Thanks Larry,

Spinoza most definitely must have used a lens-grinding lathe. This is an example of an early 17th century lathe from an optical text by Manzini:



You are very right that the kinds of lathes used were related to those employed by clock and watchmakers. In the one depicted above, we have the craftsman holding the glass in the left hand, up against a spinning metal form. By Spinoza's time his lathe was likely foot-driven, and the grinding done at eye-level.

It seems that the details generally allow that iron "templates" were made by grinding convex and concave forms against one another. These forms are then used (by one account), to make "tools" which are iron or brass, and more highly polished "dishes" or "plates". Into these plates are ground the glass blank with a bit of abrasive. It is not altogether clear that this was the universal method, but something like this was done in the lathing of glass lenses.

I still am having a hard time getting the details of this process, if indeed it was very common, and cannot get a grasp on the nature of the lathe at the Spinoza museum, or what techniques diamond polishers may have used which are different.

I do appreciate all thoughts.