In late 1646, Queen Christina of Sweden initiated a correspondence with Descartes through a French diplomat and friend of Descartes’ named Chanut. Christina pressed Descartes on moral issues and a discussion of the absolute good. This correspondence eventually led to an invitation for Descartes to join the Queen’s court in Stockholm in February 1649. Although he had his reservations about going, Descartes finally accepted Christina’s invitation in July of that year. He arrived in Sweden in September 1649 where he was asked to rise at 5:00am to meet the Queen to discuss philosophy, contrary to his usual habit, developed at La Fleche, of sleeping in late,. His decision to go to Sweden, however, was ill-fated, for Descartes caught pneumonia and died on February 11, 1650.

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There are several demonstrations of the assertion. The one presented here uses the physical definition of cycloid and the kinematic property that the instantaneous velocity of a point is tangent to its trajectory. Referring to the picture on the right,
P
1
{\displaystyle P_{1}}
and
P
2
{\displaystyle P_{2}}
are two tangent points belonging to two rolling circles. The two circles start to roll with same speed and same direction without skidding.
P
1
{\displaystyle P_{1}}
and
P
2
{\displaystyle P_{2}}
start to draw two cycloid arcs as in the picture. Considering the line connecting
P
1
{\displaystyle P_{1}}
and
P
2
{\displaystyle P_{2}}
at an arbitrary instant (red line), it is possible to prove that * the line is anytime tangent in
P
2
{\displaystyle P_{2}}
to the lower arc and orthogonal to the tangent in
P
1
{\displaystyle P_{1}}
of the upper arc* . One sees that: