Around 1646, he proved his law that pressure applied
to a confined liquid is transmitted undiminished through the
liquid in all directions regardless of the area to which the
pressure is applied. Around 1653, he laid the foundations for the
theory of probabilities, including the creation of "Pascal's
Triangle" of coefficients of (a=b) raised to the nth power. He and
lawyer and mathematician Pierre Fermat invented the theory of
probabilities. Fermat also proved that the law for refraction
(bending) of light results from light's following the path that
takes the shortest time. He founded number theory. Fermat
formulated the notion of a line tangent to a curve and started the
development of differential calculus, in which a rate of change is
expressed as a function of time in equation form and also as a
tangent to the curve associated with that equation.. This work
helped lay the foundation for analysis. He and German Gottfried
Leibniz formulated the principle that an equation with two unknown
quantities can represent a curve. Leibnitz believed that man's
mind can arrive at truths about entities by pure thought.
Since the Puritans forbade music in churches, but enjoyed it in
domestic circumstances, much secular music was composed,
published, and played. There were many musical clubs. The violin
became very popular. Solo songs were much sung. The first English
opera: "The Siege of Rhodes" was written and performed with women
on stage.
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