Somebody recently pointed me at Cistercian numerals (above), an interesting base-10 numeral system used by Cistercian monks in the Low Countries and northern France from the 1200s to the 1500s (that is, after the Liber Abaci introduced Hindu-Arabic numerals to Europe, but apparently based on an older English system, not on that).
Most extant uses of the system relate to dates and item numbering, rather than arithmetic. This online conversion tool will let you experiment with the system. It is interesting to note the relationships 5 = 4 + 1, 7 = 6 + 1, 8 = 6 + 2, and 9 = 8 + 1 = 7 + 2 = 6 + 2 + 1.
Scientific Gems 