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Last updated 12/25/05

See images and analysis of ancient mathematical objects: IMAGE GRID

UGE: a paris publisher

UGE=UGE=U.G.E.=a Paris Publisher=”Union generale d’editions.”

[B_538,8.5,UGE] CATNYP# JFC 86-1377

“L’espace et la lettre : ecritures, typographies.“

Found during search for UGE and “Cahiers Jussieu.”

Paris, UGE, 1977.

The above was noted by G. Ifrah in UHN!

Includes general Ancient Near East discussion and a phonetic table of

Ugaritic cuneiform (p. 121).

[Anne-Marie Christin has also edited several collective works :

“L'Espace et la lettre”, in Cahiers Jussieu, n°3, Université Paris 7, Paris,

UGE, 1977 ]

Other item by UGE:

Foucaud Michel; Sémiologie de la lettre, l’espace et la lettre, U.G.E.,

1977.

UHN: The Universal History of Numbers; Georges Ifrah, 2000

[B_359,HOUSE]

(MSJ sugg*LP delivered Xmas 2001,SIBL)

CATNYP# *R-SIBL QA141.I3713

“The Universal History of Numbers : from prehistory to the invention of the computer / Georges Ifrah ; translated from the French by David Bellos…[et al].”

Title: Histoire universelle des chiffres. English

New York : J. Wiley, 2000

More notes…

p. 125, suan pan=abacus=see p. 140, gesdab-dim mu

p. 134, semite=of noah’s son Shem (not Ham and not Japath)

p. 136-7 see hebrew and arabic expounded and word for myriad=riboh see alts in ugaritic et al

p. 140 see up to 1 million in assyro-babylonian

p. 144-5 , mari nos

p. 424 lalitavistara sutra!

B_359 further notes:

091302

working bkwds from end of text for no reason.

p. 591: woodcut image from Freiburg 1503; shows a similar ABACUS to the table of Salamis.

P. 589: “Sefer Ha Mispar” i.e. the Book of Number, by Rabbi Ben Ezra (1092-1167). Sifra used for Zero.

Same pg. FIBONACCI used Zephirim which led to Zefiro and then by contraction to zero. See also p. 346 for reference to Zero called Galgal [hebrew for wheel]

p. 588: Fibonacci’s Liber Abaci means “Book of the ABACUS”!

p. 579: Codex Vigilanus (Latin; 976 CE, Northern Spain) now at the Escurial Library, Madrid. Shows Hindu Arabic numerals.

p. 567: Gelosia multiplication shown in image from Arabic math treatise.

See fig 25.12. Item is Paris, BN, Ms. Ar. 2473, f-b9.

p. 566: see example of complexities of Galley division as noted in MATH PRIOR TO 1601!

Galley division AKA “A la Francaise”

P. 562: Re ABACUS/SALAMIS/ See Mesopotamian “board of sand” [arabic] “takht al turab” AKA

[persian] “takhta-yi khak”

P. 549 re Milesian accounting note the Arabs ~1000 CE astronomical tables Kaf=20 Lam Ha=35

As greeks would use Koppa=20 Lambda Epsilon=35

P. 542-3: re [Incan] QUIPU see Japanese Ketsujo of similar construct from Ryu-Kyu Islands.

See Knot=[Arabic] “aqd” od “uqda”

See UHN:p. 520-1: See Jewish astronomers in Arab lands

See Mashallah

Sanad ibn ‘Ali

Sahl at Tabari, from Khurasan.

Sahl ibn Bishr, from Khurasan.

P. 518 ASTROLABE; Pope Sylvester II (Gerbert of Aurillac) acquired an Arab Astrolabe during his time in Spain

P. 518 CONSTRUCTION/MECHANICS: Arab author Isma’il ibn al-Razzaz al-Jazzari, 1206 work on mechanics included water clocks camshafts crankshafts and automata..

p. 451: RE ALGEBRA Sanskrit name is AVYAKTAGANITA = “science of calculating the unknown”

P. 450 Indian Mathematician ARYABHATA on square roots. ~600 CE.

P. 441: See lotus plant used as a math symbol with varied color values.

See Narmer Macehead and Palette “Kumud” or “Kumuda”.

Indian values unlike AE 3000 (or 1000) were 10^25 to 10^112 many variances.

p. 440 Sanskrit arithmetic called “samkhyana” or “sankhyana”.

p. 439 typo reported 121702 via publisher.

“the product or the quotient of two debts is one debt.”

p. 431 re ZERO:

The actual name Sanskrit [Samskrita] means “complete perfect or definitive” which to me sounds like AE nfr or ZERO!

P. 424: on Buddha : Buddha’s response to the marriage quiz in “Lalitavistara Sutra”

describes an Indian cubit of 24 digits equal to two handspans; see greek cubit.

Also 4 cubits is an Arc [or a Bow]

p. 403; fig 24.77 on hieratic numerals relationship to early Khmer numerals in that a dot is added to make 200 of 100.

UHN:

p. 399 walls of cave at Nana Ghat in India with Buddhist Brahmi numerals for 24,400 [items?] ~150 BCE.

P 386 critical error of omission in fig. 24.54 in that first symbol for 30 is missing handled 121702.

p. 380 see fig 24.75; Nagari figure for 7 looks like 12^th AE dynasty hieratic.

p. 378 see fig 24.29 Brahmi figure for 6 looks like 18^th AE dynasty hieratic.

p. 376: Indian divinity of feminine energy sitting on a goose with cycle of creation similar to Nut AE sky goddess.

P. 372

TAMIL nos.

1=Uru

2=Irandu

3=Munru

4=Nalu or Nangu

5=Aindu or Ainju

6=Aru

7=Erla or Ezha

8=Ettu

9=Onbadu

compare to Malayalam

p. 321: Stela at Quirigua 775 CE MAYAN.

See MAYA calendar and astronomy. See Fig. 22.64.

p. 319: Side 2 of Stela 29 from Tikal (Guatemala) oldest Mayan inscrip. 292 CE. Calendrical.

UHN:

p. 318: Leyden Plate jade pendant from Tikal – 320 CE calendrical

See also POLISH 9= Nine =Dgeviench

p. 161:

Coded Sexagesimal Cryptograms (Sumerian & Babylonian)

ANU: god of heaven, father of all other gods, 60

ENLIL: god of Earth, 50 (Later replaced by MARDUK, 10)

EA: god of water, 40 (sometimes 60)

SIN: lunar god, month, 30

SHAMASH: solar god, 20

ADAD: ?, 10 or 6

ISHTAR: queen of heavens, daughter of ANU, 15

NINURTA: son of ENLIL, also 50

NERGAL: ?, 14

GIBIL & NISKU: companions of SHAMASH, 10 for either (and/or both?)

p. 159:TORAH; EXODUS 26 and numbers 29!!!

p.159 on ESAGIL tablet.

G. Contenau on the stated dimensions of the Temple to Marduk and Tower of Babel.:

“This difficult text looks on first reading like a bland statement of the dimensions of yards and terraces – a mere sequence of numbers, as on a stock list, with all it has to say stated plainly. However the scribe has peppered his account with the intercalated formula so often found in hieratic texts:

May the initiated explain this to the initiated and the uninitiated see it not!

We should not forget the significant role played by the oral teaching of the pupil by the master which accompanied the lessons of the invariably summary texts themselves. Even texts which appear to be utterly ordinary hid esoteric meanings which we cannot imagine.”

Compare this thought to my notes on Exodus 26:1-6.

Consider this related to my analysis, as yet unfinished, on the rest of Exodus 26.

p. 158:

fig 13.77 See astronomical table by Levi ben Gerson, a French-Jewish savant [1288-1344 CE].

p. 152: URUK {near LARSA} tablet [Louvre, AO 6484; sideB] fig. 13.60 ~200 BCE showing one of the oldest instances of the Babylonian ZERO!

p. 150: re LARSA/SENKEREH town source of mathematical cune text [Louvre, AO 8862, side IV] ZERO as a blank space. See URUK.

p. 145: MARI thousand=1000=“Li-im”

MARI “large”=10000=ribbatum=EBLA [Ri-bab]=UGARIT [Rbbt]=SYRIAN [ri-ib-ba-at]=HEBREW [ribo]

p. 144: MARI

100=Me-at

p. 140: ABACUS

gesdab-dim mu=[SUMERIAN]wooden-tablet-for-accounts

su-me-ek-ku-u=[SUMERIAN]wood-hand-rule-read.

Assyro Babylonian LIM=1000; ME=100

ME.LIM=100,000

LIM.LIM.=1,000,000

p. 137: ARABIC

G. IFRAH “…it should be noted, the units are always put before the tens: 57, for example, is sab’un wa khamsuna (“seven and fifty”), as in German (seibenundfunfzig) See next entry

p. 137: UGARIT/RAS SHAMRA in northern Syria.

“the units are always put before the tens”

p. 136: HEBREW

“what is unusual is that for all numbers from 3, the number-adjective is feminine if the noun is masculine, and masculine if the noun is feminine.”

p. 121: Sumerian tablet (sexagesimal/metrological); fig 12.1:

From IRAQ/FARA=Suruppak

See “Sumeriches Lexicon”, by A. Deimel, 1947.

p. 105 footnote reference to 3300 BCE bullae [balls of clay hollowed to receive calculi] found at Tepe Yahya, IRAN [near, but not in, SUSA] and Habuba Kabira, SYRIA {JEWISH?}

p. 97 See similar hoards of bullae [4^th millenium BCE] found at:

Chogha Mis, IRAN

Tall-I-Malyan, IRAN

P. 97: OLDEST calculi (symbolic COUNTING TOKENS)

From the 9^th to 7^th millenium BCE.

Found at:

Beldibi, ANATOLIA

Tepe Asiab, MESOPOTAMIA

Ganj Dara Tepe, IRAN

Khartoum, SUDAN

Jericho, WEST BANK

Abu Hureyra, SYRIA

More recent calculi from the 2^nd millenium BCE from:

Tepe Hissan, IRAN

Megiddo, ISRAEL

Nuzi, MESOPOTAMIA

p. 71: JEWS

Sephardic (Eastern) Jews Talit has 26 knots on each of the 4 fringes signifying the numerical value of the Tetragrammon [YHWH]

Ashkenazi (Western) Jews have 39 knots for YHWH EHD, “G-d is One”

39 also is the value of “tal”=“morning dew” [perhaps alchemical reference]

See notes on p. 251

p. 62:BRASSEMPOUY (bone)

from the Magdalenian Era [19,000-12,000 BCE]

four sets of notches “3” “7” 9 5

p. 61:FINGER COUNTING originally from EGYPT!

Tomb [#69] of Price Menna, Thebes, NK, 18^th dynasty, ~1500 BCE, reign of Thutmosis, with images of finger counting scribes.

p. 57:FINGER COUNTING

fig. 3.19

CODEX ALCOBACENSE 394, folio 152, National Library of Lisbon.

Illustrated by Spanish Theologian Rabano Mauro [780-856 CE].

p. 57:FINGER COUNTING

CODEX MATRITENSIS A19, folio 3V, 1130 CE

p. 55-6:FINGER COUNTING

Described by Saint Cyril of Alexandria [376-444 CE] in:Liber de Computo, Chapter CXXXVIII: De Flexibus digitorum, III, 135.

Spanish encyclopaedia, Liber etymologiarum, a compilation instituted by Bishop Isidor of Seville (570-636 CE).

VENERABLE BEDE in seventh century:

De computo vel loquela digitorum.

System referred to by Latin author, Juvenal [55-135 CE]

And by Apuleus [125-170 CE] in his “Apologia”

And by Saint Jerome [time of St. Augustine?]

Two arab manuscripts describe this as well:

University of Tunis (no. 6403)

Majami’ 7071/9 at the library of Waqfs in Baghdad.

p. 52 FINGER COUNTING

Persian dictionary: “Farhangi Djihangiri” 16^th century CE

UHN:

P. 51-2 GAMES…logic fun

AE Game of MORRA described on the images in these Theban tombs.

MK, Beni Hassan tomb 9

26^th dynasty tomb of Aba, no. 36

Morra played in Arab lands and called Mukharaja.

Romans played Micatio

Greeks played this GAME too!

Still played in southern France, “la mourre”

Played in CHINA and MONGOLIA, “hua quan”=“fist quarrel”

This GAME, MORRA, grew from FINGER COUNTING

p. 47: Works that mention FINGER COUNTING:

Aristophanes

Plutarch

Cicero

Seneca

Tertullian

Quintilian

PLINY

p. 47 PLINY, the Elder in his “Natural History XVI” mentions F.CTG

p. 43: Nichomachus of Gerasa [Judean Pitagorist] wrote “Arithmetical Introduction.” ~150 CE

p. 42: JUNE 22 = KEYWORD!!!

Note 1799 Definitive standard metre and kilogram made of platinum, were deposited in the French National Archives.

ULOS: reference texts

ULOS=The Union List of Serials, a great place to start.

I found many obscure things in here.

UMI: Dissertation Services

UNIVERSITY MICROFILMS. DOCTORAL THESES.
800-521-0600.
http://www.umi.com/

UMM EL-MARRA: (Syrian) City; 4300 year old complete tombs at

http://www.sciencedaily.com/releases/2000/10/001002181619.htm

200 miles northeast of Damascus; ancient city of Tuba?

UMM EL-QAAB: (AE, math?, artifacts) at town of

See ABYDOS, MDAIK, and SCORPION. See [B_269]

AKA UMM EL-Gaab

(as per AEB) Dreyer, Gunter, Umm el-Qaab I. Das Pradynastische Konigsgrab U-j und seine fruhen Schriftzeugnisse. Mit Beitragen von Ulrich Hartung und Frauke Pumpenmeier und einem Anhang von Freidel Feindt und Margaret Fischer, Mainz, Verlag Philipp von Zabern, 1998.

Copies given to me by M. St. John; 11/20/01.

*Translated excerpts in my archive. [B_269]

See OEANE.

UNNU: (AE, extinct) city

(as per E.A. Budge) See (Greek) Hermopolis.

UPPSALA: (Greek) papyri; See UPSALIENSIS

UPSALIENSIS or UPPSALA: (Greek) papyri

(as per E. G. Turner) P. UPS. 8=Der Fluch des Christen Sabinus, Papyrus Upsaliensis 8, ed. G. Bjorck, Uppsala, 1938.

See CHRISTEN SABINUS.

P.Ups.Frid: Ten Uppsala Papyri

P.Ups.Frid 1. Donatio mortis causa: (Greek; AD 48; from Dionysias)

http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0215

U.P.Z.: (UPZ; Greek) papyri

(as per E. G. Turner)

UPZ='Urkunde der Ptolemäerzeit (Ältere Funde)', 2 vols., ed. U. Wilcken, Berlin and Leipzig, 1927-1957, reprint ed., 1977 [*].

(republication of texts published in the 19^th century, up to but not including the Petrie Papyri).

Vol i, Papyri aus Unteragypten, Berlin-Leipzig, 1922-7.

Vol ii, Papyri aus Oberagypten, 1957.

UPZ: Urkunden der Ptolemäerzeit (ältere Funde)

UPZ 1.2. Petition from Harmais: (Greek; 163 bce; from MEMPHIS)

http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0245

UR: (Mesopotamian) City

http://www.upenn.edu/museum/Collections/mesopotamia.html

See TORAH; UR of the CHALDEANS

See TELL ES-SWAYHAT

URAEUS: Symbol of power

See Urerit Crown; Uraei

(as per E.A. Budge) See Goddess Uatchit (a form of Hathor) with winged Uraeus.

See snake legends, Torah (Genesis).

[B_180a,8.5,IMG, v. 1] CATNYP# *OBQ+ 73-2731 t. 82, “Hommages Serge Sauneron, Cairo, 1979. By Adolphe Gutbub.

See volume one, other images of snakes from Kom Ombo and Esna temple inscriptions.

(as per L. Bailey) See Apopis the serpent

URKUNDEN: [URK] Works

(as per EEF; M. Tilgner; 072304)

Re: English translation of Sethe's valuable work 'Urkunden der 18. Dynastie’

Fascicles 17-22 have been translated:

CUMMING, Barbara, Egyptian Historical Records of the Later Eighteenth

Dynasty. Translated into English from the Original Hieroglyphic Text as

Published in W. Helck, "Urkunden der 18. Dynastie", Heft 17-19. With

Reference to Professor Helck's German Translation. Fascicle I,

Warminster, Aris & Phillips Ltd., 1982 (17 x 24 cm; XI, 80 p.).

CUMMING, Barbara, Egyptian Historical Records of the Later Eighteenth

Dynasty. Translated into English from the Original Hieroglyphic Text as

Published in W. Helck, "Urkunden der 18. Dynastie", Heft 17-19. With

Reference to Professor Helck's German Translation. Fascicle 2,

Warminster, Aris & Phillips Ltd, 1984 (17 x 24 cm; p. 86-240).

ISBN 0-85668-272-1

CUMMING, Barbara, Egyptian Historical Records of the Later Eighteenth

Dynasty. Translated into English from the Original Hieroglyphic Text as

Published in W. Helck, "Urkunden der 18. Dynastie", Heft 17-19. With

Reference to Professor Helck's German Translation. Fascicle 3,

Warminster, Aris & Phillips Ltd, 1984 (17 x 24 cm; IV, p. 247-361).

ISBN 0-85668-284-5

DAVIES, Benedict G., Egyptian Historical Records of the Later

Eighteenth Dynasty. Fascicle IV. Translated from W. Helck, Urkunden der 18.

Dynastie, Heft 20, Warminster, Aris & Phillips, 1992. (16 x 24 cm; 78 p.).

ISBN 0-85668-579-8

DAVIES, Benedict G., Egyptian Historical Records of the Later

Eighteenth Dynasty. Fascicle V. Translated from W. Helck, Urkunden der 18.

Dynastie, Heft 21, Warminster, Aris & Phillips Ltd., 1994. (16 x 23 cm; XIX, 103 p.)

DAVIES, Benedict G., Egyptian Historical Records of the Later

Eighteenth Dynasty. Fascicle VI. Translated from W. Helck, Urkunden der 18.

Dynastie, Heft 22, Warminster, Aris & Phillips, 1995. (16 x 23 cm; XXVI, 129 p.)

ISBN 0-85668-577-1

URUK: (Cuneiform) tablets

The tablets of Uruk IV, Jemdet Nasr, archaic Ur and Shuruppak

[all?] (between 3500 and 3000 BCE.)

http://www.interpres.cz/metrolog/measures/meso_intro.htm

See Nebuchadnezzar; TORAH;

See code of Hammurabi: 1792-50 BCE

See Hero(n) of Alexandria: (c. 50 AD). In Heron's Metrica

See Zodiac; Calendar; ADT; LABS; ARAK…

ADT, ex-cavated from Babylon and possibly Borsippa in the 1880's begins in the seventh century BCE (652), with only one year represented. We have only one text from the sixth (568 BCE), four from the fifth, but thirty-five from the fourth, and a high proportion of the succeeding years down to 61 BCE. From 236 BCE to 24 BCE, possibly one in 41 CE: [See GYT], compiled from ADT. / :

As per my copy of Jim Carlson’s paper [not via LB; see link] adaru 2 in the 19^th year of the cycle was called – Ululu 2 by the babylonians – filed with [B_551] for no reason.

http://www.math.utah.edu/~carlson/history/2001/LectureOutline.pdf

See UHN: p. 152: URUK {near LARSA} tablet [Louvre, AO 6484; sideB] fig. 13.60 ~200 BCE showing one of the oldest instances of the Babylonian ZERO!

USER: (AE) diorite statuette of

(as per PM) User is the son of Sit-Hathor,

Dynasty XII statuette found at Palace of Minos (Crete).

See “Palace of Knossos Arch. Report”, 1899-1900.

See this beautiful and precise AE work.

UTS: Union Theological Seminary

[Burke Library]

3041 Broadway, (212) 280-1314

Home | Color Guide | Abbreviation Guide | Personal Library Master key | Usage Guide | Thank You A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W-X | Y-Z

See images and analysis of ancient mathematical objects: IMAGE GRID