Galileo Galilei - mathematics


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Mathematics

- To earn a living, Galilei had started tutoring students in the study of mathematics. He had did some experimenting with the floating of objects, developing a balance that could tell him that a piece of gold was 19.3 times heavier than the same volume of water. Or any other piece of object. He also started campaigning for his life's ambition; a position on the mathematics faculty at a MAJOR university. Even though Galileo Galilei was obviously brilliant, he had offended many people in the field, who would choose other candidates for vacancies.
His mathematical methods are the standars one of today. His proofs and anaylsis relied, highly, on the Eudoxian theory of proportion, as set in the book of the Euclid's Elements. This theory had became available only about a century before. Thanks to the highly accurate translations by Tartaglia and a plentyful amounts of others. By the end of Galileo Galilei's life, his methods were being superseded by the alegbraic methods of Descartes.
Galileo Galilei had produced one piece of the original and even prophetic work in mathematics. Galileo Galilei's paradox, which had shown that there are as many perfect squares as there are whole numbers, even though most numbers are not perfect squares. Such contradictions were brought under control 250 years later in the work of Georg Cantor.