The English teach mechanics as an experimental science, while on the
Continent, it has always been considered a more deductive and a priori
science. Unquestionably, the English are right. * H. Poincare, Science
and Hypothesis Descartes, Leibnitz, and Newton As is well known, the
basic principles of dynamics were stated by New- ton in his famous work
Philosophiae Naturalis Principia Mathematica, whose publication in 1687
was paid for by his friend, the astronomer Halley. In essence, this book
was written with a single purpose: to prove the equivalence of Kepler's
laws and the assumption, suggested to Newton by Hooke, that the
acceleration of a planet is directed toward the center of the Sun and
decreases in inverse proportion to the square of the distance between
the planet and the Sun. For this, Newton needed to systematize the
principles of dynamics (which is how Newton's famous laws appeared) and
to state the "theory of fluxes" (analysis of functions of one variable).
The principle of the equality of an action and a counteraction and the
inverse square law led Newton to the theory of gravitation, the
interaction at a distance. In addition, New- ton discussed a large
number of problems in mechanics and mathematics in his book, such as the
laws of similarity, the theory of impact, special vari- ational
problems, and algebraicity conditions for Abelian integrals. Almost
everything in the Principia subsequently became classic. In this
connection, A. N.
