Thank you Larry, perhaps we are getting somewhere:

This is what I have found regarding the diamond cutting and polishing near the period we are talking about.

"The diamond finishing industry comprised various occupations, which each required separate skills. Rough diamonds were cleaved first, then cut into shape, and finally polished. Cleavers and sawyers were at the top of the diamond workers’ hierarchy, followed by the cutters. The cutters consisted of brilliant cutters and rose cutters. Brilliant cutting was slightly more complex than rose cutting. Master polishers came next, followed by apprentice polishers.

Diamond polishing involved positioning the stones horizontally on a rotating disc attached to a polishing mill. They were soldered onto a so-called cap (a kind of copper retainer). The diamond had to be rotated inside the cap. This was done by turners. Disc sanders sanded these discs. Although disc sanders were not actually part of the diamond industry, they were obviously affected by the ups and downs there."

As you can see, a different person likely did the different processes, and probably with different tools. I am in particular interested in the polisher, the least skilled in the bunch. I believe that only the "rose" cut was evolved at this time (1650):



It is quite like a plano-convex lens. While you may be very right that contemporary polishing is not done with a spherical surface, the text seems to indicate that at the time they may have been. I cannot quite see the technique that is being described. It seems to suggest that the diamond was rotated within a cap (I imagine that the diamond was held by hand, but cannot be sure).

If Spinoza learned his polishing from diamond polishers, it is possible that he also used comparable devices or techniques.