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**1 - 2**of**2**### Part 1. Euclid’s Way of Building Mathematical Theories 3

"... Abstract. The persisting gap between the formal and the informal mathematics is due to an inadequate notion of mathematical theory behind the current formalization tech-niques. I mean the (informal) notion of axiomatic theory according to which a mathemat-ical theory consists of a set of axioms and ..."

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Abstract. The persisting gap between the formal and the informal mathematics is due to an inadequate notion of mathematical theory behind the current formalization tech-niques. I mean the (informal) notion of axiomatic theory according to which a mathemat-ical theory consists of a set of axioms and further theorems deduced from these axioms according to certain rules of logical inference. Thus the usual notion of axiomatic method