Rene Descartes' Treatise

The Father of Philosophy

on physics and mathematics....and a statement of his philosophy regarding first principles and the

Scientific Method

Descarte's first discusses specific problems in physics, including an echo, resonance and water pressure. He then considers mathematical problems, including the drawing of a tangent at an angle of 45 degrees to a curve, and sets out his working of the complete equation in detail (adding dismissively that this calculation took him nothing like the fortnight that another mathematician had supposed, since when he is working for himself he abbreviates heavily). He goes on to consider the problem of perfect numbers, stating his belief that he will be able to demonstrate that no even numbers are perfect except those of Euclid.

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.

The letter also contains a remarkable statement of his philosophy regarding first principles and scientific method.