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Euler states the theorem as follows:

Theorema.Quomodocunque sphaera circa centrum suum conuertatur, semper assignari potest diameter,cuius directio in situ translato conueniat cum situ initiali.

or (in English):

When a sphere is moved around its centre it is always possible to find a diameter whose direction in the displaced position is the same as in the initial position.

200px===Proof===

Euler's

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