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- Publisher
- Springer International Publishing
- Copyright
- © Springer International Publishing AG 2018
- ISBN
- 978-3-319-58309-9
- Pages
- 1 –67
- DOI
- 10.1007/978-3-319-58310-5_1
- Publisher site
- See Chapter on Publisher Site
Abstract
[Greek mixed mathematics, optics, music, astronomy, and mechanics, reached their apex in the Hellenistic era. Their logical structure was quite similar: from some premises of empirical character expressed in mathematical language, theorems were derived to be interpreted as phenomena detectable by the senses. The apex in optics, music, and astronomy was reached with Ptolemy in the second century AD, and in mechanics with Archimedes in the third century BC. A fundamental difference in the use of experience crossed the various mixed mathematics. In some of them, such as astronomy and music–not only in the formulation due to Ptolemy–principles had a hypothetical form to be verified indirectly by experience. In others, such as mechanics and optics, principles came directly from experience, or at least this was the opinion of the mathematicians of the time who did not doubt the possibility of induction.]
Published: Jul 9, 2017