By Tito M. Tonietti
We convey into complete mild a few excerpts on musical matters that have been before scattered in the course of the most renowned medical texts. the most clinical and musical cultures outdoor of Europe also are considered. the 1st and most crucial estate to underline within the medical texts tested here's the language they're written in. which means our multicultural heritage of the sciences inevitably additionally turns into a evaluation of some of the dominant languages utilized in the several ancient contexts. during this quantity, the historical past of the advance of the sciences is instructed because it occurred in genuine contexts, no longer in an alienated perfect world.
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Extra resources for And Yet It Is Heard: Musical, Multilingual and Multicultural History of the Mathematical Sciences - Volume 1
278. Euclid 1956, II, p. 412. 48 Euclid 1956, II, p. 413. 49 Euclid 1956, I, p. 155. 4 Euclid 33 parallel; because in that way, they would appear to be equally numerous, whereas intuition tells us that even numbers are only a part, there are fewer of them. The paradox became the new definition, which, in the new language that had now entered even primary school textbooks, stated: a set is called infinite when it admits a biunique correspondence with one of its own parts. In other words, when the whole is ‘equal’ to a part, it is a case of infinity.
This appears in the Elements only in books five and six. If he had used it (the necessary proposition would have been number eight of book six), he would have broken the linear chain of deductions, forming a circle that he would perhaps have considered vicious. Furthermore, he would have raised the particularly delicate question of incommensurable ratios, necessary to obtain a valid demonstration for every right-angled triangle. Euclid would succeed in avoiding the obstacles, but he would be forced to pay a price: following a route which seems as intelligent as it is artificial.
For him, the truth of a geometrical proposition should be made independent of the everyday world, practical activities or the senses. The organs of the body would provide us with ephemeral illusions, not properties that are certain and eternal. As in the myth of the cave described by Plato, Euclid would like to detach himself from the distorted shadows of the earth, which are visible on the wall, to arrive at the ideal objects that project them. It was only on these that he based the truths of his geometry, which were thus believed to have descended from the heavens of the eternal ideas.
And Yet It Is Heard: Musical, Multilingual and Multicultural History of the Mathematical Sciences - Volume 1 by Tito M. Tonietti