  Confocal quadrics capture (encode) and geometrize spectral properties of
symmetric operators. Certain metric-projective properties of confocal quadrics
(most of them established in the first half of the XIX$^{\mathrm{th}}$ century)
{\it carry out} (stick and transfer) by rolling to and influence surfaces {\it
applicable} (isometric) to quadrics and surfaces geometrically linked to these,
thus providing a wealth of integrable systems and projective transformations of
their solutions. We shall mainly follow Bianchi's discussion of deformations
(through bending) of quadrics. Interestingly enough, {\it The Method} of
Archimedes (lost for 7 centuries and rediscovered in the same year as Bianchi's
discovery (1906), so unknown to Bianchi) applies {\it word by word in both
spirit and the letter} and may provide the key to generalizations in other
settings.
