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Definition of cartesian : 1. An adherent of Descartes.
2. Of or pertaining to the French philosopher Rene Descartes, or his philosophy.

Usage examples:

• Descartes was still living when Leroy transferred to the human soul the Cartesian construction of animals, and explained the soul as a mode of the body and ideas as mechanical movements, similarly to Lamettrie in the eighteenth century. - "Selected Essays", Karl Marx.
• This, though open to criticism from the point of view of the logician, had a very great influence in making the methodical treatment and clear luminous exposition which were characteristic of the Cartesian school common in French writers. - "A Short History of French Literature", George Saintsbury.
• Until then a firm, resolute, and patriotic stand was made by the Cartesian Vortices; whilst only forty years previously, this same Cartesian philosophy had been forbidden in the French schools; and now in turn d'Agnesseau, the Chancellor, refused Voltaire the Imprimatur for his treatise on the Newtonian doctrine. - "The Art of Literature", Arthur Schopenhauer.