Original scientific paper
Where was Marin Getaldić the closest to Descartes?
Andrija Bonifačić
Abstract
Marin Getaldić (1586—1626), the Dubrovnik nobleman, improved mathematical science by applying algebra in solving geometrical problems. He followed the method of Francois Viete, who was his acquaintance and friend. These his works were published four years after his death in 1630 under the title De Resolutione et Compositione Mathematica. It was 7 years before the publication of Descartes's Geometrie (1637). Descartes found out that geometrical figures — curves in general — could be demonstrated with algebraic terms treating them in that way.
He is considered, with all reason, the founder of analytic geometry. Getaldić was not so lucky to find out the algebraic term for a curve, but however he came very close to it. Where could it be seen?
The 5th book of the mentioned work »De Resolutione« deals with final and additional works which are not important from the point of view of the main intention. The third chapter deals with aritmmetical problems with innumerable results. The author calls them Trifling und Unimportant problems, Problemata Vana et Nugatoria. Very important problems are the 4 th and the 5th which have countless results, but not every result can be satisfactory. The point, which represents the result, is changing continuously and so it forms in the 4th problem a hyperbola and in the 5th it forms an ellipse when we change at will a certain length, independent variable, on which the point depends and length which is the result.
In these two problems Getaldić prepared everthing to demonstrate a curve in the form of an Equation which determines the functional correlation of two variables. Getaldić had only to find out that correaltion which he anticipated. In that way he would out do Descartes in discovering the analytic method as he out did Descartes's Geometrie with his posthumous work.
Keywords
Hrčak ID:
244705
URI
Publication date:
30.6.1978.
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