Roman Fractions Based on Weights and Measures:
Although the Romans did not have a "zero," they did have fractions. The Roman fraction system was derived from weights and measures of land. Basically, it was a duodecimal (base 12) system. A unit of weight was called an uncia; 12 of which formed an as. A scripulum was a unit of land about 10'X10', that was 1/288 of a iugerum. "S" meant 1/2 -- probably as an abbreviation for semis.
Columella - Ancient Source:
In De re rustica, Columella describes an interest rate of semis or semissis on 100 units for a period of a month. Annually the figures amount to 6 percent interest, although Columella appears to have either used a complicated multiplication table or rounding to arrive at a figure slightly different from modern calculations. [See Maher and Makowski's article listed below for specifics.]
Victorius of Aquitaine - Ancient Source:
In the fifth century A.D., Victorius provided a multiplication table for what were probably basic computations. The table had 98 columns and covers the products of whole numbers with whole numbers and whole numbers with fractions, but no fractions with fractions. Two lines (325-26) from Horace's Ars poetica hint at the possibility that school boys memorized tables of equivalents for parts in a hundred.
Frontinus - Ancient Source:
In about 98 A.D., Frontinus wrote De aquae ductu urbis Romae for the Emperor Nerva. In it he describes the size of water pipes. Units include the digitus (1/16 of a foot) and the uncia (1/12 of a foot). Frontinus compares the size of the largest circle that can be inscribed in a square. To arrive at his figure, his unexplained calculation must have included a value of 22/7 for pi (according to Maher and Makowski).
Some Roman Fractions:
The symbols in parentheses are modern forms for the fractions. Romans had symbols, like the 'S' for half. Some symbols were ordered dots like a quincunx.
- deunx (11/12)
- decunx (10/12)
- nonuncium/dodrans (9/12)
- bes/bessis (2/3)
- septunx (7/12)
- semis (1/2)
- quicunx (5/12)
- triens (1/3)
- quadrans/teruncius (1/4)
- sextans (1/6)
- sesuncia (1/8)
- unica (1/12)
- semiuncia (1/24)
- binae sextulae/duella (1/36)
- siculus (1/48)
- sextula (1/72)
- dimidia sextula (1/144)
- scripulum (1/288)
Reference:
"Literary Evidence for Roman Arithmetic With Fractions", by Maher, David. W. J. and John F. Makowski. Classical Philology Vol. 96 #4 pp. 376-399.
