The Development of the Ancient Theories of Proportions

Zbigniew Król

This paper is devoted to the reconstruction of the development of ancient theories of proportion. I argue that the development of ancient theories of proportion was motivated by the quest for one general mathematical theory and by inquiries of the mutual relations between the highest principles of Plato’s protology: the One (i.e. that which is arithmetical) and the Dyad (i.e. that which is geometrical). Six main types of the theory of proportion are analyzed, with a historical, mathematical and philosophical background.

Keywords: proportions · ancient mathematics · ancient philosophy · history of mathematics · Euclid · Eudoxus · Theaetetus

Zbigniew Król – Associate Professor at the department of the Philosophy of Science, Sociology and Foundations of Technology, Faculty of Administration and Social Science, Warsaw University of Technology, and at the two departments at the Institute of Philosophy and Sociology of the Polish Academy of Sciences (Warsaw, Poland): of the Philosophy and Hermeneutics of Mathematics and of the Inquiries on Ancient Philosophy and the History of Ontology. His research concerns the philosophy of mathematics and science, history of mathematics and science, logic, mathematics, ontology and epistemology.   »  

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