**Marino Ghetaldi** was a Croatian mathematician who published work with early applications of algebra to geometry.

- Beginning in 1590, Ghetaldi carried out a number of tasks in administration including working in the State Office for Weapons and working in the Office for the Sale of Salt.
- Ghetaldi first went to Rome before travelling extensively in Europe.
- Ghetaldi certainly impressed Viète who gave him many of his papers to study.
- Leaving Paris, Ghetaldi returned to Italy, spending some time in Padua where he came into contact with Galileo in 1600.
- This was an important opportunity for Ghetaldi who attended Galileo's lectures on mathematics, mechanics and astronomy.
- Galileo showed him his geometric and military compass, and Ghetaldi decided that after he returned to Dubrovnik he would make one for himself.
- Ghetaldi's first paper Promotus Archimedes seu de variis corporum generibus gravitate et magnitudine comparatis Ⓣ(Work of Archimedes on various gravitating bodies and their magnitude) appeared in Rome in 1603 and it was on the physics of Archimedes - it is, in fact, Ghetaldi's only physics paper.
- In the middle of 1603 Ghetaldi seems to have got into difficulties in Rome but the exact nature of the problem has never been ascertained.
- For example who funded Ghetaldi during these many years of travel and study?
- Ghetaldi found this a very difficult assignment for the area was rife with malaria and there were frequent attacks by bands of Uskok soldiers, mainly involving acts of piracy, while he was helping with the defences.
- Ghetaldi took over this work of Viète.
- Also in 1607 Ghetaldi produced a pamphlet Variorum problematum collectio Ⓣ(Collection of various problems) with 42 problems with solutions.
- While on the mission to Constantinople, Ghetaldi had tried to find an Arabic translation of the works of Apollonius.
- After he returned to Dubrovnik following his mission, Ghetaldi became interested in developing scientific instruments.
- He conducted his experiments with mirrors in Bete's cave, a location on the coast outside the city so named because Ghetaldi was known by the nickname of "Bete".
- We must not think of Ghetaldi's interest in mirrors and mathematics as being distinct for he certainly used the interplay between the physical construction of mirrors and the mathematical theory of the parabola as being two-way.
- Some of Ghetaldi's work is described in Pierre Hérigone's 1634 work Cursus mathematicus Ⓣ(Course on mathematics).
- After his return from Constantinople, Ghetaldi held various government posts, working as an official in the Office for Wine, in the Office for Processing Wool, as a consul for civil litigation, and again as a judge of the Appellate Court.
- It is reasonable to ask: what is the most impressive ideas contained in Ghetaldi's work?
- We now think of Descartes as founding the application of algebra to geometry, and although Ghetaldi never quite managed to achieve this breakthrough (nowhere in his work are there algebraic equations for geometric objects) nevertheless he came very close.
- Perhaps it is just as well since somehow 'Ghetaldian geometry' does not quite have the same ring as 'Cartesian geometry'.
- It is interesting to look at the kind of person Ghetaldi was.

Born 2 October 1568, Ragusa, Dalmatia (now Dubrovnik, Croatia). Died 11 April 1626, Ragusa, Dalmatia (now Dubrovnik, Croatia).

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Astronomy, Origin Croatia

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive