Niccolò Guicciardini

“Mechanica rationalis” and “philosophia naturalis” in the Auctoris Praefatio to Newton’s Principia

The first half of the Auctoris Praefatio to Newton’s Principia is devoted to define “rational mechanics” as opposed to “practical mechanics”, to discuss its relationship with geometry, and its use in the investigation of nature. Newton affirms that geometry is founded upon mechanical practice. He also denies that exactness appertains exclusively to geometry: quite the contrary geometry receives its exactness from mechanical practice. In holding these theses Newton was distinguishing his mathematical method from the one defended by Descartes in the Géométrie (1637). Descartes had defined “geometrical” as “what is perfect and exact” and “mechanical” as what is not so. He had therefore banished “mechanical” curves from geometry. The fact that the Auctoris Praefatio is related to Newton’s anti-Cartesian mathematical writings is clear enough from textual evidence which can be gained, most notably, from the opening passages of a Geometria composed in the 1690s and from the appendix to the Arithmetica Universalis. However, when we attempt to analyze Newton’s motivations for rejecting Descartes’ mathematical methodology, the question gets considerably intricate. The Auctoris Praefatio is a complex and stratified text which reveals a number of exigencies that motivated Newton’s mathematical cosmology. Newton’s quest for certainty in natural philosophy — his deeply rooted conviction that probabilism and hypotheticism could be avoided by interrelating mathematics and experiment — made a priority to warrant the certainty of his mathematical methods. In order to mathematicize Keplerian planetary cosmology, Newton had to reject Descartes’ ideas concerning the relationship between exactness, geometry and mechanics: his concern in the Auctoris Praefatio was to show that he was not loosing certain mathematical ground with such a bold move.