Abstract
The aim of the paper is to argue for the cognitive unity of the mathematical results ascribed by ancient authors to Thales. These results are late ascriptions and so it is difficult to say anything certain about them onphilological grounds.
I will seek characteristic features of the cognitive unity of the mathematical results ascribed to Thales by comparing them with Galilean physics. This might seem at a first sight a rather unusual move.
Nevertheless, I suggest viewing the process of turning geometry into an axiomatic-deductive science as aprocess of idealization in mathematicsthat is parallel to the process of idealization in physics. In Kvasz (Acta Phys Slovaca 62:519-614, 2012) I offered an epistemological reconstruction of the process of idealization in physics during the scientific revolution of the seventeenth century.
In the present paper I try to employ these epistemological insights in theprocess of idealization in physicsand propose a reconstruction of the cognitive unity of the mathematical results ascribed to Thales, who can, on the basis of these ascriptions, be seen as one of the initiators of idealization in mathematics.