## Career as a Math Tutor Begins

Each summer, Galileo returned home to Florence during school break, and while his father pushed him to study medicine, he

Galileo's Famous Cannonball Experiment

It was during his student years at Pisa that Galileo conducted his legendary experiment with gravity and mass. Up until this time, the theories of Aristotle (384-322 B.C.E.) and Ptolemy (ca. 87-150 C.E.) had remained unquestioned, not just on astronomy but on everything. That included Aristotle's conclusions about falling objects, which Galileo decided to put to the test.

Aristotle wrote that heavier objects fall faster than lighter ones. He further stated that an object weighing twice as much as another would fall twice as fast. This meant that, according to Aristotle, an object weighing 50 pounds would fall 50 times faster than an object weighing one pound.

To test this theory, Galileo climbed to the top of the famous leaning tower in Pisa and dropped two cannonballs of very different weights, or, more precisely, of very different masses. Time and again, they arrived on the ground at the exact same moment, proving that objects of different masses fell at the same rate. This is only one of the experiments that he conducted at Pisa, and it was highly apparent that he had a gift for reasoning in the fields of mathematics and physics.

stubbornly concentrated on mathematics. It was during one of these summers, in 1583, that Galileo attempted to change his father's mind about his interests. He invited one of his university professors, Ostilio Ricci, to come to his home and talk to his father. Ricci tried to convince Galilei that his son's talents lay in the way of math, not medicine. Reluctantly, his father allowed him to study mathematics, such as the writings of the Greek philosophers and mathematicians Archimedes of Syracuse (287-212

b.c.e.) and Euclid of Alexandria (ca. 325-265 b.c.e.), providing that Galileo continue his medical studies at Pisa. Despite this arrangement, in 1585 Galileo quit his medical studies at Pisa without finishing his degree and began teaching mathematics privately in Florence and Siena. Now he was free to explore the discipline he so enjoyed, away from the pressure put upon him by his father to become something he was not.

By 1586, he was back at Vallombrosa, this time as a teacher of math rather than as a student. While at Vallombrosa, he wrote a book called La balancitta (The little balance) in which he explained Archimedes' technique of finding the density of objects using a balance scale. The next year Galileo went to visit a professor of mathematics in Rome named Christopher Clavius (1538-1612), who taught at the Collegio Romano, a Jesuit seminary founded by Ignatius Loyola in 1551. Galileo took with him his personal experiments and findings on the subject of the center of gravities. He had heard that the Jesuit mathematicians were fond of the subject and thought that if he could impress them with his work he might be able to obtain an appointment as a professor at the University of Bologna. Clavius was duly impressed, yet Galileo did not win the job.

Galileo left Rome without work, yet he gained a friend in Clavius. By 1588, they were writing each other regularly and exchanging mathematical notes. By now, Galileo had begun to make a reputation for himself through lectures given on mathematics at the Florence Academy and the strong support given him by Christopher Clavius. When, in 1589, the University of Pisa found it was in need of a mathematics professor, Galileo was chosen for the task. This was a fine step forward for Galileo, but he looked ahead to larger career goals.

During the time he spent teaching at Pisa, Galileo wrote a series of unpublished essays titled De motu (On motion), in which he describes the theory of motion. He did not view the series as a complete work, which is perhaps why he never had it published. Many of the ideas it held were not correct, but it did address the important issue that through experiments one could come to relative conclusions. The Greeks were responsible for cementing the practice of arriving at conclusions purely through debate. That is to say, by talking something through to its end, people could arrive at answers. Galileo, on the other hand, was a believer in experiments and observations, not speculation. In De motu, for example, he discusses how using a sloping plane to slow the rate of descent can test the theory of falling masses.

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