Ratio in early Greek mathematics
Отношение в ранней греческой математике
1979-01-01
SCID: 54.1/mnrxnhwb
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anthyphairesiscontinued fractionsearly Greek mathematicsincommensurable magnitudesratio theory
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Abstract (AI)
Introduction 2. Arithmetike and logistike 3. The notion of ratio 4. Multiplication and addition of ratios 5. Pre-Eudoxan uses of incommensurable magnitudes and proportion theory 6. Anthyphairesis 7. Anthyphairesis and the discovery of incommensurability 8. Anthyphairetic ratio theory 9. Arithmetical implications of anthyphairesis 10.Theoretical and practical logistic 11.A new perspective on Book X Appendix: Approximation by rational numbers, and continued fractions NOTES Referencing.The following abbreviated titles are used for books to which frequent page-references are made: Burkert, LS = Lore and science in ancient Phythagoreanism.Euclid, EE = Elements, ed. and tr.T. L. Heath, 3 vols.Heath, HGM = A history of Greek mathematics, 2 vols.Knorr, EEE -The evolution of the Euclidean elements.
Key Findings
1
It distinguishes theoretical and practical forms of Greek logistic and proposes a new perspective on Euclid’s Book X.
2
It identifies anthyphairesis as a central method for analyzing ratios and explains its role in the discovery of incommensurable magnitudes.
3
The study develops an anthyphairetic account of ratio theory and considers its arithmetical implications.
4
The work connects ancient ratio analysis with approximation by rational numbers and continued fractions.
5
The work examines how early Greek mathematics conceptualized ratio, including its arithmetic operations and relationships to proportion theory.
Research Object
ratio theory in early Greek mathematics
Research Subject
the development, uses, and arithmetical implications of ratios, including incommensurability, proportion theory, and anthyphairesis
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1979-01-01
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