The "15" is probably a 'serial number' to keep the mating parts together.
The sizes are somebody's standard of small screws, used in clocks and other scientific-type instruments. Most surely of European origin.
This pre-dates our understanding of standardization. They were not intended to be interchangeable with any others, just be repeatable in and for themselves. There would have been corresponding taps that are usually lost to breakage.
Originally often, one 'master' male threaded 'tap' could generate the dies which could generate more taps and so on and so on.
FYI, they were not used to 'cut' threads, like we usually do today, but to 'swedge' them, or form them. Softer metals were usually encountered, such as brass and occasionally wrought iron, but will not hold up to most steels.
Larger versions of the same process are encountered in 19th century blacksmith work.
Commercially available taps with true radial relief allowing for 'cutting' threads as we know today, blossomed right around the close of the Civil War. This was a huge change and really set the stage for standardization of fasteners.
