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Original scientific paper

The Opinion of Stjepan Gradić on the Application of Indivisible Parts (Indivisibilia) in Physics

Zdravko Faj ; Pedagoški Fakultet, Osijek, Hrvatska

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page 31-44

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Stjepan Gradić (1613-1683) discussed the problems of indivisible parts (indivisibila) with H. Fabri and M. A. Ricci. His opinions have come to us from the dissertations published; also, many details are contained in his letters and notes that have been preserved in his manuscript. In his letter to Fabri he expresses his opinion on the Cavalieri method; namely, that from the relations of the indivisibles it can be deduced on the relations of the continuum. Further, he proves on an example that by applying the method quoted and with the understanding that the surface is made of lines, and the lines made of points, a paradox follows. Thus, he concluded that the indivisibles should be excluded from the application. Therefore, when explaining the free fall, he admits that the contraction of time intervals may continue infinitely, so they tend to zero and in that process the surface of a dentate plane figure turns into the Galilei triangle. From the discussion on the triangle mentioned, it can be deduced that Gradić believed that a point in the length only marks a moment of time. However, a point is not part of the continuum, just like a line is not part of the surface. Such an opinion of Gradić is very much close to that of Bradwardine, which actually leads to the concept of a continuum which never stops and never disperses into individual points, and in which points are but outer limits. Such understanding of the continuum could have developed, via new ideas in the works by Newton, Leibniz and Cauchy, into the theory of infinitely small values which are the basis of the calculus.


Stjepan Gradić, physics, indivisibilia

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