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Ghetaldi's first paper appeared in 1603 and it was on Archimedes. In this he gave an accurate table of specific weights. In a second work he studied parabolas obtained as sections of a right circular cone.
Viète had been working on constructing Apollonius's lost works. In fact Viète was often known as Apollonius Gallus because of this. Ghetaldi took over this work of Viète. He followed Pappus's description of the contents of certain lost books and to do this he had to solve the problems which the books were supposed to contain.
Ghetaldi produced a pamphlet with 42 problems with solutions. These contain early application of algebra to geometry.
Ghetaldi's work is described in Herigone's 1634 work Cursus mathematicus .
It is interesting to look at the kind of person Ghetaldi was. He turned down a chair at Louvain when he was a young man. Descriptions of him say he had the morals of an angel and to be a Ragusan gentleman of discernment.
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