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Marn Getaldić, restitutor of Apollonius work of contacts
Radmila Žarković
Sažetak
Marin Getaldić appeared in the world of the European scientific mind, especially in the field of mathematics, in the late XVI and the early XVII century; that was the time when cultural prosperity flourished over Dubrovnik.
Mathematicians all around Europe were, at that time, greatly interested in the works of antique mathematicians like Euclid, Archimedes and Apollonius.
Since many of their works were lost they were making effort to restitute them, relying upon some quotations in the works of other antique mathematicians.
Francois Viète, Marin Getaldić and John Lawson dealt with the restitution of the lost Apollonius work of contacts. French mathematician, Francois Viète, was the first to get down to work on the Apollonius work of contacts. He restituted the problems which, in modern terms, could be expressed in this way: to draw a circle which falls through m points, it touches n lines and p circles so that m + n + p = 3 and m, n, p -G(0,1,2,3).
Marin Getaldić, a citizen of Dubrovnik, showed some greater interest for the work of contacts. He had solved one of Viéte's problems in the most convenient way and discovered that the work of contacts contained also the problems which could be expressed, in modern terms, as following: to draw a circle of the given radius which falls though m points, it touches n lines and p circles in the way that m + n + p = 2 and m, n, p-G(0,l,2). There are six problems. The most interesting among them is this one: to draw a circle of the given radius that touches two other given circles. The restitution of these problems was expressed in the work of Marini Ghetaldi, patritii Ragusini, Supplementum Apollonii Galli seu exucitata Apollonii pergaei tactionum geometriae pars reliqua, Venetiis apud Vencentium Fiorinam MDCVII.
By solving problems Getaldić first formulated a problem in his restitution. Then he introduced limitations, as in many cases can happen that you cannot draw a circle on the basis of some given elements. He introduced those limitations because of different ways of drawing the circle. Getaldić’s limitations are important because they help to do the discussion of the problem. Getaldić, by his restitution, showed himself as an extraordinary geometrician. He wanted his restitution to be true to the original and he succeeded in guessing the spirit and style of Apollonius geometry of contacts.
Thanks to two top mathematicians, Francois Viète and Marin Getaldić, Apollonius work of contacts cannot be forgotten. The work has soon become very up-to-date. Some mathematicians (Camerer, Schwenter) use it in their courses of mathematics whereas others inspired by their works (Fermat, Toricelli, Simson, Lawson and Newton) deal more with the contact problems.
In the restitution of Apollonius work of contacts Marin Getaldić takes an important place so that Paul Guldman had real reasons to call him »Apollonius Head«.
The problems which were restituted by Marin Getaldić do not go over elementary geometries in current sense of the subject, and are included in the program of the secondary school so that the same problems have been studied by many authors. They are included into some textbooks but very incomplete. In fact, the problems are given mainly for some special examples.
Getaldić's restitution can contribute to adequate solutions to problems in some current way and the problems could be discussed thoroughly.
Ključne riječi
Hrčak ID:
240899
URI
Datum izdavanja:
30.6.1991.
Posjeta: 944 *