Overview

• The Breakthrough. Galileo, \(d \propto t^2\), then Newton. \(F = ma\).
• Key is the notion of force which is intuitive, at least to us moderns. Nonetheless, since XXXX, other notions such as the the principle of least action (Lagrangian mechanics) or the Hamiltonian formulation of mechanics have been the driving notions in physics.
• Historical note: the influence of optics on the development of mechanics: Hero of Alexandria, Ibn Saal (??), Pierre de Fermat, Lagrange. Is this working?

\[ \int_0^1 x^n dx = \frac{1}{n+1} \]