Next he discusses the work of his contemporary, Desargues, on the center of gravity of a sphere, once more illustrating his point with a diagram. He admits that their theories are very close, but he now thinks that they are both mistaken, and consequently asks his correspondent to delete the last paragraph of his copy of a treatise on mechanics that Descartes had sent, adding that he must have been falling asleep when he wrote those lines. He also points out the disadvantage in Galileo's work on balances and levers. With regard to Fermat's work on the tangent of the wheel, Descartes finds his method similar to that of Archimedes, which he thinks is the only way of approaching the problem. Roberval's work on the subject, on the other hand, he considers worthless.

He expresses surprise at Fermat's reaction to his Dioptrique , and explains by means of a diagram, a point concerning burning glass. He also states firmly that he has done enough in the theoretical field towards the development of spectacles for old men; the practical aspect is up to the craftsmen. He also discusses condensation and rarefaction, the law of falling bodies, and his theory of matiere subtile.