The pes was a Roman foot of 296 mm. Its divisions were the digitus of 1/16 pes or 18.5 mm, the uncia of 1/12 pes or 24.67 mm and the palmus of 74 mm. The subdivisions of the pes, pous and bd are important because they tell you a lot about where the system is coming from. The system that underlies the English foot only makes sense if you follow the logic from Alpha to Omega and that applies to the pes as well.
Mesopotamian feet of 300 mm are divided into three hands of 100 mm and 15 digits Egyptian feet of 300 mm are divided into four palms of 75 mm and 16 digits Persian feet of 300 mm are divided into six ells of 50 mm and 18 digits Greek feet or pous can be divided into hands or palms and from 15-19 digits Roman feet or pes are divided into four palms of 74 mm and 16 digits Architecturally the Romans inherit their decimal proportions from the Greeks but their octal standards of measure from the Egyptians
The Greeks had derived their Pous from ancient Mesopotamian standards of measure which were essentially sexigesimal. The Egyptians had derived their bd or foot from the same source but converted the great cubit of 6 hands and 600 mm that the Mesopotamian system was based on from a sexigesimal system divided into 6 hands of 100 mm to a septenary system with a royal cubit of 525 mm divided into 7 palms of 75 mm. The Greek pous was thus three hands of 15 daktylos and 300 mm while the Egyptian foot was four palms of 75 mm or 300 mm.
The Greeks developed their original Doric orders of architecture c 700 BC complete with entasis and canons of proportion from Hatshepsets mortuary temple at Deir el-Bahri shortly after the first Greek mercenaries had penetrated that far up the Nile. The earliest Greek pous were based on a Mesopotamian esse of 3 hands or 300 mm and easily converted to an the Egyptian bd or foot of four palms or 300 mm. proto-doric
"Mortuary Temple of Hatshepsut The colonnade of the second terrace north wing. This temple is characterized by its 16-corner pillars called protodoric by Champolion. The 8-corner pillars and 16 corner pillars were seen at the Triple-aisled cult chamber in Beni Hasan (XII Dynasty). Those kind of pillars were made by cutting off from square pillars and the capitals were leaved as square."
In the Ptolomaic period The Greeks developed the Ionic orders as a more subtle cannon of proportion modifying a standard taken from Egyptian inscriptian grids using a foot of 300 mm to a Greek system based on column diameters, pi and phi using a pous of 296 mm. The Roman Pes was derived from the Ionic orders Pous by the Romans c 600 BC as the Romans began incorporating the Ionic Greek orders of architecture into their own Corinthian order.
As the illustration above makes clear the conversions between different standards were systematic and in general, integrally commensurate. An area of 3600 SF with a side of 60 feet is equivalent to an area of 2304 square remen with a side of 48 remen which is equal to an area of 2000 square cubits with a side of 44.72 cubits and so forth.
At a radius of 60 feet one degree of arc has a chord of about 1 foot and that seems to be the point at which the conversions between the different systems are most frequently resolved.
- A Roman Pes has 16 fingers, 12 inches and 4 palms = 296 mm
- An Attic Greek Pous has 15 fingers, and 3 hands = 304.8 mm
- An English fote has 12" and 3 hands = 296 mm
Looked at in terms of practical application the difference in the standard length between Greek and Roman and English feet is less than the variations in any one category.
The measures divided in hands originate in Mesopotamia, the measures divided in palms originate in Egypt. Body measures are at some point resolved with the much longer measures of plowed and irrigated fields using the remen, elle, yard, pace and fathom.
Some of the multiples of the pes were the remen, passus, stadium, milliare and degree. Its immediate predecessor was an Ionic Greek Pous of 296 mm
- Other related Greek feet included
- An Ionian Greek Pous has 16 fingers, 12 inches and 4 palms = 296 mm
- An Attic Greek Pous has 15 fingers and 3 hands = 308.4 mm
- An Athenian Greek Pous has 15 fingers and 3 hands = 316 mm
Their immediate predecessors were an Egyptian bd which has 16 fingers, 3 hands, and four palms = 300 mm aMesopotamian ñušur which has 15 fingers and 3 hands = 300 mm
- there were 5/4 pes to a remen of 15" = 381 mm
- There were 5 pes to a passus or pace = 1.48 m
- There were 625 pes to a stadium = 185 m
- In England the stadium was the basis for the
- English furlong
- 1 English furlong = 625 fote
- 8 English furlong = 1 English Myle
- In 1670 Abbe Mouton suggested a primary length standard
- equal to 1 minute of arc on a great circle of the earth.
- For this basic length Mouton offered the name milliare.
- This was to be subdivided by seven sub units with each one
- to be 1/10 the length of the one preceeding or
- Milliare = 1 minute of arc = 36524 English feet = 1.11 km
- Centuria =.1 minute of arc = 3652.4 English feet = .111 km
- Decuria = .01 minutes of arc = 365.24 English feet = 111.1 m
- Virga = .001 minutes of arc = 36.524 English feet =11.1 m
- Virgula = .0001 minutes of arc = 3.6524 English feet = 1.11 m
- Decima = .00001 minute of arc = .36524 English feet = .111 m
- Centesima = .000001 minute of arc .36524 = English feet = 113.25 mm
- Millesima = .0000001 minute of arc .036524 = English feet = 11.325 mm
- Abbe Mouton may or may not have known that
- The Milos was based on a stadion equivalent to the Egyptian minute of march.
- Sir Issac Newton who attempted to restablish the measures of the ancient world
- from the math problems in Kings 1 may not have known that
- But its certain that Jomard, one of the French savants accompanying Napoleon
- to Egypt entrusted with the measurement of ancient architecture to attempt
- to restablish the correct value of ancient measures by measurement
- knew that because he cites the Greeks who knew that
- "In 1798, Edme-Francois Jomard visited the Great Pyramid
- as a young savant on Napoleon's expedition.
- The French had the debris cleared away from
- the two northern corners of the Pyramid and discovered the corner sockets
- where the corner casing stones had apparently originally been placed.
- These were ten by twelve foot mortises, perfectly level,
- and perfectly level with each other, cut twenty inches into the limestone bedrock.
- Although, there were still piles of rubble between them,
- Jomard was able to measure the north side of the base to be 230.902 meters (757.5 feet).
- For the height, he measured each step. They added up to a total of 144 meters (481 feet).
- By means of trigonometry Jomard calculated a slope of 51* 19' 14", and
- an apothem of 184.722 meters. Because the casing stones were missing,
- these figures were both estimates, but the length of the apothem
- looked virtually perfect in light of various ancient classical texts
- which Jomard was familiar with."
- Diodorus Siculus and Strabo both claimed that the apothem of the Great Pyramid
- was one stadium long. The Olympic stadium was 600 Greek feet, and
- was supposed to be related to the size of the earth.
- Jomard found the stadium of Eratosthenes and Hipparchus to be 185.5 meters,
- and thus within one meter of his figure for the apothem. He also found that
- distances quoted by the ancients in stadia matched the distances found by
- Napoleon's surveyors, if a stadium was taken to be 185 meters.
- The ancient stadium was also reported to have been 1/600 of a degree.
- When Jomard took the length of a degree at what he believed to be
- the mean latitude of Egypt, 110,827.68 meters, and divided it by 600,
- he arrived at a stadium of 184.712 meters, which was
- within ten centimeters of his figure for the length of the apothem!
- In addition, several Greek authors had reported that the perimeter
- of the base was equal to half a minute of a degree.
- This would mean that a degree of latitude divided by 480 should
- equal the length of one side of the base.
- Again Jomard used the length of a degree at his mean latitude of Egypt,
- 110,827 meters, and dividing by 480 arrived at 230.8 meters,
- again within 10 centimeters of his measured base.
Classical references
editMathmatical and metrological references
edit- H Arthur Klein (1976). The World of Measurements. Simon and Schuster.
- R. A. Cordingley (1951). Norman's Parrallel of the Orders of Architecture. Alex Trianti Ltd.
- Francis H. Moffitt (1987). Surveying. Harper & Row. ISBN 0060445548.
- Gillings (1972). Mathematics in the time of the Pharoahs. MIT Press. ISBN 0262070456.
- Lucas N. H. Bunt, Phillip S.Jones, Jack D. Bedient (1976). The Historical Roots of Elementary Mathematics. Dover. ISBN 0486255638.
{{cite book}}: CS1 maint: multiple names: authors list (link) - Somers Clarke and R. Englebach (1990). Ancient Egyptian Construction and Architecture. Dover. ISBN 0486264858.
- Gardiner (1990). Egyptian Grammar. Griffith Institute. ISBN 0900416351.
Linguistic references
edit- J. P. Mallory (1989). In Search of the Indo Europeans. Thames and Hudson. ISBN 050027616-1.
- Anne H. Groton (1995). From Alpha to Omega. Focus Information group. ISBN 0941051382.
Archaeological historical references
edit- Michael Grant (1987). The Rise of the Greeks. Charles Scribners Sons.
- Lionel Casson (1991). The Ancient Mariners. PUP. ISBN 06910147879.
{{cite book}}: Check|isbn=value: length (help) - James B. Pritchard, (1968). The Ancient Near East. OUP.
{{cite book}}: CS1 maint: extra punctuation (link) - Nelson Glueck (1959). Rivers in the Desert. HUC.
Medieval references
edit- Jean Gimpel (1976). The Medieval Machine. Holt Rheinhart & Winston. ISBN 0030146364.
- H Johnathan Riley Smith (1990). The Atlas of the Crusades. Swanston. ISBN 0723003610.
- Elizabeth Hallam (1986). The Plantagenet Chronicles. Weidenfield & Nicholson. ISBN 1555840183.
- H.W. Koch (1978). Medieval Warfare. Prentice Hall. ISBN 0135736005.