The Cavalieri estimator is a bit of a misnomer. Cavalieri did not do estimates. Cavalieri did not point count.
Back in 1902 two geologists were trying to determine the size of crystals viewed through a microscope. They modeled the crystals as rectangular prisms and made use of the Cavalieri principle to determine the volume of the crystals. A mistake made in the application of the Cavalieri principle was that two objects must have the same height. This was not true in the work done. This misuse of the Cavalieri principle has not stopped the name from being used.
One of the odd things of stereological papers is making reference to Cavalieri's 1536 book when stating that point counting is being used. The reference has nothing whatsoever to do with stereological methods.
The citation of a 450 year old work that is an improper citation has fortunately become less of a fad.
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