The famous French philosopher Rene Descartes is Latinised as Renatus Cartesius. Those unfamiliar with this, or with his thought in general, might then not realise that some words are derived from his name. For instance, Cartesian is a common term used in philosophy and mathematics (e.g. Cartesian dualism and Cartesian system of coordinates, respectively).
Why is the Latinisation of Descartes Cartesius? In particular, where is "Des"? Is it omitted because Descartes is literally translated as "of the + card/maps", and Latin generally omits prepositions? It seems however that cartesius is not a Latin word (although charta and carta are).
Is this Latinisation style common? Notice that, for example, the Dutch painter Vincent van Gogh is translated as Vincentius van Gogh, even that van also means "of/from". Miguel de Cervantes (contemporary with Descartes) is another example where the "of" is not omitted. Is there a rule here or is this just arbitrary?