Inspired perhaps by Isaac Beeckman's famous Journael or Tafelboeckje, Descartes kept a kind of diary in 1619 and 1620 that is mentioned as item number C in the inventory of his possessions made up in Stockholm in 1650. This petit registre en parchemin has not survived, but various seventeenth-century descriptions indicate that Descartes divided the notebook into separate chapters with titles such as Parnassus, Olympica, Democritica, Experimenta, and Praeambula. It contained miscellaneous scientific and mathematical notes and was arranged in such a way that the booklet could be read from both sides.

What is now left of these texts is known in part as the Cogitationes privatae, the Latin part of the title (Pensées / Cogitationes privatae) that Alexandre Foucher de Careil (1826–91) gave to his edition of the mathematical, scientific, and philosophical notes that he found in a copy made by Gottfried Wilhelm Leibniz in Paris on or around June 5, 1676. The other surviving part consists of Descartes’ description of the famous dreams he had in Germany following Saint Martin's Eve in 1619. This latter text has been preserved by Adrien Baillet (1647–1706), who quoted it in full in his biography La vie de Monsieur Des-Cartes (1691).

During the short period Descartes spent with Isaac Beeckman at the end of 1618, the two friends discussed a variety of questions: the nature of light and free fall of bodies, as well as hydrostatic problems (see hydrostatics) and questions of musical theory. Some of these problems derive from the work of Simon Stevin (1548–1620) and illustrate the way in which Beeckman first inspired Descartes’ interest in natural philosophy, as well as an interest in the mathematical representation of physical phenomena. Descartes, for his part, impressed Beeckman with his mathematical skills.

The mathematical passages Leibniz copied from Descartes’ notes contain descriptions of the “new compasses” Descartes had devised for trisecting angles and finding mean proportionals. One of these, the so-called mesolabium for mean proportionals, inspired him to sketch various extended versions by which cubic equations could be solved. These instruments were not meant for reading off the results directly; rather they served to draw curves by which the mean proportionals or the roots themselves could be constructed.