Original scientific paper

Consectarium and Porisme in Getaldić’s Works

Žarko Dadić

Abstract

In his work Variorum problematum collectio, published in Venice in 1607, Getaldić distinguishes three groups of geometrical problems. Getaldić solves the first group of problems constructively in accordance with Greek synthetic method. For the second one he, first, makes geometrical analysis of a problem and then, on its basis achieves the construction. The third one is solved constructively, but to its solution he adds consectarium which is the
generalisation of the solution, and thus makes possible the geometrical or numerical interpretation of the problem. In his last work De resolutione et compositione mathematica, published posthumously in Rome in 1630, Getaldić solves problems in the line of Viète’s algebraic method. The most of the problems published in Variorum problematum collectio we can find again in De resolutione et compositione mathematica.
In the first work, Variorum problematum collectio, Getaldić achieves the statement — consectarium — through geometrical relations obtained from construction. It is general formulation and formally identical with the formulation of porisme, what is recognizable while comparing the same problems in both works. When the consectarium is formulated, Getaldić applies it to the numerical solution, because after formulating consectarium, Getaldić gives numerical solution. Thus consectarium plays the same role as the porisme. There is no equation, which is specific for algebraic method, in consectarium, but its formulation is general and it can be applicable to geometrical as well as to the numerical solutions of problems, just as is the case with the porisme.

Keywords

Marin Getaldić; consectarium; porisme

Hrčak ID:

243331

URI

https://hrcak.srce.hr/243331

Publication date:

30.6.1980.

Article data in other languages: croatian

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