What is the origin of "tablet" as in a pill?

The OED seems to think it's the shape of the pills (flat and rectangular) that gave rise to the word tablet.

Their definition for this meaning of tablet starts

A small, flat, or compressed piece of a solid substance, originally of rectangular form; spec. a measured quantity of a medicine or drug, ...

Their second citation for tablet meaning pill (1558) is

Bringe it al into a masse, or lumpe, or into little tablettes, or into what fourme you will.

And from the OED, there are lots of other rectangular objects that were also called tablets in the 15th through 17th centuries:

• a small slab intended to bear an inscription, drawing, or painting,
• roof or flooring tiles,
• jewelry consisting of a "flat ornament of precious metal or precious stone",
• "a flat cake of soap",
• candy made in "squares or tablets",
• a broad, square, "peece of glass".