John Paul II gave an address on behalf of the Catholic Church in which he admitted that errors had been made by the theological advisors in the case of Galileo. He declared the Galileo case closed, but he did not admit that the Church was wrong to convict Galileo on a charge of heresy because of his belief that the Earth rotates round the sun.
J J OConnor and E F Robertson
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