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Last updated 12/25/05


See images and analysis of ancient mathematical objects: IMAGE GRID


FAM. TEBT.: (greek) papyri



FARA: (Sumerian Cune, tablets, math, archives).i


[B_513,8.5,IMG] CATNYP# *OCP 01-9162

“The Fara tablets in the University of Pennsylvania Museum of Archaeology and Anthropology / [edition, translation, and commentary by] Harriet P. Martin, Fransesco Pomponio, Guiseppe Visicato and Aage Westenholz.

Maryland, 2001.

Available from OXBOW catalog [B_332 alt]


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

From IRAQ/FARA=Suruppak

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


FAYUM: [Oasis]; (AE; Greek) papyri and ostraca

AKA P. Fay.


(as per D. Fowler) Seek P. Fay. 9; math.


Keyword def?=Desert settlement or Dune?


See Amherst.


[B_075,rvw] CATNYP# *OBKQ+ (Grenfell, B. P., Fayum towns and their papyri), "Fayum towns and their papyri, by Bernard P. Grenfell, Arthur S. Hunt, and David G. Hogarth, with a chapter by Grafton Milne. Maps illustrations, and four collotype plates. London 1900.

This text refers to excavations at:

Kasr et Banat,


Kom Ushim,

and Umm et Atl...


[B_076,rvw] CATNYP# *OBKQ+ 91-14068, "Das Buch vom Fayum : zum religiosen Eigenverstandnis einer agyptischen Landschaft / Horst Beinlich." Weisbaden : Otto Harassowitz, 1991.


(as per E. G. Turner) Kom el-Fari is the (mound) Capitol of the Fayum.

Keyword search Arsinoe.

Seek ostraca from Karanis from the University of Michigan collection.




O. Fay.: (Greek; 25 bce)


P.Fay. 11. Petiton of Dêmêtrios: (Greek; 115 bce; Theadelphia)

Drachmas and some fractions. Math?


[B_075=O_002] CATNYP# *OBKQ+ (Grenfell, B. P., Fayum towns and their papyri), Fayum towns and their papyri, by Bernard P. Grenfell, Arthur S. Hunt, and David G. Hogarth, with a chapter by Grafton Milne. Maps illustrations, and four collotype plates. London 1900.

BOBST# PA 3315 .F3

See BOBST Archive: O 1

Includes plates:

Maps; image of sandals; tools; accessories; Temple at Kasr Karun;

Shield; tombstones; papyri; Euclid fragments and other Classical

fragments (Homer; Demosthenes..) tax and other receipts; letters.

Accounts, math..

See indices VIII: Metrology


[B_480=O_050,rvw] CATNYP# *OBH 78-285 Bd. 7

BOBST# PA3308 .B48 Bd.7 Oversize

“Papyri, Ostraca und Wachstafeln aus Philadelphia im Fayum / bearbeseit von Paul Viereck und Friedrich Zucker. Mit 5 Lichdrucktafeln.”

Berlin, 1926.

Original also published as Agyptische Urkunden aus den Staatlichen Museen Berlin. Greichische Urkunden; Bd. 7.

CATNYP has reprint from Milan, 1972 with this title extension:

[Ristampa anastatica inalterata dell’edizione originale autorizzata dalla Verlag Weidmann]”

Paul Viereck, 1865-1944

Studies include Greek Papyri, Ostraca and Tablets.

See plates.



FERMAT: (French) Mathematician

Show all work!

See Erdos; Mersenne; Numbers; Taniyama-Shimura…


[B_403,HOUSE] CATNYP# JSD 98-165

“Fermat’s Enigma / The Epic Quest to Solve the World’s Greatest Mathematical Problem.” by Simon Singh, NY, 1997.

My thoughts: Consecutive primes greater than five when squared vary by a multiple of four factorial, why?


See Carmichael numbers:

The Carmichael numbers under 100,000 are

561, 1105, 1729 [1729: which Ramanujan noted was the lowest number to be produced as the sum of two cubes in two ways!], 2465, 2821, 6601, 8911, 10585, 15841,

 29341, 41041, 46657, 52633, 62745, 63973, and 75361.



The 1,000,000th prime number is: 15473891:


Gilbreath's Conjecture:



FIBONACCI: 12-13th century Italian Mathematician

AKA Leonardo di Pisano [and variants]

For late use of unit fractions see LIBER ABACI.


See UHN; p. 346 and 589; use of zero; zephirim; See EZRA


FINGER COUNTING: quiet negotiations

See UHN: p. 61: originally from EGYPT!

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


fig. 3.19

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

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


CODEX MATRITENSIS A19, folio 3V, 1130 CE


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.


Persian dictionary: “Farhangi Djihangiri” 16th century CE

P. 51-2 AE GAME of MORRA described on the images in these Theban tombs. MK, Beni Hassan tomb 9

26th dynasty tomb of Aba, no. 36

Morra played in Arab lands and called Mukharaja.

Romans played Micatio

Greeks played this 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:







PLINY the Elder in his “Natural History XVI”




FLORENCE: (Greek) papyri




(as per E. G. Turner) See “Papiri greco-egizii”, ed. D. Comparetti and G. Vitelli. Milan, 1906-15, 3 volumes. Reprinted 1962.


P.Flor.: Papiri greco-egizii, Papiri Fiorentini

P.Flor. 1.1. Loan of money with hypothêkê:

(Greek; 153 AD; from Hermoupolis Magna)

200 Drachmas. Math entry.


(as per B. Porten, [R_008])

P. Flor. XIX by M. Capasso, G. Messeri, R. Pintaudi eds, Miscellanea papyrologica in occasione del bicentenario dell’edizione della Charta Borgiana, Florence, 1990



FLORENTINE: (Mixtec) codex



FLORIDA: (Greek) ostraca

O. Florida: “The Florida Ostraka: Documents from the Roman Army in Upper Egypt.”



FONTS: tough ones

See index/archive items filed with [O_001]

See greek font help at:

Has sampi et al!




FOUAD or FUAD: (Greek) papyri

(as per E. G. Turner) Les Papyrus Fouad I, ed. A. Bataille et al, Cairo, 1939.


P. Fouad I Univ. = Fouad I University Papyri, ed. D. S. Crawford, Alexandria, 1949.


P.Fouad 8. : (Greek)

[Document concerning the visit of Vespasian to Alexandria]


P.Fuad I Univ.: Fuad I University Papyri

P.Fuad I Univ. 1dupl.: (Greek; 227 bce)


See P. Fouad 11; 12; 13; 14: See SOKNOBRAISIS; [O_022]

(as per E. G. Turner) See [O_078]


BOBCAT# PA3339 .S6 t.3

“Les Papyrus Fouad I: nos 1-89/ edites par A. [Andre] Bataille…[et al].”

Cairo, IFAO, 1939.


See NECROPOLIS; [B_524] by A. Bataille.


FRANKFURT: University; (Greek; Demotic) papyri

(as per ZAS, index# 1888) Seek ZAS 54, 1918.


(as per E. G. Turner) = Greichische Papyri aus dem Besitz des Rechtswissenschaftlichen Seminars der Universitat Frankfurt, ed. H. Lewald, Heidelberg, 1920.


P.Frankf. 1. Antichretic lease: (Greek; 214 bce; from THOLTHIS)


P. Frankf. = Lewald, Griechische Papyri aus dem Besitz des rechtwissenschaftlichen


FRANKINCENSE: smells so fine

The Malaysian dictionary, however, directs us to the source of the "frankincense" which is Java. The Lebeun, however, is not identified as the genus Bosweillia. Instead, it identifies "frankincense" with the Styrax benzoin. [footnote 66] This is the possible reason why the plates of the temple at Deir El-Bahari showing the incense producing trees do not match the genus Bosweillia. The identification of the word also reinforces the identification of Indonesia with Punt, the source of Egyptian incense.



Serpico, Margaret, and Raymond White. "The Botanical Identity and

Transport of Incense During the Egyptian New Kingdom." Antiquity 74(2000): 884-897.



Classical Greek=libanos



Groom, Nigel Saint John. 1981. Frankincense and Myrrh: A Study of the

Arabian Incense Trade. Arab Background Series. London and Beirut,

Longman Group Limited and Librairie du Liban.


Hepper, F. Nigel. 1969. "Arabian and African Frankincense Trees."

JEA 55, p. 66-72.


STEINER, Richard C., Albounout "Frankincense" and Alsounalph


Phoenician-Punic Botanical Terms with Prothetic Vowels from an Egyptian Papyrus and a Byzantine Codex, Orientalia 70 (2001), 97-103

(as per A. Eyma; EEF; 122002)

Having followed the thread and browsing some literature, I wonder

with how much certainty we are able to know what is covered by

the AE terms?


1) AE _snTr_  (> Coptic _sonte_) is sometimes taken to be "frankincence" (Boswellia) (e.g., Hannig, with reserve), but by others to be "resin of the terebinth". So I wonder whether it is not a very generic term. For the Coptic seems to refer to "(balsamic) resin" (Crumm p.346), and _snTr_ basically has a meaning comparable to German 'Weihrauch', i.e. "that what makes something holy" (_s-nTr_ "make divine"), so could apply to every fragrant 'purifying' product burned in cults. Further, Hoch (Semitic Words in Egyptian Texts, p. 305) lists a term that occurs several times in Dyn 20 texts: _snTr qdrt_. The second word is  a syllabic writing of a Semitic word for "incense", "smoke", "aroma", _qtr_ (Biblical Hebrew  _qtrt_). So I presume this is an imported type of _snTr_- perhaps ca. "Asiatic incense"? -, which could perhaps also indicate that _snTr_  is a generic term.

2) AE _antyw_ is generally taken to mean "myrrh" (e.g., Hannig),

but also this term seems to have a more general meaning? I think it

is the product in the Hatshepsut texts, but writers differ as to

whether those trees were Boswellia or Commiphora or even something else. Myrrh was I think used as conservative in some wines. Do we know

this practice in AE? I found in my notes that an ancient Greek writer (Hesychios) wrote that _aention_ was "an Egyptian myrrh" - obviously a rendering of AE _antyw_ - which might have been the basis for the idea

that this must be myrrh and nothing else.

3) I further noticed another AE word (LP) for a myrrh species: _xry_ (i.e. _xly_ > Coptic _shal_) (Vycichl  p. 260), of which I could not find whether it is also a loan from some foreign language (which could give clues about origin and thus plant species), and what the difference is with _antyw_. Anyone?



FREER: (Greek and Coptic) papyri; Bible manuscript

P.Freer: Greek and Coptic Papyri in the Freer Gallery of Art

P.Freer 1+`2. Account of Payments in Kind:

(Greek; from Aphroditopolis)

Significant arithmetical content. Math. Land Accounts.)

Freer Codex of Deuteronomy and Joshua; fifth or sixth century; images

Freer Codex of the Minor Prophets; 3rd century; images


FREIBURGER: (Greek and demotic) papyri

See Berol.


(as per Duke Univ.; E. G. Turner):

Mitteilungen aus der Freiburger Papyrussammlung.

I, Literarische Stücke, ed. W. Aly. Ptolemäische Kleruchenurkunde, ed. M. Gelzer. Heidelberg 1914. (SBHeidelberg 1914, Abh. 2). Nos. 1-7; no. 7 reprinted as SB I 5942. [MF 1.80; rp. CG]


II, Juristische Texte der römischen Zeit, ed. J. Partsch. Heidelberg 1916. (SBHeidelberg 1916, Abh.10). Nos. 8-11. Texts reprinted as SB III 6291-6294. [MF 1.81; rp. CG]


III, Juristische Urkunden der Ptolemäerzeit, ed. J. Partsch. Heidelberg 1927. (AbhHeidelberg 1927, Abh. 7). Nos. 12-38. [MF 1.82; rp. CG]


Nos. 39-44 are listed in P. Freib. IV as follows:

39 = SB V 7600;

40-41 = SB III 6094-6095;

42 = SB IV 7351;

43 = SB VI 9562;

44 = P. Customs 266.


IV, Griechische und demotische Papyri der Universitätsbibliothek Freiburg, ed. R.W. Daniel, M. Gronewald, H.J. Thissen. Bonn 1986. (Pap.Texte Abh. XXXVIII). Nos. 45-71 Greek; nos. 72-75 Demotic.

There are two additional Demotic texts,

P.Berlin P.15791 and P.Berlin P.23742,

published here. [o.e. RH]


P.Freib. 1.2.: (Greek)



FRONTINUS: (Roman) Surveyor





FULDENSIS: (Latin; early Christian) Codex


The Epistle to the Laodiceans appears in more than 100 manuscripts of the Latin Vulgate, including the oldest surviving manuscript, the celebrated Codex Fuldensis 546 CE, commissioned by Victor, bishop of Capua. The appearance in these Vulgate manuscripts may derive from Old Latin ones. There are about 10,000 extant manuscripts of the Vulgate, though only about 2,500 have been catalogued.



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See images and analysis of ancient mathematical objects: IMAGE GRID