By Tito M. Tonietti
We convey into complete mild a few excerpts on musical matters that have been in the past scattered during the most renowned medical texts. the most medical and musical cultures outdoor of Europe also are considered. the 1st and most vital estate to underline within the clinical texts tested this is the language they're written in. which means our multicultural heritage of the sciences inevitably additionally turns into a evaluation of a number of the dominant languages utilized in the various historic contexts. during this quantity, the background of the advance of the sciences is informed because it occurred in genuine contexts, now not in an alienated excellent world.
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Additional resources for And Yet It Is Heard: Musical, Multilingual and Multicultural History of the Mathematical Sciences - Volume 1
29. Zanoncelli 1990. Euclid 2007, pp. 677–776, 2360–2379 and 2525–2541. 31 Euclid 1557, p. 10 and 16; Bellissima 2003, p. 37. 4 Euclid 27 explanation met with a first clear contradiction, which was later to be attacked by Claudius Ptolemaeus. The interval of the octave added to a consonance generates (for the ear) another consonance; thus the octave added to the fourth generates the consonance of the 11th. But its ratio becomes 8:3, which is not among the epimoric forms permitted. The 12th, on the contrary, possesses the ratio 3:1.
I will return at the end of this chapter to the hallmark of dualism thus impressed by this Greek culture. “A military man must needs learn them in order to range his troops; and a philosopher because, leaving the world of generation, he must reach the world of being : : :”. Thus he went so far as to impose mathematics by law, in order to be able to “contemplate the nature of numbers”. 21 Even geometry has an “application in war”. But the philosopher criticised practical geometricians: “They speak of ‘squaring’, of ‘constructing on a given line’ : : :”.
33 In reality, they are often lapsus not noticed during the reasoning, which reveal aspects of their personality that would otherwise remain hidden. They are a precious help to better understand events that are significant for the evolution of the sciences, and not just useless details which become acts of lèse-majesté in the pages of hostile historians. Tannery discovered the error at the beginning of last century, when European mathematical sciences were undergoing a profound transformation. Among other things, modern mathematical logic was developing, and some scholars were even re-considering Euclid in the light of the crisis of the foundations.