VULGAR OR COMMON FRACTIONS Relation to Compound Numbers.—The ancients had such difficulty in representing fractions that they generally resorted to compound numbers in order to avoid their use. Thus the Roman fractions of weight and of value were referred to the as. A twelfth part of the as was an uncia, as was also the twelfth part of a foot, whence our words "ounce" and "inch." Since 16 asses (in early times, io asses) made a denarius, the Romans were able to avoid speaking of 2 of a denarius by referring to 8 asses, just as we may refer to 8 ounces instead of to of a pound, avoir dupois. To
of a denarius the Roman would say denarii uncia semuncia; that is,
and _2 of
of a denarius. This use of unit fractions goes back to some of the earliest fraction forms known, appearing in the Rhind (Ahmes) Papyrus of c. 1650 B.C., where the ratio of 2 to 43 is expressed (to use modern symbols) as 412 -i- gig — 9 +2- . The same plan was used by Heron (Hero) of Alexandria (possibly c. 200), in the Akhmim Papyrus (c. 8th century), by Rabbi Sa'adia ben Joseph el-Fayyumi (c. 930), and even, for certain purposes, up to modern times. Such compound numbers as 3yd. ift. 6in., instead of 3yd., and as L2 Ios. instead of £21, are late evidences of the desire to avoid frac tions whenever possible.
In the Egyptian hieroglyphics the unit fraction was represented by a symbol resembling the outline of an eye, the denominator being represented underneath. In hieratic a dot replaced this symbol, - appearing in somewhat such form as Iii. The Greeks had various forms, one being two short lines above a numeral, as in F' for A, and , for 1. The most common of all their fractions, the half, had a special symbol resembling our initial parenthesis (. Aristarchus (c. 26o B.c.) wrote the word or its initial for the numerator and the numeral for the denom inator, as we might write "ten 71 st,"—in Greek, AdA. The Greeks also used the plan of writing the numeral for each term, but doubling it for the denominator, as if we should write
for 3.
On their coins the Romans commonly represented the half by the symbol S (for semis), or the Greek or (; 3 (the triens) was .... (that is, A), and (the sextans) was .. They also used bars instead of dots, as in =— (that is, -) for 4 (the quadrans).
Our present fractions seem to have had their genesis in India. Brahmagupta (c. 628) and Bhaskara (c. II50) wrote 3 for .. The Arabs introduced the bar, but they did not make use of it in all cases. When Abraham ben Ezra (Rabbi ben Ezra, c. 114o) adopted the Moorish forms he generally omitted it; but it is commonly found in manuscripts after his time.
The fractions that were commonly used by mer chants in the late middle ages were called fractiones vulgares, whence the French use of fractions vulgaires (Trenchant, 1566) and the English "vulgare or common Fractions" (Digges, 1572).
the early American writers did the same ; but about the beginning of the 19th century the latter changed to "common fractions." In English the word numerator (numberer) has given place to such terms as numeeus, "topternie," "top," superior, and denom inato, the denominator having such equivalents as "base," inferior, and denominate.
