Classical Studies 2700B

Numerals, Measurements and Surveying

Numerals:

Unlike the Babylonians, who used a combination of decimal and sexagesimal (sixties) numbers, all the peoples of the Bronze age and later in the Aegean area and in Italy used decimal systems for numerical calculations The Minoans had a very simple but easy system of writing numerals, while the later Greeks (in the Classical period) had two systems based on their alphabet (both capitals and small letters); the Greeks also wrote fractions (sometimes like our vulgar fractions, but with denominator on top) and eventually in astronomical calculations they used an inverted omega for zero. Roman numerals are well known to us today (for some unfathomable reason, the copyright symbol © in movies is always accompanied by the year date in Roman numerals: 2010 is MMX): there are only seven symbols used—based on the fingers of the hand, the hand doubled, and some letters of the Greek alphabet not used in Italian alphabets. How the Romans wrote large numbers. (Fractions, however, were cumbersome--and messy.) How were calculations done?

Units of measurement:

The Greeks used bits of the body to express linear measurement, starting with “finger-breadths”; so, 2 f-bs = 1 kondylos (length of the middle joint of the index finger); 4 f-bs = 1 palm; 8 f-bs = a half-foot; 10 f-bs = span of thumb and index finger; 12 f-bs = span of all fingers; 16 f-bs = 1 foot. Beyond this, there is the “cubit” = elbow to finger-tips; the “fathom” = stretch of both arms; and the “stadion” = 600 feet (whatever the size of the foot; so very variable).

The Romans had two versions of the foot: the “standard version” is usually said to be 296 mm, though it may have been slightly less; and the “long foot”, used in Gaul and Germany, was c.330 mm. The foot consisted of 12 unciae (means either “inches” or “ounces”) and the standard foot was equal to 11.6 of our inches. 5 feet = 1 passus (a “pace”, somewhat oddly defined); 125 passus = 1 stadium (cf. the Greek stadion); 1000 passus/ 8 stadia = 1 Roman mile (mille passus, which > our “mile”; it equals 1480 m.)

Surveying:

For an additional file with info. about Roman Surveying, click here.

To hold land, you have to know where it is and how extensive it is. So boundaries have to be marked; these are often regarded as “sacred”. Knowing exact location of land was extremely important in ancient Egypt: why? Hence Egyptian origin of most ancient surveying devices. This was particularly important under the Ptolemies (who? when?). Heron of Alexandria (called Hero in Landels) perfected many of these; his date? See Landels pp. 206-207; White pp. 170-172: dioptra; levelling devices; measuring-poles; and hodometer; in addition, the Romans used a thing called the groma (coming a bit later in the lecture). Romans were greatest surveyors of antiquity. When they conquered a territory, they took part of its land as ager publicus (state-owned land) and rented it out on lease; also they established colonies, where much more elaborate land surveys were undertaken.

The process: the basic unit of measurement was an actus (120 R. feet) > square actus (120’ x 120’); two of these = 1 iugerum (the standard R. unit of land; = 0.623 acres/0.252 ha); 2 iugera (in a square) = a heredium (= “estate”, the basic allocation of land in colonies in Italy during the R. republic). 100 heredia, again in a square, = 1 centuria (20 x 20 actus, a square with sides of 2,400 R. feet). The surveying process was called “centuriation”; and this can still be seen on modern maps of Italy and N. Africa.

The method: main instrument used was the groma (illustration in file referenced above)—for measuring exact right angles. Surveyors were called gromatici (“groma people”) or agrimensores (“land measurers”). 10’ measuring rods used as well. The main axes were called Kardo (usually N.-S.) and Decumanus (usually E.-W.) This is similar to what was done in R. religion—in augury. Centuries marked out from central starting point and boundary lines for each century (limites) were 8 to 12 feet wide; every 5^th limes would be 20 feet wide. There was a tendency to think of the numbers as referring to roads rather than chunks of land (same thing today: what is the “Seventh Concession of London Township”?).

Once survey was completed, lands were allocated to settlers and details were formally recorded, both locally and in Rome, to which a copy was sent. The usual land allocation in time of Augustus and later to a settler in a colony in a R. province was one-third of a centuria (= 66.66 iugera).