This entry first provides an overview of the historical, cultural and epistemological
background that is key for Hamilton’s positions on mechanics. We consider the investigations on
geometrical optics in the 17th and 18th centuries, Euler’s and Lagrange’s foundations of variational
calculus in the 18th century to find extrema of physical quantities expressed as infinite sums of infinitesimals
(today, we would say ‘definite integrals’), and Lagrange’s introduction of a revolutionary
analytical mechanics, all of which are all fertile grounds for Hamilton’s steps—first, in what we
could call analytical optics, then in an advanced form of analytical mechanics. Having provided
such an overview, we run through some of Hamilton’s original papers to highlight how he posed his
principle(s) in the wake of his forerunners and how his principles are linked with the search for a
unitary view of physics.
