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Last updated 12/25/05

 

 

 

See images and analysis of ancient mathematical objects: IMAGE GRID

 

WAARDEN: (Author) B. L. Van der

[AKA] VAN DER WAERDEN, B(artel) L(eendert),
Die Voraussage von Finsternissen bei den Babyloniern, Berichte der sächsischen Akademie Leipzig, mathem.-phys. Kl. n. 92, 1940 ****
"The Egyptian Eternal Tables", PAPhS, 50 (1947) 536-547 y 782-788.
"Babylonian astronomy. II. The Thirty-Six Stars", JNES, 8 (1949) 6-26.
"Babylonian astronomy. III. The earliest calculations", JNES, 10 (1951) 20-34.
Die Astronomie der Pythagoreer, Amsterdam, 1951.
"Das große Jahr und die ewige Wiederkehr", Hermes, 80 (1952) 129-155.
"Das große Jahr des Orpheus", Hermes, 81 (1953) 481-483.
"History of the Zodiac", AO, 16 (1952-1953) 216-230.
"Bemerkungen zu den händlichen Tafeln des Ptolemaios", en Sitzungsberichte der Bayerischen Akademie, Mathem. Naturwiss. Klasse, München, 1953, p. 261.
"Die handlichen Tafeln des Ptolemaios", Osiris, 13 (1958) 54-78.
"Drei umstrittene Mondfinsternisse bei Ptolemaios", Museum, 15 (1958) 106.
"Ptolemaios (66) Klaudios", RE, 23.2 (1959) 1788-1859 y 2484.
"Babylonische Methoden in ägyptischen Planetentafeln", Vierteljahrsschrift d. Naturforsch. Ges. in Zürich, 105 (1960) 97-144.
"Pythagoreer, Pythagoreismus", RE, XXIV (1963) 209-300****.
Die Anfänge der Astronomie, Groningen, 1966 (= Boston/Basel/Stuttgart, 1980).
"The Date of Invention of Babylonian Planetary Theory", AHES, 5 (1968) 70.
"Die Wissenschaften der Pytagoreer", 13e Congrès International d’Histoire des Sciences (Moscou, 1971), Colloques, Moscou, 1971. pp. ****
"Die Ägypter und die Chaldäer", Sitzungsberichte der Heidelberg Akademie der Wissenschaften, (math.-naturwiss. Kl.), 5 (1972) 201-227.
"Aegyptische Planetenrechnung", Centaurus, 16 (1972) 65-91.
Science Awakening, II. The Birth of Astronomy, Leiden-New York, 1974.
"The ‘Babylonians’ and the ‘Persians’", Prismata...Festschrift für Willy Hartner, ed. Y. Maeyama, W. G. Saltzer, Wiesbaden, 1977, pp. 431-440.
"The Great Year in Greek, Persian and Hindu Astronomy", AHES, 18 (1978) 359-383.
"Mathematics and Astronomy in Mesopotamia", DSB, XV, suppl. I, 1978, 667-680.
"Astrologie", Der kleine Pauly, I, München, 19792 (1975) 660-664.
"Astronomie", Der kleine Pauly, I, München, 19792 (1975) 664-667.
Die Pythagoreer. Religiöse Bruderschaft und Schule der Wissenschaft, Zürich-München, 1979.
"Greek Astronomical Calendars. IV. The Parapegma of the Egyptian and Their ‘Perpetual Tables’", AHES, 32 (1985) 95-104.
Die Astronomie der Griechen. Eine Einführung, Darmstadt, 1988.
 
See WAERDEN below.

 

WADI: (Arabic word for) an Oasis or Valley [settlement]

French=Ouadi

 

(as per AEMT) Other WADI's:

Abu Gerida; Kubbaniya; Wadi Maghara and Natrun.

 

 

WADI AL-‘ARRUB: (Byzantine) inscriptions

Near Jerusalem aqueduct where it crosses by the Wadi.

 

[B_HOUSE,R_006,NO CATNYP] “Measuring and Weighing in Ancient Times.”

Published: Haifa, Israel, 2001 by the Reuben and Edith Hecht Museum.

“Flavios Aeneas Silentiarios [makes it known] to the proprietors, land tenants and farmers: you shall know that the divine and pious master has ordered that no person has the right to plant or sow in the space up to a distance of 15 feet from the aqueduct. Whoever trespasses this order will risk his head, and his property will be seized.”

 

 

WADI ARABAH: (Late Neolithic) artifacts in Israel at Timna.

(as per OEANE) "Late Neolithic Copper Smelting", See the Prestige Objects of Nahal Mishmar (on the west bank of the Dead Sea), See Judean Desert Caves,

Note: Chalcolithic copper mining at Norsuntepe may have been source of ore for objects found at Nahal Mishmar.

 

 

WADI BA'BA: (AE) inscriptions

Ba'Ba=Father (Arabic)

 

(as per AEB) Seek inscriptions at copper mine from MK and NK.

 

See the nice Palm Garden.

 

http://translate.google.com/translate?hl=en&sl=fr&u=http://perso.wanadoo.fr/jean-marc.mercier/sinai/kharig.htm&prev=/search%3Fq%3DWADI%2BBA%2527BA%26hl%3Den%26sa%3DG

 

See also WADI KHARIG and WADI MAGHARA.

 

 

WADI BAKARIYA & SOKARI: (Roman) Goldmines

The Wadi is situated at the same latitude as Marsa Alam, a small town along the Red Sea coast. The site can be reached via the Marsa Alam - Edfou highway, connecting the Red Sea with the Nile Valley. Near Wadi Baramiya, another Roman goldmine, one leaves the highway and continues into the mountains. Wadi Bakariya is situated about 30 km north of Wadi Baramiya. The Wadi extends into another, larger one: the Wadi Miya. A temple built by, among others, Pharaoh Sethi I, is located here. A thorough survey is planned for the area, where traces of other settlements have been observed in the vicinity. In Wadi Bakariya not only traces of the Ptolemaic and Roman era, but also of the 20th century AD have been spotted. It is a small wadi where the working areas were situated in between the many trenches and exploitation pits. The living quarters, however, seem to have been built in another area. Here as well, several surveys are planned to clarify the situation.

http://www.leidenuniv.nl/interuniv/nvic/ResEn.html

 

 

WADI BARRAMIYA: (AE) village; inscriptions

[B_406,8.5,JARCE] CATNYP# *OBH (American research Center in Egypt. Journal)

“Journal of the American Research Center in Egypt.”

Volume #33 [1996]:

“The Festival Structure of Thutmose III’s BUTO Stele.” p.69-76

By Anthony Spalinger.

Refers to his other work of more import to my query:

“Sothis and ‘Official’ CALENDAR Texts.” Pursue!

See extensive Bibliography.

BUTO Stele makes no clear-cut demarcation between the recurrent and non-recurrent feasts..”

Includes accounts of bread, beer, incense etc.; distributions by Festival vary.

 

“New Hieroglyphic Evidence for Pharaonic Activity in the Eastern Desert of Egypt.” P. 77 ff

Reference to WADI BARRAMIYA; BIR DUNQASH and BIR MUEILHA.

See page 91 for image of this inscription:

“A well, it is 22 CUBITS distant from this mountain…”

 

See page 100 for image of this inscription:

“…It is 10 CUBITS distant from this inscription..”

 

 

WADI BRISSA: (Babylonian) inscriptions

Noted in Rec. de Trav. 28 (1906); See [B_304].

 

Seek:

POGNON, Les inscriptions babyloniennes de Wadi-Brissa (Paris, 1888)

 

Seek image “proving” AE visit by Nebuchodnossor:

[Found in H. Pognon, `Inscriptions Babyloniennes' (1905), Plate IV.; F.H. Weissbach, `Die Inschriften Nebukhadnezars II im Wadi Brissa und am Nahr el-Kelb', (Leipzig, 1906), p. 3.]

http://www.geocities.com/Athens/Pantheon/5061/marriage.html

 

 

WADI DALIYEH: (Aramaic) scrolls

AKA SAMARIA PAPYRI. Fourth century legal papyri.

 

See the following info gleaned from this site:

http://www.flash.net/~hoselton/deadsea/deadsea.htm

 

From several caves 9 miles north of Jericho, discovered and excavated, 1962-64, papyri written in Aramaic and dated between 375 and 335 BCE were found. Nearly 200 human skeletons covering all age groups were discovered there; apparently killed by Macedonian soldiers of Alexander the Great when he conquered Samaria in 331 BCE.

 

 

WADI EL HOL: (Proto Canaanite or Proto Sinaitic, MK) inscriptions

(as per EEF; A. K. Eyma)

…a report on the findings of Dr. John Coleman

Darnell (Yale) on the inscriptions of Wadi-el-Hol was forthcoming from

a meeting of the SBL to take place in Boston on November 1999.

 

The curent issue of Goettinger Miszellen (GM180) has a brief

article ("preliminary remarks"/ "a first try") about the two inscriptions,

by Stefan Jakob Wimmer and Samaher Wimmer-Dweikat (p.107-112).

(the Wadi-el-Hol script resembles Proto-Sinaitic, a lot).

 

The alphabet was invented earlier than we thought. That is the initial conclusion reached by scholars studying two newly discovered inscriptions at Wadi el-Hol, in Upper (southern) Egypt.

"These may be the oldest alphabetic inscriptions ever found, dating to 1800 B.C. or earlier," P. Kyle McCarter, Jr., a professor at Johns Hopkins University and a specialist in ancient inscriptions, told BAR [Biblical Archaeology Review]. "We have to reevaluate the earliest history of the alphabet."

The inscriptions were discovered at a site north of Luxor by John and Deborah Darnell, a professor at Yale and a Ph.D. student at the University of Chicago, respectively. The inscriptions were scratched on a rock wall alongside a military road; they were surrounded by graffiti and even snatches of Egyptian literary texts written in hieroglyphics. The site's name, Wadi el-Hol, translates roughly to "Terror Gulch."

The inscriptions are thought to be the work of Semites living in Egypt during the Middle Kingdom period (c. 2040-1674 B.C.).

http://www.bib-arch.org/barjf00/strata.html

 

http://www-oi.uchicago.edu/OI/AR/93-94/93-94_Desert_Road_fig3.html

 

 

WADI EL HUDI: (AE) inscriptions

(as per H. Papazian) Amethyst quarries; inscriptions; seek work by Fakhry, Ahmed.

 

See these links related to quarries.

http://www.duke.edu/~jpw5/quarries/home.html

 

http://www.geology.utoledo.edu/research/archaeology/geoarc3.html

 

Sadek, Ashraf. The Amethyst Mining Inscriptions of Wadi el-Hudi, 1: Text (= Modern Egyptology Series). Warminster, 1980. [AEB 80.237 English]

 

…graffiti from the Twelfth and Thirteenth Dynasties at Wadi el-Hudi.

http://www-oi.uchicago.edu/OI/AR/93-94/93-94_Desert_Road.html

 

 

WADI ES-SEBOUA: (AE) inscriptions; stelae

[B_139,OS,IMG] CATNYP# OBKM++(Egypt. Antiquities, Service des Temples immerges de la Nubie. Temple de Ouadi es-Seboua)

“Le temple de Ouadi es Seboua” Henri Gauthier, Le Caire 1912.

From a restoration survey of 1909.

See related work by G. Maspero.

150 kilometers south of Aswan. (Sudan/Nubia).

AKA Valley of the Lions.

An ancient postal station.

See Avenue of Sphinxes (12).

Pair of larger Sphinxes.

Note the familiar stonework of the temple façade.

The occasional stone joint at an angle less steep than the structure, and inverted. Stress cracks through the center of the pylon. Well crafted glyph inscriptions.

Reign of Ramses II?

 

See also? Henri Gauthier, 2 BdE.

 

AKA Oasis of el-Kharga; Active during the reign of Darius I. ~450 BCE.

 

AKA Es-Sabiyah [Kuwait]?

http://users.ox.ac.uk/~neareast/bsainl4.htm

 

 

WADI GARAWI: (AE, OK) canal, water storage systems

(as per AEB) Seek 4th or 5th Dyn. Dam Project.

Seek info on water storage systems=Sadd-El-Kafara.

See Lake Moeris=Lac-Moeris.

See Fayum from 2600 BCE. @ 30 Km South of Kairo.

 

(as per EEF F. W. Niedenfuhr)

“I think a good place to look is in Dr. Rushdi Said's book on the geology of the Nile. He discusses climactic factors in some depth. The book is

available in both English and Arabic.”

Rushdi Said, “The River Nile. Geology, Hydrology and Utilization”

Oxford, 1993

 

the first known dam was built near Helwan, some 20 miles south of Cairo at a date between 2950 and 2750 BC. This was built to create a reservoir for irrigation purposes in the Wadi el-Garawi with a crest length of 106m and a base length of 81m, and a maximum height of 11.3m. Twin dry-stone masonry walls, each 24m in thickness, had a core of gravel 36m in thickness. Substantial remains of this structure have a gap in them 46m across with a lack of silt, suggesting a wash-out of the unmortared structure soon after construction.

http://www.icomos.org/studies/canals2b.htm

 

The dam was probably constructed in the reign of Amenemhat III and collapsed under Sekhemkarê Amenemhat V. Its main purpose would have been to facilitate navigation on the stretch of river south of Semna, primarily for military reasons.

http://www.leidenuniv.nl/nino/aeb94/aeb94_8.html

 

 

WADI GASUS: (AE, OK) Stele

[B_136,rtrn cpy,IMG] Seek “Stelen aus Wadi Gasus bei Qoser”, ZAS 20, p. 203-205, 1882.

Some calendrical data. No other math.

 

1976 Alessandra Nibbi, «Remarks on the two Stelae from the Wadi Gasus», JEA 62, p. 45-56.

http://www.egyptologues.net/chaire/geographiet3.htm

 

 

WADI HAMMAMAT: (AE, Hieroglyph, Hieratic) inscriptions

(as per H. Papazian) Inscriptions; seek work by Goyon, Georges.

See [B_135].

(as per B. Gunn and T.E. Peet) See an inscription meaning square cubits.

Seek Griffith in Proc. Soc. Bibl. Arch.,1892, 419-420.

 

[B_135,rtrn cpy,IMG] CATNYP# *OBL (Goyon, G. Nouvelles …),

“Nouvelles inscriptions rupestres du Wadi Hammamat.”

Paris, 1957. See Plates. I cannot locate square cubits.

See Pepi I inscription. See also inscription #61.

Sharing content with the tombs found at Giza by G. Reisner.

Minor math content with calendrical data.

 

See work by Goyon, G. in Ann. Serv.[ASAE], “Le Papyrus Turin dit”

<<des mines d’or>>, et le Wadi Hammamat.”, t. XLIX, p. 337-392.

 

(as per G. Goyon) See work by J. Couyat et P. Montet,

“Les Inscriptions hieroglyphiques et hieratiques du Ouadi Hammamat”,

MIFAO, 1912, Le Caire.

 

(as per PM) See prodynastic Bark of Horus (or Sokari).

In work by Engelbach, Notes of Inspection,

In Ann.Serv. [ASAE] XXXI, pl. I, pp. 133-4.

See also [B_230]

 

O.Wadi Hamm. 20.: (Greek)

http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0047

 

 

WADI KHARGEH: (AE, Hieroglyphic) inscriptions and Greek ostraca

AKA Ain Waqfa

 

(as per ZAS, index# 1029) Seek “Hieroglyphische Inschriften in den Oasen Xarigeh und DaXileh, 1874. See ZAS 12, 73-80.

 

[B_180b,8.5,IMG, v. 2] CATNYP# *OBQ+ 73-2731 t. 82, “Hommages Serge Sauneron, Cairo, 1979.

Map shows Wadi Kharga nearly due east of Luxor across the Plateau of the Libyan Desert. North of Bulaq.

 

* A dyn 27 temple, made of straw bricks, was discovered in the

Kharga Oasis, near the Roman town of Dosh, with 300 bronze statues

of Osiris. Two brief reports of Oct 8:

 

http://www.uk.sis.gov.eg/online/html5/o081021e.htm

 

http://dailynews.yahoo.com/h/nm/20011008/od/temple_dc_1.html

 

(as per EEF) Story of a recent discovery.

http://www.arabicnews.com/ansub/Daily/Day/011027/2001102732.html

 

O.Waqfa 1.: (Greek)

http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0048

 

 

WADI KHARIG-BAR NASIB: (AE) inscriptions

Name means: Oasis of the Sea of Fate.

 

(as per AEB) Seek copper mines, inscriptions.

 

1977 Raphaël Giveon, «Inscriptions of Sahureë and Sesostris I from Wadi-Kharig (Sinaï)», BASOR 226, p. 61-63.

http://www.egyptologues.net/chaire/geographiet3.htm

 

 

WADI MAGHARA: (OK; AE) mining site

http://translate.google.com/translate?hl=en&sl=fr&u=http://perso.wanadoo.fr/jean-marc.mercier/sinai/kharig.htm&prev=/search%3Fq%3DWADI%2BBA%2527BA%26hl%3Den%26sa%3DG

See turquoise mine.

WADI MENE’IYEH: (AE; MK) mines

(as per EEF; 031303; D. Hunt)

* The valley of Timna, where there were major Egyptian mines, was

originally  known by the Arabic Wadi Mene'iyeh.  <snip>

Mene'iyeh <snip> bears a superficial resemblance to Egyptian divine name Min-Ioh, the god Min as moon.

Min, <snip> was the god of the Eastern Desert. <snip>

 

WADI MURABBA’AT: (Arabic; Aramaic; Hebrew; Greek) Manuscripts from

Includes a 7th Century BCE palimpsest, some Arabic texts, some 1st century CE remains, and other documents in Hebrew, Aramaic, Greek, and Latin from the time of the Bar Kokhba revolt. This was all published in DJD II as Les grottes de Murabba’at by Paul Benoit, J. T. Milik, and R. de Vaux

 

http://home.flash.net/~hoselton/deadsea/deadsea.htm

 

Ask for information at JH.

 

(as per E. G. Turner) The oldest papyri found outside of Egypt were (Hebrew) found at WADI MURABBA’AT near the Dead Sea.

 

See BABATHA; QUMRAN.

 

 

WADI QUM HELEEG: (AE, MK) engravings

(as per EEF; 102204)

* "Important archaeological discoveries in eastern desert unearthed"

http://www.sis.gov.eg/online/html11/o201024h.htm

132 prehistoric engravings depicting livestock were found in the

WADI QUM HELEEG in the Sharkeya desert.

 

 

WADI SANNUR: (AE, MK) stelae

(as per AEB 1965) See two Ramesside Stelae.

 

 

WADI SARGA: (Coptic and Greek) ostraca; texts

(as per ZPE, D. Fowler) Seek O. Wadi Sarga 24-28,

“potshards of division tables”, Coptic (math).

See W. Brashear, “Quisquiliae”, BSAC [=BASC?] 26 (1984) 19-22.

 

(as per ZPE, D. Fowler) also Seek O. Wadi Sarga 22 and 23,

“multiplication tables”, Coptic (math).

 

(as per Duke Univ.)

Wadi Sarga, Coptic and Greek Texts, ed. W.E. Crum and H.I. Bell, with an introduction by R. Campbell Thompson. Copenhagen 1922. (Coptica III). The Greek and Coptic texts are listed on p. xv; no. 9 is on vellum, no. 12 on papyrus, the remainder on ostraca (= O.Sarga). All the documentary texts listed in P.Sarga on page xv as Greek, nos. 121-7, 147, 150-1, 155-6, 159-60, 195, 199-201, 205-374, 380-5 are reprinted in SB XVIII. There is a concordance in SB XIX, Abschnitt 7. Many of these texts contain a word or more in Coptic.

(as per E. G. Turner) See above texts.

 

O. SARGA 121: (Greek; late ptolemaic?)

http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0041

 

 

WADI SEIYAL: (Aramaic, Hebrew) Manuscripts of

The earliest manuscripts were acquired from Bedouins between 1952 and 1954 by the erstwhile 'Palestine Archaeological Museum'. They were represented as from this location; see DJD VIII. Subsequent discoveries at Nahal Hever make it the almost certain source for at least some of those manuscripts. Additional documents were actually discovered here by an Israeli expedition in 1960. The two collections are still stored separately and will be published separately.

 

http://home.flash.net/~hoselton/deadsea/deadsea.htm

 

Ask for information at JH.

 

 

WADI SIWA: (AE tomb at) Oasis near Libyan border.

(as per EEF) See these links about the Lost Persian army of ~500 BCE.

The army set out to crush the Sacred Oracle at Siwa and never reappeared.

Until recently…

http://www.lineone.net/express/00/11/16/features/f0100splash-d.html

 

http://www.ngnews.com/news/2000/12/12082000/wirpersia_3408.asp

 

 

(as per ZAS, index# 1838) Seek “Ein agyptisches Grab in Siwa”,

ZAS 61, p. 94-98, 1926.

 

(as per PM) See work by Ahmed, Fakhry, Siwa Oasis,

“The Necropolis of Gabal el-Mota at Siwa”.

In Ann. Serv. [ASAE]. XL, pp. 779-87.

See plate XXIII with image of Wenamun Text.

 

 

WADI SURA: cave dwellers; west of the Al Galf Al Kabir plateau

http://www.uk.sis.gov.eg/online/html4/o200921m.htm

 

 

WADI TUMILAT: (AE) Study progress of digs at

See PITHOM

 

(as per AEB 85.1358) See work by Weimar, Peter.

 

 

WAERDEN: (Author)

Bartel Leendert Waerden, 1903-?

 

See Akhmim.

 

[B_221,8.5,IMG] CATNYP# OEC (Waerden, B. L. van der. Erwachende Wissenschaft (488 p.))

“Erwachende Wissenschaft; agyptische, babylonische und grieschische Mathematik. Aus dem Hollandischen ubersetzt von Helga Habicht, mit Zusatsen vom Verfasser.”

Basel, 1956.

At the Science Library.

With comments and some analysis of the RMP and the Moskow P. and Senmut(h)’s Astronomical tomb decorations and the Mastaba of Meri (4th Dynasty).

A good intro to Sumerian math symbols and cuneiform.

See Sumerian tablet VAT 12593 at Berliner Museum.

See photo page 72 of Babylonian approximation of the square root of two; tablet YBC 7289 (at Yale Univ.)

Page 85, discussion of the development of “modern” number symbols.

P. 125, Plimpton 322 tablet with Pythagorean triples.

One good image of the EMLR.

 

See Science awakening, A. Dresden; [B_344,HOUSE]

See top of this page for more bibliographical entries at WAARDEN.

 

WAGES: through the ages

My efforts to clarify ancient maths lead me here.

(as per EEF; M. Silver) Seek the following texts:

 

Eyre, Christopher J. (1987) “Work and the Organisation of Work in the OK (5-47) [in the NK, 167-221] in Marvin A. Powell (ed.), Labor in the Ancient Near East. New Haven. Yale Univ. Press

 

Mueller, Dieter. (1975) “Some remarks on Wage Rates in the MK”, JNES, 34, 249-63.

 

Muller-Wollerman, Renata. (1985) “Warren austausch im Agypten des Alten Reiches.” JESHO [B_380], 28, 121-68. Especially page 148.