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Last updated 12/25/05



See images and analysis of ancient mathematical objects: IMAGE GRID


MAA: association

Follow this link to the MAA, The Mathematical Association of America.



MAES: Manchester Ancient Egypt Society



MAGDALENE: (Christian) Manuscript [New Testament]



MAGDOLA: (Greek) papyri

(as per B.P. Grenfell, [B_051] HIBEH) seek P. Magd. work(s) by:

Jouget and Lefebvre;

"P Magd. Deuxieme Serie", p. 205. A collection of Greek Papyri.


Also note: P. Magd. 2, 4, 6 from the reign of Euergetes.


(as per E. G. Turner) P. Magd. = P. Lille ii.

AKA Medinet Nehas.


“In the case of the fragments of P. Magdalen 17, these steps are

described in the beginning of Colin Roberts's first publication

of the fragments (HTR 46, 1953). A sound basis in method is

crucial to the further exercise of critical thought.”


"Papyrus Magdalen Greek 17 (Gregory-Aland {P}64 ):

A Reappraisal," appears in Vol. 105 of ZPE.

pp. 13-20, and Plate IX.



MAGIC: [heka] (AE, Coptic, Greek, Jewish…) remnants

abracadabra an old AE word

See ALCHEMY; praxis; harris mag.; paracelsus; schemhamphoras; HERMES



CATNYP# *OBKQ 90-1286 Vol. 1.

BOBST# BF1622.G8 G74 1986

“The Greek magical papyri in translation, including the Demotic spells / edited by Hans Dieter Betz.”

Chicago, 1986.

Translations of Greek, Coptic and Demotic as gleaned from Papyri graecae magicae, 2nd edition and including fifty added items.


MAHAVIRA: (Indian) Mathematician

See similarities to AE efforts.


See work of RAMANUJAN.


(see this post to HM by M. Gardner)



MAHGAR DENDERA 2: Archaeological AE site

(as per S. Hendrickx, EEF)

Available text:

By Hendrickx, S.; Midant-Reynes, B. & Van Neer, W..

“Mahgar Dendera 2 (Haute Egypte), un site d'occupation Badarien.”

Egyptian Prehistory Monographs 3. Leuven: Leuven University Press, 2001.

ISBN 90 5867 163 1, 21 x 29,5 cm, 112 pgs. + 56 pl. + 1 map. 20

To be ordered from: Leuven University Press, Blijde Inkomststraat 5,

B-3000 Leuven, Belgium.



The site of Mahgar Dendera 2, in Upper Egypt, is the only new Badarian site excavated for over 50 years. It features a seasonal campsite, dating to about 4100 BC. The faunal remains indicate that people arrived at the site with their flocks at the moment when the Nile was low. Because the site is located close to the Nile, this allowed them to herd their animals when grazing possibilities became scarce in the vicinity of the permanent settlement.

Furthermore, they were fishing, probably in the main channel of the Nile. The site was left when the Nile started to rise, and the flooded zones became fordable and work in the fields started again.

The lithic material represents a specialised industry, apparently orientated towards working perishable materials such as wood and reed. Pottery was not produced at the site itself and served largely for storage purposes. The occupation features consist of hearths, post holes and storage holes. As an important part of the site was already destroyed at the time of the salvage excavation, it was impossible to identify well defined constructions. This volume contains the final excavation report, illustrated by a large number of drawings and photo's. (text in French with English summary)




(as per EEF; V. Solkin; 090103)
<snip>..the Book of the Dead of Maiherpri, a child of
Royal nursery and royal fan-bearer, found in his tomb in the Valley of the
Kings (KV36) in 1899 by Loret. Reign of Thutmosis IV. (See Reeves N.,
Wilkinson R. The Complete Valley of the Kings. - London, 1996, pp. 179-181).

MALLET [Dominique]: author/ AE papyrus



(as per Lange) P. Mallet in Louvre.


See work by Gaston Maspero.


[B_405,rvw] CATNYP# *OBKG (Mallet, D. Culte de Neit a Sais)

“La Culte de Neit a Sais.”

By Dominique Mallet, Paris, E. Leroux, 1888.


[F] Maspero, G., Le Papyrus Mallet, Recueil de travaux rélatifs à la philologie et à l'archéologie égyptiennes et assyriennes 1 (1870), pp. 47-59.

P. Mallet = P. Louvre E 11006. Probably not from Deir el-Medîna, but elsewhere in Thebes. For photograph and transcription, see A. el-M. Bakir, Eg. Epistolography, Le Caire, 1970 (= Bibliothèque d'étude, 48), Pl. 21-23 and XXVII-XXX.


MALTA: World’s oldest Temples at?

(052698) Joan Marler — “The Temples of Malta and the Megalithic Traditions of Western Europe” The temples of Malta, dating from the fourth millennium, B.C. are the oldest freestanding megalithic monuments in the world. Since their discovery, there has been a great deal of bizarre speculation as well as reputable research concerning their origin, construction and ritual function within prehistoric Maltese society.


[via GOOGLE search of megalthic+malta]


See above: spirals and dots! Nice spacing; any radii? See MNAJDRA



The remains of the Mnajdra Temples lie at the foot of the hill on which are located the temples of Hagar Qim. Mnajdra was first cleared of debris by C. Lenormant in 1840. T. Ashby excavated the remaining intact parts in 1910. Further remains came to light during the conservation and restoration works that the Museum Department undertook between 1952 and 1954. The small temple was the first to be built, and the middle one the last. The site dates from 3,600-2,500 BCE.

MANCHESTER: University

See RYLANDS; [B_093].


MANETHO: (Greek) Author

(as per EEF; T. Sagrillo)

There are also 2 Arabic extracts of Manetho: 1 from Muhammad al-Biruni (var. al-Bayruni; AH 362-442/973-1048 CE), and 1 from Taqi al-Din al-Maqrizi (AH 767-846/1364-1442 CE); al-Maqrizi's extract is a quote of al-Biruni's, with slight differences. (NB: al-Biruni was a Persian-speaking Uzbeki, but wrote in Arabic)

Both extracts basically start with Dynasty 21 and list the kings through Alexander the Great, albeit in a confused manner. One rather amusing mistake is that the first king is "Dayusfulita," who is said to have reigned 178 (al-Biruni), or 78 or 88 years (al-Maqrizi). This is of course a misreading of "Diospolite."

However, neither al-Biruni nor al-Maqrizi give the Manethonic quote
contained in `Abd al-Latif.
al-Biruni al-Khwarizmi, abu al-Rayhan Muhammad ibn Ahmad, and C. Eduard Sachau
    1878    Chronologie orientalischer Völker von Albêrûnî. Leipzig: F. A.
Brockaus. (Reprinted Leipzig: Otto Harrassowitz, 1923). Arabic text, pp
    1879    The Chronology of Ancient Nations; An English Version of the
Arabic Text of the Athâr-ul-Bâkiya of Albîrûnî, or, “Vestiges of the Past,”
Collected and Reduced to Writing by the Author in A. H. 390-1, A. D. 1000.
Translated by C. Eduard Sachau. London: Oriental Translation Fund of Great
Britian and Ireland. (Reprinted Frankfurt: Minerva GmbH, 1969). English
translation, p 102
al-Maqrizi, Taqi al-Din Ahmad ibn `Ali ibn `Abd al-Qadir ibn Muhammad, and
Gaston Wiet
    1922    el-Mawâ`iz wa'l-I`tibâr fî dhikr el-khitat wa'l-âthâr. Volume 3:
Deuxième partie, chapt. I-XLIX. Mémoires publiés par les membres de
l'Institut français d'archéologie orientale du Caire 46. Cairo: Imprimerie
de l'Institut français d¹archéologie orientale du Caire. Arabic text with
French editorial footnotes, pp 65-70


MANICHAEAN: (Greek) codex

(as per E. G. Turner) From the Chester Beatty collection, this Greek codex includes portions of Genesis; Gospels; Acts and Enoch.






MAPQUEST: to help you get there





MARESHA: (Aramaic) ostracon

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

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

See page 26 [Hebrew] showing a marriage agreement [Kettuva] from the Hellenistic period of the Edomite community of Maresha ~176 BCE.



MARI: (cuneiform) tablets

Several thousand tablets were found at Mari, on the River Euphrates, from 1933 onwards. These describe customs and give common names for both individuals and cities of the period in question. The term Habiru appears again in this archive. In OC terms, they date from the period of Zimri-Lin, around 1700 BCE. The Babylonian ruler Hammurabi sacked the city. Hammurabi's reign is redated to 1565-1522 BCE in the NC. Since he sacked Mari, the archive's date can be set in the region 1650-1500 BCE.



MARIETTE: (Author); papyrus

Auguste Mariette 1821-1881.


(as per ZAS, index# 0492) Seek “Notiz uber die Todtengesprache des Papyrus Mariette”, ZAS 6, 1868.


[B_161,IMG,8.5’s and OS]

CATNYP# *OBL+++(Mariette, A. E. Serapeum de Memphis),

“(Le) Serapeum de Memphis, decouvert et decrit par A. Mariette

Conservateur-Adjoint au Musee Imperial du Louvre

Membre de la Societe Imperiale des Antiquaires de France,


de l’Academie Royale des Sciences de Turin

Ouvrage dedie A S. A. I. Mgr Le Prince Napoleon

Et publie sous les auspices

De S. E. M. Achille Fould

Ministre d’Etat


Gide, Libraire-Editeur

5, Rue Bonaparte


This text is an contains extensive desription with French translations of the many fabulous items first uncovered at the Serapeum.


[B_255,8.5’s and OS2] CATNYP# *OBM+(Mariette, Mastaba de l’ancien empire),

Les mastaba


 l’ancien empire

 fragment du dernier ouvrage


A. Mariette

publiee d’apres le manuscrit de l’auteur


G. Maspero

Professeur au College de France, Directeur General des Musees Egypte



F. Vieweg, Libraire-Editeur

67, Rue de Richelieu, 67



Handwritten script, French text with detailed descriptions.

Discussions of Abbott papyrus.

Carefully prepared plans of tombs showing alignments (compass).

Carefully prepared glyph sketches.

See [B_149] p.12 error.

Error was not resolved by this [Marriette’s] text.



MARMARICA: (Greek) papyri

(as per E. G. Turner) Il papiro vaticano greco II, ed. M. Norsa and G. Vitelli, Citta del Vaticano, 1931.


P.Marm.: Il papiro vaticano greco 11

P.Marm. v.: (Greek; AD 190; Marmarica)

Math content is minor.



MARRIAGE: do it once, do it right

See KETTUBAH; jews from about 1000 ce


MARSA MATROUH: discoveries near



MASADA: (Hebrew ; Aramaic; Greek and Latin) Manuscripts; fragments

From (near) Herod’s mountain fortress



Texts discovered during the excavation of the fortress, including Hebrew and Aramaic ostraca and fragments of Latin papyri, several biblical texts, a Hebrew manuscript of Ben Sira, a copy of Songs of the Sabbath Sacrifice, a composition also known from Qumran, many fragments of Hebrew, Aramaic, Greek and Latin. Not all of this collection has been published.





MASPERO: (Author); papyrus

Sir Gaston Camille Charles Maspero 1846-1916.


[B_083,rvw] CATNYP# *OBH (Cordier, H. Bibliographie des oeuvres de Gaston Maspero), "Bibliographie des oeuvres de Gaston Maspero...", Paris, 1922.


(as per H.O. Lange) seek Maspero's Guide to the Cairo Museum 3rd edition, 1906.




(as per LEX) see P. Maspero=CG 67001-67539.



CATNYP# 3-MAF (Maspero, G. C. C. Ars-Una species mille)

My rare house copy is in German, titled:

“Geschichte der Kunst in Aegypten”

Stuttgart, 1913.



MATH: prior to 1601 [and after Guttenberg’s invention]

[B_253,8.5’s,IMG,RARE] CATNYP# *KAB (Smith, D. E. Rara Arithmetica)

“Rara Arithmetica; a catalogue of the arithmetics written before the year MDCI, with a description of those in the library of George Arthvr Plimpton, of New York, by David Eugene Smith…[D. E. Smith, 1860-1944]

Boston, London, Ginn and company, 1908. [2 Volumes].

This looks like fun. It is!

With images of the cover pages of rarer texts.

Special permission required. Access 6/2/01.

John Rathe is the resident expert [Curator?].

J. Rathe usually available 10 am – 6 pm.

See Galley division method.

See references to the Plimpton Library.

See references to the Manuscript of Boethius circa 1294.


Volume one, P. 56, Gelosia multiplication by Paciuolo; 1494.

Volume one, P. 56, Finger Symbolism by Paciuolo; 1494.

See the 1507 “Algorithmus”

See the 1551 Euclid; “Euclidis elementorum”

See the 1556 Boissiere.

See Boissiere’s “Rythmomachia”.

See 1559 “Libri vnvs et triginta” by Ramus.

See 1569 Mercado.

See Thomas Masterson’s 1592 text.

Reference to the Dogomari Manuscript.

See the work of Benedetto de Firenze [Florence].

Volume one, P. 82, Margarita Philosophica; plate B and A

Volume two is more of the math goodies from 1500-1601 with little useful content or analysis of the math but excellent clarification of the source’s locations.

This has been reprinted and is available for US$60.

Contact Oak Knoll Books (Delaware)

Phone: 302 328 7232



See Plimpton 322, cuneiform pythagorean triples. See GREEK.


See this link by Kim R. W. Zahrt:


See this fascinating compilation of number texts:

and home page supreme:


(as per L. Bailey) See:

“Histoire de fractions, fractions d’histoire.” In

Science Networks Historical Studies, volume 10.

Boston: Birkhauser Verlag, 1992 NO CATNYP.

See also [B_334,rvw]


[B_334,rvw,SIBL] CATNYP# *R-Science QA21 .B767 1989

Carl Benjamin Boyer [1906-?]

“A history of Mathematics / Carl B. Boyer ; revised by Uta C. Merzbach.”

NY, Wiley, c1989.


[B_335,rvw] CATNYP# JSE 91-2418

William Dunham, [1947-]

“Journey through genius : the great theorems of mathematics / William Dunham.” NY: Wiley, c1990.




David Eppstein: “Ten Algorithms for Egyptian Fractions.”

Mathematica in Education and Research, vol. 4, no. 2, (1995)

Note: There is almost nothing ancient or Egyptian about this work.

The results offered in no way can be used to generate the Rhind 2/n table.


[B_336,rvw,SIBL] CATNYP# OFA (Gillain, O. Science egyptienne)

“La science egyptienne; l’arithmetique au moyen empire.[AEME]

Avec une preface de H. Bosmans, S. J.”

Bruxelles, [Edition de la] Fondatation egyptologique reine Elisabeth, 1927.

Pages 245-250 and bibliography on file.

Numerous circular references and this:

1. Aben-Ezra, Sepher ha-mmispar, ecrit a Rodez en 1156.

2. Thureau-Dangin, Numeration et Metrologie sumeriennes.

In: Revue d’Assyriologie, XVIII, 1921, p. 123.



Hurd, Spencer P., “Egyptian Fractions: Ahmes to Fibonacci to Today.”

Mathematics Teacher [NO CATNYP], vol. 84, no. 7, (October 1991),: p. 561-568.


[B_337,rvw,LB,SIBL] CATNYP# OEC (Neugebauer, O. Exact Sciences in antiquity. 1951)

Otto Neugebauer, [1899-?]

“The exact sciences in antiquity.”

Copenhagen, E. Munksgaard; Princeton N.J., Princeton University Press, 1951.


See also:

[B_337b,rvw] Parker, Richard A., “Demotic Mathematical Papyri”

Providence, Brown University Press, 1972.


[B_338,rvw,LB] CATNYP# Sc 913.32-H

John Richard Harris, editor.

“The legacy of Egypt; edited by J. R. Harris. Second edition.”

Oxford, Clarendon Press, 1971.

See “The Calendars and Chronology.”

See also [B_338b,rvw]


[B_338b,rvw] CATNYP# Sc 913.32-H

See “Mathematics and Astronomy.” By G. J. Toomer.


[B_339,rvw] CATNYP# OAC (American Oriental Series. V. 68)

“Labor in the Ancient Near East / edited by Marvin A. Powell.”

New Haven Conn., OAS, 1987.

See also [B_342a,rvw,LB] also by Marvin Powell.


[B_342a,rvw,LB] CATNYP# *O-*OAL+ 95-5473

Civilizations of the Ancient Near East / Jack M. Sasson, editor in chief.”

Article: “Metrology and Mathematics in Ancient Mesopotamia.” By Marvin Powell.

In: Civilizations of the Ancient Near East, vol. 3. Edited by Jack M. Sasson.”

NY, Charles Scribner’s Sons, 1995.


See also:

[B_342b,rvw,LB] by Gay Robins.

“Mathematics, Astronomy, and Calendars in Pharonic Egypt.”

In: Civilizations of the Ancient Near East, vol. 3. Edited by Jack M. Sasson.”

NY, Charles Scribner’s Sons, 1995.


See also:

[B_342c,rvw,LB] by Francesca Rochberg.

“Astronomy and Calendars in Ancient Mesopotamia.”

In: Civilizations of the Ancient Near East, vol. 3. Edited by Jack M. Sasson.”

NY, Charles Scribner’s Sons, 1995.


[B_343,rvw,] CATNYP# JSE 99-1817

The Babylonian theory of the planets / N. M. Swerdlow.”

Princeton, N. J., c1998.

See also [B_343b,rvw,LB]


[B_343b,rvw,LB] NO CATNYP

Noel M. Swerdlow

“Ancient Astronomy and Celestial Divination.”

Cambridge: The MIT Press, 1999.


See [B_344] SCIENCE AWAKENING, B. L. Van der Waerden.


See also [unassigned]; NO CATNYP!:

“Vorgreichische Mathematik I: Vorgeschichte und Agypten. Mathematische Studienhefte fur den mathematischen Unterricht an Hoheren Schulen, book 1. Edited by H. Athen and G. Wolff.”

Hannover: Herman Schroedel Verlag, 1958.


[B_345,rvw] CATNYP# OAA 72-689 Bd. 20

“Karl Richard Lepsius (1810-1884) : Akten der Tagung seines 100. Todestages,

10.-12.7.1984 in Halle / herausgegeben von Elke Freier und Walter F. Reineke.”

Berlin, Akademie-Verlag, 1988.


See also unassigned:

“Karl Richard Lepsius (1810-1884) Begrunder der Agyptologie in Deutschland.” By Erika Endesfelder.


See also unassigned:

Lepsius, le disciple inspire.”

By Dietrich Wildung.


[B_352,8.5;IMG] CATNYP# OAA (Societe Asiatique. Journal asiatique)

“Journal Asiatique.”

Paris [1822-?].

See article(s) by Rodet in: [7TH SERIES,TOME 18, 1881]



Septieme serie



Imprime par autorisation de M. le Garde des Scraux



Article “Les Pretendus problemes d’algebre.”

Shows RMP workings.

Works of Aben-Ezra

Works of [Mohammed ibn Musa al-Khowarizmi] AKA Al-Kharizmi;

see Mokhraj.[LCD]. See text: “Al-Jabr wal-Muqabalah.”

See also:

ASAW=Abhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig (Berlin) [B_358a]


Note that Ahmes is called Ahmesu and Aahmesu.


[B_353,8.5,SIBL] CATNYP# OAC (Rey, A., Science dans l’antiquite)

“La science dans l’antiquite.” Paris, 1930-48. Abel Rey.

(Pages 201-304 and bibliography on file.)

P. 201-287: “La Mathematique Egytienne.”

P. 288-304: “l’Astronomie Egyptienne.”

Five volumes.


Discussions of:



(as per Peet, [B_226a]) See pp. 251 ff., pp. 281 ff.


Reference: Quibell, “Hieraconpolis I”, pl. XXXVI.


Reference: G. Millhaud, “Nouvelles Etudes sur la Pensee Scientifique, P. C8 in [?] J.-C. Heath’s: “A History of Greek Mathematics, I, 122.


Reference: Paul TANNERY, “Pour l’histoire de la science Hellene”, Paris (Alcan), 1887. [B_388,rvw]. See KESKINTO.


Reference: Paul TANNERY, “La Geometrie Grecque”, Chapters VI and VII. [B_389,rvw]. See KESKINTO.


Reference: “Memoires scientifiques”, ed. Par Mme. P. Tannery, Paris, 1912-1929. [B_390,rvw]. See KESKINTO.


Reference: “Le progressioni aritmetiche presso gli Egiziani” in:

Bolletino di Matematica, 1923.


Reference: “ad usum Delphini” – define?


Reference: Bailly, “Histoire de l’astronomie ancienne”, Paris, 1775.

(Note that Gillain [B_336] also refers to the below Bailly, 1787)

and, “Histoire [Traite?] de l’astronomie indienne et orientale”, Paris, 1787. and, “Lettres sur l’origine des sciences”, Paris,

[and or in?]: “Histoire de l’astronomie”, 1784, and, Recueil de pieces interessantes sur les sciences, Paris, 1810.


Reference: Biot (J.-B.), Articles Nombreaux dans le “Journal des Savants”, (Paris) et les Comptes Rendus de l’Academie des Inscriptions et de l’Academie des Sciences [B_356,rvw,KESKINTO], Paris, entre 1831 et 1845. Cf. les references particulieres dans le present ouvrage, a propos de l’astronomie egyptienne et de la science chinoise (Melanges scientifiques, 1858).


Reference: Biot (J.-B.), “Recherches sur plusiers points de l’astronomie egyptienne”, 1823.

Reference: Biot, “Recherches sur l’annee vagae des Egyptiens, in: Memoire relatifs a l’astronomie egyptienne, p. 53-54 (note).


Reference: Favaro (A.), Sulla interpretazione matematica del Papiro Rhind (Mem. Acad. Scienze, lett. Ed arti, Modene, vol. XIX, 1879, p. 89-143.)

(as per Gillain, [B_336]) See also p. 18 from above.

(as per Vogel, [B_296]) See also p. 89-143 of the above.


Reference: Schiaparelli; See SCHIAPARELLI; CUBIT.


Reference: Thureau-Dangin, Revue d’Assyrologie, t. XVIII, Paris, 1921.


Reference: Turaiev, Ancient Egypt, 1917, p. 100 [MMP]


Reference: Vetter, Bolletino di matematica, 1923 (sur les progressions)


Reference: Virolleaud (Ch.), l’astrologie chaldeene, 1908 et suiv. Vorderasiatische Bibliotek, Berlin.


Reference: Weidner, “Sur l’origine du theoreme de Pythagore”, (Orient Litt.-Zeitung, t, XIX, 1916, p. 261)


See also the works of PLATO; Eratostenes…


Hudson, M., How Interest Rates Were Set, 2500 BC - 1000 AD: Másh, tokos and f#+-#œ#+.#nus as Metaphors for Interest Accruals: JEShO [JESHO=[B_380]] 43 ('00), p. 132-61 (1 Tab.).



(MSJ sugg*LP delivered Xmas 2001,SIBL)


“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


Very limited overview of AE math but most other cultures are well discussed.


7.1. Boyer, Carl B. A History of Mathematics. New York: John Wiley, 1968, Chapter XV, “The Renaissance” (pp. 297–332), worth 1 paper.

7.2. Kline, Morris. Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press, 1972, chapter 12 (pp. 231–249), worth 1 paper.

7.3. Smith, David Eugene. History of Mathematics. Boston: Ginn & Co., 1923–25. 2 vols. Reprinted New York: Dover, 1958.

7.4. Wightman, W. P. D. Science and the Renaissance An Introduction to the Study of the Emergence of the Sciences in the Sixteenth Century. Edinburgh: Oliver and Boyd, 1962, Chapters VI (pp. 87–99) and VIII (pp. 129–147), worth 1 paper each.

7.5. Wightman, W. P. D. Science in a Renaissance Society. London: Hutchinson University Library, 1972, chapters 3 (pp. 42–56) and 10 (pp. 130–140), worth 1 paper each.

7.6. Van Egmond, Warren. Abbacus Arithmetic”. In I. Grattan-Guinness, ed. Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. Vol. I. London: Routledge, 1994, 200–209.

7.7. Reich, Karin. The ’Coss’ Tradition in algebra”. In I. Grattan-Guinness, ed. Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. Vol. I. London: Routledge, 1994, 192–199.

7.8 van der Waerden, B. L. A History of Algebra from al-Khwarizmi to Emmy Noether. Berlin: Springer-Verlag, 1985, pp. 32–69, worth 1 paper.

7.9. Kloyda, Mary T.K. Linear and Quadratic Equations: 1550-1660. Ann Arbor: Edwards Brothers, 1935.

7.10. Russo, François. “La constitution de l’algèbre au XVIe siècle: étude de la structure d’une évolution”. Revue d’histoire des sciences 12 (1959), 193–208.

7.11. Swetz, Frank. “Fifteenth and Sixteenth Century Arithmetic Texts: What Can We Learn from Them?” Science & Education 1 no. 4 (1992), 365–378.

7.12. Cajori, Florian. A History of Mathematical Notations. Vol I. Notations in Elementary Mathematics. Chicago: Open Court, 1928. Reprinted 1974.

7.13. Williams, Jack. “Mathematics and the Alloying of Coinage 1202-1700”. Annals of Science 52 (1995), 213–263.

7.14. Allen, Michael T. Nuptial Arithmetic: Marsilio Ficino’s Commentary on the Fatal Number in Book VIII of Plato’s Republic. Berkeley: University of C liforni Press, 1994.

7.15. Schneider, Ivo. “The Market Place and Games of Chance in the Fifteenth and Sixteenth Centuries”. In Cynthia Hay, ed. Mathematics from Manuscript to Print: 1300–1600. Oxford: Clarendon Press, 1988, 220–235.

7.16. Ineichen, Robert. Dante-Kommentare und die Vorgeschichte der Stochastik”. Historia Mathematica 15 (1988), 264–269.

7.17. Takacs, Lajos. “The Problem of Points”. The Mathematical Scientist 19 no. 2 (1994), 119–139.

7.18. L’Huillier, Hervé. “Practical Geometry in the Middle Ages and the Renaissance”. In I. Grattan-Guinness, ed. Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences.Vol. I. London: Routledge, 1994, 192–199.

7.19. Meskens, Ad. “Wine Gauging in Late 16th- and Early 17th-Century Antwerp”. Historia Mathematica 21 no. 2 (1994), 121–147.

7.20. Homann, Frederick A. “Christopher Clavius and the Renaissance of Euclidean geometry”. Archivum Historicum Societatis Iesu 52 (1983), 233–246.

7.21. Bond, John D. “The Development of Trigonometric Methods down to the Close of the XVth Century”. Isis 4 (1921), 295–323.

7.22. Thoren, Victor E. “Prosthaphaeresis Revisited”. Historia Mathematica 15 no. 1 (1988), 32–39.

7.23. Laird, W. R. “Archimedes among the Humanists”. Isis 82 (1991), no. 314, 629–638.

7.24. Edgerton, Samuel Y., Jr. The Renaissance Rediscovery of Linear Perspective. New York: Basic Books, 1975.

7.25. Edgerton, Samuel Y., Jr. The Heritage of Giotto’s Geometry: Art and Science on the Eve of the Scientific Revolution. Ithaca: Cornell University Press, 1991.

7.26. Field, J. V. The Invention of Infinity: Mathematics and Art in the Renaissance. Oxford: Oxford University Press, 1997.

7.27. Field, J. V. “Perspective and the Mathematicians: Alberti to Desargues”. In Cynthia Hay, ed. Mathematics from Manuscript to Print: 1300–1600. Oxford: Clarendon Press, 1988, 236–263.

7.28. Wittkower, Rudolf. Architectural Principles in the Age of Humanism. 3rd ed. London: Alec Tiranti, 1962. 4th ed. London: Academy Editions; New York: St. Martin’s Press, 1988.

7.29. Van Egmond, Warren. “The Contributions of the Italian Renaissance to European Mathematics.” In Symposia mathematica. Vol. XXVII. London/New York: Academic Press, 1986, 51–67.

7.30. Rose, Paul Lawrence. The Italian Renaissance of Mathematics: Studies on Humanists and Mathematicians from Petrarch to Galileo. Geneva: Droz, 1975.

7.31. Franci, Raffaella, and Laura Toti Rigatelli. “Towards History of Algebra from Leonardo of Pisa to Luca Pacioli”. Janus 72 (1985), 17–82.

7.32. Franci, Raffaella, and Laura Toti Rigatelli. “Fourteenth-century Italian Algebra”. In Cynthia Hay, ed. Mathematics from Manuscript to Print: 1300–1600. Oxford: Clarendon Press, 1988, 11–29.

7.33. Van Egmond, Warren. “The Algebra of Master Dardi of Pisa”. Historia Mathematica 10 no. 4 (1983), 399–421.

7.34. Swetz, Frank J. Capitalism and Arithmetic: The New Math of the 15th Century, Including the full text of the Treviso Arithmetic of 1478 Translated by David Eugene Smith. La Salle, IL: Open Court Publishing Co., 1987.

7.35. Biagioli, Mario. “The Social Status of Italian Mathematicians, 1450–1600”. History of Science 27 no. 75, part 1 (1989), 41–95.

7.36. Van Egmond, Warren. “How Algebra Came to France”. In Cynthia Hay, ed. Mathematics from Manuscript to Print: 1300–1600. Oxford: Clarendon Press, 1988, 127–144.

7.37 Sesiano, Jacques. “Une arithmétique médiévale en langue provençale”. Centaurus 27 no. 1 (1984), 26–75.

7.38. Margolin, Jean-Claude. “L’enseignement des mathématiques en France (1540-70): Charles de Bovelles, Fine, Peletier, Ramus”. In Peter Scharratt, ed. French Renaissance Studies, 1540-70 Humanism and the Encyclopedia. Edinburgh: University Press, 1976, 109–155.

7.39. Benoit, Paul. “Arithmétiques commerciales et comptabilités dans la France médievale”. In Paul Benoit, Karine Cheml , and Jim Ritter, eds. Histoire de fractions, fractions d’histoire. Basel: Birkhauser, 1992, 307–323.

7.40. Cifoletti, Giovanna C. “La question de l’algèbre: M thématiques et rhétorique des hommes de droit dans la France du 16e siècle”. Annales HSS 6 (1995), 1385–1416.

7.41. Struik, Dirk J. The Land of Stevin and Huygens: A Sketch of Science and Technology in the Dutch Republic during he Golden Century. Dordrecht: D. Reidel, 1981. Pp. 32-60 (worth 1 paper).

7.42. Smeur, A. J. E. M. The Sixteenth Century Arithmetics Printed in the Netherlands. The Hague, 1960.

7.43. Meskens, Ad. “Mathematics Education in Late Sixteenth-century Antwerp”. Annals of Science 53 (1996), no. 2, 137–155.

7.44. Taylor, Eva G. R. The Mathematical Practitioners of Tudor and Stuart England, 1485–1714. Cambridge: The University Press, 1954.

7.45. Richeson, A. W. “The First Arithmetic Printed in English”. Isis 37 (1947), 47–56.

7.46. Molland, A. George. “Cornelius Agrippa’s Mathematical Magic”. In Cynthia Hay, ed. Mathematics from Manuscript to Print: 1300–1600. Oxford: Clarendon Press, 1988, 209–219.

7.47. Jayawardene, S. A. “The Influence of Practical Arithmetics on the Algebra of Rafael Bombelli”. Isis 64 (1973), 510–523.

7.48. Cardano, Girolamo. The Great Art, or the Rules of Algebra. English translation by T. Richard Witmer. Cambridge, Mass.: MIT Press, 1968.

7.49. Naux, Charles. “Le père Christophore Clavius (1537–1612): sa vie et son oeuvre”. Revue des Questions Scientifiques 154 (1983), 55–67, 181–193, 325–347.

7.50. Knobloch, Eberhard. Sur la vie et l’oeuvre de Christophore Clavius (1538–1612)”. Revue d’Histoire des Sciences 41 no. 3-4 (1988), 331–356.

7.51. Knobloch, Eberhard. “L’oeuvre de Clavius et ses sources scientifiques”. In Luce Girard, ed. Les Jésuites à la Renaissance: Système éducatif et production du savoir. Paris: Presses Universitaires de France, 1995, 263–283.

7.52. Swerdlow, N. M., and O. Neugebauer. Mathematical Astronomy in Copernicus’s De revolutionibus. New York: Springer-Verlag, 1984.

7.53. Panofsky, Erwin. “Dürer as Mathematician”. In J. R. Newman, ed. The World of Mathematics. Vol. I. New York: Simon nd Schuster, 1956, 603–621.

7.54. Peiffer, Jeanne. “Le style mathématique de Dürer et sa conception de la géométrie”. In Joseph W. Dauben, Menso Folkerts, Eberhard Knobloch, and Hans Wussing, eds. History of Mathematics: States of the Art Flores quadrivii—S udies in Honor of Christoph J Scriba. San Diego: Academic Press, 1996, 49–61.

7.55. Walton, Karen Doyle. “Albrecht Dürer’s Renaissance Connections between Mathematics and Art”. The Mathematics Teacher 87 (1994), 278–282.

7.56. Leonardo da Pisa. The Book of Squares. Boston: Academic Press, 1987.

7.57. Cassinet, Jean. “The First Arithmetic Book of Francisco Maurolico, Written in 1557 and Printed in 1575: A Step Towards Theory of Numbers”. In Cynthia Hay, ed. Mathematics from Manuscript to Print:  1300–1600. Oxford: Clarendon Press, 1988, 162–179.

7.58. Mackinnon, Nick. “The Portrait of Fra Luca Pacioli”. The Mathematical Gazette 77 (479) (1993), 130–219.

7.59. Taylor, R. E. No Royal Road: Luca Pacioli and His Times. Chapel Hill: University of North Carolin Press, 1942.

2060. Schultz, Phillip. “Tartaglia, Archimedes and cubic equations”. The Australian Mathematical Society Gazette 11 no. 4 (1984), 81–84.


All of the above and more as per this link:


See also:

(AEB 87.1008) Bibe, Celia, Nouveaux recherches sur la mathematique pharaonique, partie II..., GM 100 (1987), 19-22.


[B_389,8.5,NO KESKINTO,SIBL] CATNYP# OKA (Tannery, P. Geometrie Grecque)

“La geometrie grecque, comment son histoire nous est parvenue et ce que nous en savons. Essai critique par Paul Tannery. 1. ptie. Historie generale de la geometrie elementaire.” Paris, 1887.

Good stuff: Plutarch; Euclid; Heron/Hero; Works by George Pachymere

PAPPUS; Pythagore/Pitagorus; Some Pyramidiocy

Plato; Meton; Zenon; Proclus; Aristophane; Aristote/Aristotle


See UHN; [B_359]

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; Galley division AKA “A la Francaise”


Aben-Ezra, Sepher ha-mmispar, ecrit a Rodez en 1156.

[B_530,rvw,microform in German]

CATNYP# *ZP-1103 no.5

Ibn Ezra AKA Abraham ben Meir, lived~1092-1167

“Sefer ha-mispar [Book of Number] /cmeturgam u-meforash bi-leshon Ashkenaz me’ et Mosheh Zilberberg [Moses Silberberg].”

September 2002: Same book in print is available at JTS!


(As per EEF; 041803)

From HARRASSOWITZ publishers

Annette Imhausen, "Aegyptische Algorithmen. Eine Untersuchung zu

den  mittelaegyptischen mathematischen  Aufgabentexten"


Abhandlungen 65)   2003. XI, 386 Seiten, br,  ISBN 3-447-04644-9

EUR 58,- [D] / sFr 99,-, appr. 63,- US $

New edition of all the hieratic mathematical 'problem/procedure texts'.


(as per EEF; 071503; L. Bailey; and EISENBRAUNS)

Subject: [Booknews] New Book: Astronomy & Mathematics in the ANE


To order the following title visit the Eisenbrauns web site:

"Under One Sky: Astronomy and Mathematics in the Ancient Near East."

Alter Orient und Altes Testament (AOAT) 297. Edited by John M. Steele and

Annette Imhausen. Ugarit-Verlag, 2002, vii + 496 pages, Cloth, English.

ISBN: 3934628265. $118.00  

"Under One Sky" presents 26 revised and expanded contributions to the

conference that took place at the British Museum June 2001. The

authors examine the many-faceted interdependencies of Egyptian and

Mesopotamian astronomy and mathematics, ranging from Sumerian Ur III mathematical

problems (J. Hoyrup), astronomical and mythological references in

Egyptian texts (R. Krauss), and the Babylonian Diviner's Manual (C. Williams)

to gnosis and astrology in the 4th book of the Pistis Sophia (A. von

Lieven) and Babylonian lunar theory in Roman Egypt (A. Jones).

Eisenbrauns is the exclusive North American distributor of "Under One

Sky" and the entire AOAT series that features monographs and collected

volumes on the ancient Near East and biblical studies. To view the entire list

of available AOAT volumes, visit our web site and search by series




On Columns H and J in Babylonian Lunar Theory of System B - Asger



Predictions of Lunar Phenomena in Babylonian Astronomy - Lis



Treatments of Annual Phenomena in Cuneiform Sources - John P. Britton


History of the heleq - Leo Depuydt


Measuring Egyptian Statues - Friedhelm Hoffmann


How to Educate a Kapo or Reflections on the Absence of a Culture of

Mathematical Problems in Ur III - Jens Hoyrup


The Algorithmic Structure of the Egyptian Mathematical Problem Texts


Annette Imhausen


Babylonian Lunar Theory in Roman Egypt. Two New Texts - Alexander



Early Babylonian Observations of Saturn: Astronomical Considerations


Teije-de Jong


The Eye of Horus and the Planet Venus: Astronomical and Mythological

References - Rolf Krauss


The Historicity Question in Mesopotamian Divination - Daryn Lehoux


Gnosis and Astrology. 'Book IV' of the Pistis Sophia - Alexandra von



Ration Computations at Fara: Multiplication or Repeated Addition -

Duncan J. Melville


Square Tablets in the Yale Babylonian Collection - Karen R.



A Goddess Rising 10,000 Cubits into the Air . . . Or Only One Cubit,

One Finger? - Joachim F. Quack


Aristarchos and the 'Babylonian' Month - Dennis Rawlins


Closing the Eye of Horus - Jim Ritter


More than Metrology: Mathematics Education in an Old Babylonian

Scribal School - Eleanor Robson


A Study of Babylonian Normal-Star Almanacs and Observational Texts -

Norbert A. Roughton


Egyptian Festival Dating and the Moon - Anthony Spalinger


A Simple Function for the Length of the Saros in Babylonian Astronomy

John M. Steele


The Earliest Datable Observation of the Aurora Borealis - F. Richard

Stephenson and David M. Willis


The 'Transit Star Clock' from the Book of Nut - Sarah Symons


Enuma Anu Enlil Tablets 1-13 - Lorenzo Verderame


The Role of Astronomical Techniques in Ancient Egyptian Chronology:

The Use of Lunar Month Lengths in Absolute Dating - Ronald A. Wells


Signs from the Sky, Signs from the Earth: The Diviner's Manual

Revisited - Clemency Williams


MATH: after 1601

[B_316,HOUSE] CATNYP# JFD 00-7977

“Uncle Petros and Goldbach’s Conjecture / Apostolos Doxiadis.”

London, 2000.

A charming work. A gift from M. St. John.

See also “Tuesdays with Morrie”. UNASSIGNED in PHILOSOPHY.


[B_317,HOUSE] CATNYP# JSD 00-140

“Philosophiae naturalis principia. English”

ALT “Sir Isaac Newton’s Mathematical principles of natural philosophy and his system of the world / translated into English by Andrew Motte in 1729 ; the translations revised, and supplied with an historical and explanatory appendix, by Florian Cajori.”

Berkeley : University of California Press, 1962, c. 1934.



[B_318,HOUSE] CATNYP# OFO (Ore, O. Number theory and its history)

“Number theory and its history.”

NY, 1948

Great find and the Chinese remainder theorem.


[B_319,HOUSE] CATNYP# JSD 92-196

“The crest of the peacock : non-European roots of mathematics / George Gheverghese Joseph.”

London, 1999

With a contribution from Milo Gardner.




10.1. Bos, H. J. M. Lectures in the History of Mathematics. Providence, R.I., London: American Mathematical Society/ London Mathematical Society, 1993.

10.2. Feingold, Mordechai. The Mathematician’s Apprenticeship: Science, Universities and Society in England, 1560– 1640. Cambridge: Cambridge University Press, 1984.

10.3. Whiteside, D. T. “Patterns of Mathematical Thought in the Later Seventeenth Century”. Archive for History of Exact Sciences 2 (1960–1962), 179–388.

10.4. Pycior, Helena M. Symbols, Impossible Numbers, and Geometric Entanglements. British Algebra throug the Commentaries on Newton’s Universal Arithmetick. Cambridge: University Press, 1973.

10.5. Baron, Margaret E. The Origins of the Infinitesimal Calculus. Oxford: Pergamon, 1969. Reprinted New York: Dover, 1987.

10.6. Bos, H. J. M. “Differentials, Higher-Order Differentials and the Derivative in the Leibnizian Calculus”. Archive for History of Exact Sciences 14 (1974–1975), 1–90.

10.7. Boyer, Carl B. The History of the Calculus and Its Conceptual Development. New York: Dover, 1959; first published as The Concepts of the Calculus, a Critical and Historical Discussion of the Derivative and the Integral. New York: Columbia University Press, 1939. Reprinted New York: Hafner, 1949.

10.8. Edwards, C. H., Jr. The Historical Development of the Calculus. New York, Heidelberg, Berlin: Springer Verlag, 1979.

10.9. Grattan-Guinness, Ivor, ed. From the Calculus to Set Theory, 1630– 1910. An Introductory History. London: Duckworth, 1980.

10.10. Boyer, Carl B. History of Analytic Geometry. NewYork: Scripta Mathematica, 1956.

10.11. Dickson, L. E. History of the Theory of Numbers. Washington, D.C.: The Carnegie Institution, 1919–1923. Reprinted New York: Stechert, 1934, and New York: Chelsea, 1952, 1971.

10.12. Ore, Øystein. Number Theory and Its History. New York, Toronto, London: McGraw-Hill, 1948.

10.13. Hacking, Ian. The Emergence of Probability. Cambridge: Cambridge University Press, 1975.

10.14. Maistrov, L. E. Probability Theory. A Historical Sketch.Translated by S. Kotz from Teoriia Veroiatnostei. Istoricheskii Ocherk, Moscow, 1967. New York and London: Academic Press, 1974.

10.15. Pearson, Karl. The History of Statistics in the 17th and 18th Centuries. Edited by E. S. Pearson. London: Charles Griffin, 1978.

10.16. Cohen, H. Floris. Quantifying Music. The Science of Music at the First Stage of the Scientific Revolution, 1580– 1650. Dordrecht, Boston, Lancaster: D. Reidel Publ. Co., 1984.

10.17. Goldstine, Herman H. A History of Numerical Analysis from the 16th throug the 19th Century. New York, Heidelberg, Berlin: Springer-Verlag, 1977.

10.18. Feingold, Mordechai, ed. Before Newton. The Life and Times of Isaac Barrow. Cambridge, New York: Cambridge Uni ersity Press, 1992.

10.19. Andersen, Kirsti. “Cavalieri’s Methods of Indivisibles”. Archive for History of Exact Sciences. 31 (1985), 291–367.

10.20. Grosholz, Emily. Cartesian Method and the Problem of Reduction. Oxford: Clarendon Press, 1991.

10.21. Scott, J. F. The Scientific Work of René Descartes (1596– 1650). London: Taylor & Francis, [1952]. Reprinted 1976.

10.22. Vuillemin, J. Mathématiques et métaphysique chez Descartes. Paris: Presses Universitaires de France, 1960.

10.23. Mahoney, Michael Sean. The Mathematical Career of Pierre de Fermat (1601 – 1665). Princeton, N.J.: Princeton Uni ersity Press, 1973. 2nd edition, 1994.

10.24. Aiton, E. J. Leibniz. A biography. Bristol/Boston: Adam Hilger, IOP Publishing, 1985.

10.25. Bertoloni Meli, Domenico. Equivalence and Priority: Newton versus Leibniz. Including Leibniz’s unpublished manuscripts on the Principia. Oxford: Clarendon Press, 1993; Oxford: Oxford University Press, 1997.

10.26. Hall, A. Rupert. Philosophers at War. The Quarrel between Newton and Leibniz. Cambridge: Cambridge University Press, 1980.

10.27. Hofmann, Joseph E. Leibniz in Paris, 1672– 1676, His Growth to Mathematical Maturity. Cambridge: Cambridge University Press, 1974.

10.28. Gjertsen, Derek. The Newton Handbook. London, New York: Routledge & Kegan Paul, 1986.

10.29. Hall, A. Rupert. Isaac Newton. Adventurer in Thought. Oxford: Blackwell Publishers, 1992.

10.30. Harman, P. M., and Alan E. Shapiro, eds. The Investigation of Difficult Things: Essays on Newton and the istory of the exact sciences in honour of D. T. Whiteside. Cambridge: Cambridge University Press, 1992.

10.31. Westfall, Richard S. Never at Rest. A Biography of Isaac Newton. Cambridge: Cambridge University Press, 1980.

10.32. Westfall, Richard S. The Life of Isaac Newton. Cambridge: Cambridge University Press, 1993.

10.33. Whiteside, D. T. “Isaac Newton: Birth of a Mathematician”. Notes and Records of the Royal Society of London (1964), 53–62.

10.34. Whiteside, D. T. “Newton’s Marvellous Year: 1666 and All That”. Notes and Records of the Royal Society of London (1966), 32–41.

10.35. Dariulat, Jacques. L’arithmétique de la Grace: Pascal et les carrés magiques. Paris: Les Belles Lettres, 1994.

10.36. Edwards, A. W. F. Pascal’s arithmetical triangle. London: Griffin, and New York: Oxford University Press, 1987.

10.37. Taton, René, ed. L’oeuvre scientifique de Pascal. Paris: Presses Universitaires, 1964.


The above and more via this link:



MATH: after 1701

11.1. Cajori, Florian. “Frederick the Great on Mathematics and Mathematicians”. American Mathematical Monthly 34 (1927), 122–130.

11.2. Gillispie, Charles Coulston. The Edge of Objectivity: AnEssay in the history of Scientific Ideas. Princeton: Princeton Universit Press, 1960. Reprinted Princeton, New Jersey: Princeton University Press, 1990.

11.3. Goldstine, Herman H. A history of Numerical Analysis from the 16th through the 19th Century. (Studies in the History of Mathematics and Physical Sciences, Vol. 2.) New York, Heidelberg, Berlin: Springer-Verlag, 1977, especiall pp. 119–260.

11.4. Goldstine, Herman H. A history of the Calculus of Variations from the 17th through the 19th Century. (Studies in the Histor of Mathematics and Physical Sciences, Vol. 5.) New York, Heidelberg, Berlin: Springer, 1980, especiall pp. 50–150.

11.5. Greenberg, John. The Problem of the Earth’s Shape from Newton to Clairaut. Cambridge, New York: Cambridge Universit Press, 1995.

11.6. Hofmann, Joseph E. Classical Mathematics. A Concise history of the Classical Era in Mathematics. Translated by H. O. Midonick. New York: Philosophical Library, 1959, esp. pp. 115–154.

11.7. Kline, Morris. Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press, 1972. Reprinted New York: Oxford University Press, 1990.


The above and more via this link:



MATH: after 1801

12.1. Bourbaki, Nicolas. Eléments d’histoire des mathématiques. Paris: Hermann, 1960; revised 2nd ed., 1969 ; new ed., rev. and augmented, 1974; nouv. tirage. Paris: Masson, 1984. Translated as Elements of the History of Mathematics, Berlin; New York: Springer-Verlag, 1994.

12.2. Kline, Morris. Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press, 1972. New York: Oxford University Press, 1990.

12.3. Ore, Øystein. Niels Henrik Abel. Minneapolis: University of Minnesota Press, 1957. Reprinted New York: Chelsea Pub. Co., 1974.

12.4. Rigatelli, Laura Toti. Evariste Galois, 1811–1832. Basel: Birkhauser, 1996.

12.5. Taton, René. “Evariste Galois : de l’histoire aux légende . Un parcour en histoire des mathématiques: travaux et recherche ”, Sci. Tech. Perspect. (Univ. Nantes, Nantes) 26 (1993), 155–172.


The above and more via this link:


See also Pillow Problems by Lewis Carroll/ AKA C. L. Dodgson


[B_410,SIBL] CATNYP# OER (Dodgson, C. L. Curiosa mathematica)

“Curiosa mathematica: Pt. 2. Pillow Problems.”

London, 1895

Not easy problems!


See also:


“The Lewis Carroll picture book : a selection from the unpublished writings and drawings of Lewis Carroll, together with reprints from scarce and unacknowledged work / edited by Stuart Dodgson Collingwood.”

London, 1899.


[B_579;HOUSE reprint] CATNYP# OEZ (Abbott, E. A. Flatland. 1885)
“Flatland: A romance of many dimensions” Boston, 1885
Under the pseudonym: A. Square by [Clergyman] Edwin Abbott Abbott.

An introduction to a grander perspective of ourselves.



MATH: after 1901

13.1. Albers, Donald J., and G. L. Alexanderson, eds. Mathematical People. Boston: Birkhauser, 1985.

13.2. Albers, Donald J., Gerald I. Alexanderson, and Reid, Constance, eds. More Mathematical People. Boston: Harcout Brace Jovanovic , 1990.

13.3. Birkhoff, Garrett, ed. “Proceedings of the American Academy Works on the evolution of Modern Mathematics...” Historia Mathematica 2 (1975), 425–615.

13.4. Same as 12.1.

13.5. Casacuberta, C., and M. Castellet. Mathematical Research Today and Tomorrow: Viewpoints of Seven Fields Medalists. (Lecture Notes in Mathematics, No. 1525.) Berlin: Springer-Verlag, 1992.

13.6. Dieudonné, Jean. “Present Trends in Pure Mathematics”. Advances in Mathematics 27 (1978), 235–255.

13.7. Same as 12.2. Chapters 43–51.

13.8. May, Kenneth O. “Growth and Quality of the Mathematical Literature”. Isis 59 (1968), 363–371.

13.9. Monastyrsky, Michael. Modern Mathematics in the Light of the Fields Medal. Wellesley, MA: AKPeters Ltd., 1997.

13.10. Piers, Jean-Paul, ed. The development of Mathematics, 1900–1950. Basel: Birkhauser, 1994.

13.11. Tropp, Henry S. “The Origins and History of the Fields Medals”. Historia Mathematica 3 (2) (1976), 167–181.

13.12. Beaulieu, Liliane. “A Parisian Café and Ten Proto-Bourbaki Meetings (1934–1935).” The Mathematical Intelligencer 15 (1) (1991), 27–35.

13.13. Berndt, Bruce C. “Srinivasa Ramanujan”. American Scholar 58 (1989), 234–244.

13.14. Chandrasekharan, K. Hermann Weyl. 1885–1985. NewYork: Springer-Verlag, 1986.

13.15. Cooper, Necia Grant. From Cardinals to Chaos: Reflections on the Life and Legacy of Stanislaw Ulam. Cambridge, New York: Cambridge University Press, 1987.

13.16. Guedj, Denis “Nicolas Bourbaki, Collective Mathematician: An Interview with Claude Chevalley”. Mathematical Intelligencer 7 (2) (1985), 18–22.

13.17. Halmos, Paul R. I Want to be a Mathematician: An Automathography. New York: Springer-Verlag, 1985.

13.18. Hardy, G. H. A Mathematician’s Apology. Cambridge: Cambridge University Press, 1967.

13.19. Kanigel, Robert. The Man Who Knew Infinity: A Life of the Genius Ramanujan. New York: Scribner’s; Toronto: Collier Macmillan, 1991.

13.20. Kennedy, Hubert C. Peano: Life and Works of Giuseppe Peano. Dordrecht: Reidel, 1980.

13.21. Reid, Constance. Hilbert. New York: Springer, 1970.

13.22. Reid, Constance. Courant in Goettingen and New York: The Story of an Improbable Mathematician. New York: Springer, 1976.

13.23. Wang, Hao. Reflections on Kurt Goedel. Cambridge, MA: MIT Press, 1987.

13.24. Weil, André The Apprenticeship of a Mathematician. Basel: Birkhauser, 1992.

13.25. Biggs, Norman L., E. Keith Lloyd, and Robin J. Wilson, eds. Graph Theory 1736–1936. Oxford: Clarendon, 1976.

13.26. Harary, Frank. “On the History of the Theory of Graphs”. New Directions in the Theory of Graphs. Edited by F. Harary. New York: Academic Press, 1973, 1–17.

13.27. Kadvany, John. “Reflections on the Legacy of Kurt Goedel: Mathematics, Skepticism, Post Modernism”. Philosophical Forum 20 (1989), 161–181.

13.28. Lesort, Marc. “How Fractals Were Discovered”. Mathematics Education 3 (4) (1987), 11–17.

13.29. Weintraub, E. Roy, ed. Toward a History of Game Theory. Durham, NC: Duke University Press, 1992.

13.30. Dieudonné, Jean. “The Work of Nicolas Bourbaki”. American Mathematical Monthly 77 (1970), 134–145.

13.31. Rowe, David. “Klein, Hilbert, and the Goettingen Mathematical Tradition”. Osiris (2nd series) 5 (1989), 186–213.


The above and more via this link:



MATRITENSIS: (Greek) papyri

P.Matr.: Dieci Papyri Matritenses

P.Matr. 1. Official report: (Greek; AD 119; from Oxyrhynchus)

Accounts; math; fractions.



MAYA: extinct mesoamerican people


CATNYP# HBC (Locke, L. L. Ancient quipu)

“The ancient quipu or Peruvian knot record, by Leland L. Locke.”

NY, 1923


MAYER: (Author, Hieratic; AE); papyri

Joseph Mayer 1803-1886.



CATNYP# *OBH+++(Peet, T.E. Mayer papyri A & B) "Papyri Mayer", v.2, 1920.

The discourse of a trial of thieves.

The oversized images at NYPL may be photographed, not copied.

Full Title:

“The Mayer papyri A & B; nos. M. 11162 and M. 11186 of the Free public museums, Liverpool. Pub. by authority of the Libraries, museums and arts committee of the Corporation of Liverpool, by T. Eric Peet.”

See page 8, line 16, note hieratic #2000+; extremely cursive

See name list of 188 persons!


[B_041a,041b,PIX r05.1] CATNYP# *OBH (Peet, T. E. Great Tomb Robberies of the 20th Egyptian Dynasty),Oxford 1930.




(as per S. Katary, [B_100])

Mayer A = No. M. 11162

Mayer B = No. M. 11186



MAYERIANUS: codex (historical forgeries)

[B_162,rvw] CATNYP# *YN+(Sim onid es [Simonides], K. Fac-similes of certain portions of the Gospel of St. Matthew), “Fac-similes of certain portions of the Gospel of St. Matthew, and of the Epistles of Ss. James & Jude, written on papyrus in the first century, and preserved in the Egyptian museum of Joseph Mayer…”

London, 1861.



MCT: publication

MCT=”Mathematical Cuneiform Texts” by Otto Neugebauer.

[B_259,8.5,IMG;notes filed with]

CATNYP# *OAC (American Oriental series. V. 29)

”Mathematical Cuneiform Texts edited by O. Neugebauer. And A. Sachs; with a chapter by A. Goetze”

New Haven, Conn., 1945

Note the special Babylonian/Akkadian signs for:






See image/evidence of the early use of the square root of two.

Item# YBC 7289 obverse. 1.414125


See Plimpton 322.

See wages for a laborer in everyday use.

See Seked/ squared secants!           


[B_005,IGNR,NO IMG] CATNYP# *OCQ 95-5298

”Cuneiform Mathematical Texts as a reflection of everyday life in Mesopotamia / by Karen Rhea Nemet-Nejat.”

New Haven, Conn., AOS, 1993

No useful images. No copies made. Discussions of Akkadian.


[B_016,IGNR,NO IMG] CATNYP# *OCO+(Virolleaud, C. Premier Supplement a la liste des signes cuneiformes de Brunnow)

” Premier Supplement a la liste des signes cuneiformes de Brunnow / par Ch. Virolleaud.” Paris, 1903.

No useful images. No copies made. Discussions of Akkadian.

References to George Reisner.


See Math: prior to 1601.


[B_373,rvw,SIBL] CATNYP# *VBA p.v. 1502 [and 1509]

“Nouvelles decouvertes sur les mathematiques babyloniennes; conference faite au Palais de la decouverte le 1er decembre 1951.”

By Evert M. Bruins., Alencon, 1952.



The 36 times table:


See image grid

Note the PLIMPTON 322 tablet shows squared secants and NOT cotangents.


MDAIK: publication

MDAIK=[B_269]=Mitteilungen des Deutschen Archaeologischen Instituts, Abteilung Kairo


[B_269;rvw more]

CATNYP# *OBH+(Deutsches Archaologisches Institut. Abt. Kairo. Mitteilungen)

NYPL has: 14(1956)-56(2000)


Band 55 (1999) has NARMER glyph; Ostracon Cairo SR 12202

(1999) has Tafel 54; P. VINDOB D6500

(1999) has Tafel 55; P. VINDOB D6502; recto and verso

(1999) has Tafel 59; Ramsesnacht-Ostrakon, recto and verso


(1997) has Tafel 3; Turinschriften des SERAPEUMS von MEMPHIS.

(1997) has Tafel 37; Demotic graffiti at ELEPHANTINE.


See [B_269] copies from M. St. John 11/21/01 of:

(1998) “Umm el-qaab I / Das pradynastische Konigsgrab U-j und seine fruhen Schriftzeugnisse.”

“von Gunter Dreyer Mit Beitragen von Ulrich Hartung und Frauke Pumpenmeier

und einem Anhang von Friedel Feindt und Margaret Fischer.”




MED.: (Greek) papyri

(as per E. G. Turner) See P. Mil.




MEDICINE: in ancient times

In German MEDIZIN.


Extant Medical Papyri

NAME/years BCE            LOCATION            CONDITION            CONTENT

KAHUN/1900                London              Fragment            Women’s Diseases

EDWIN-SMITH/1600            NY                    Unfinished            Surgery (48 cases)

EBERS/1550                Leipzig              Complete            General Medicine

HEARST/1550              Berkeley            Unfinished            Potions

ERMAN/1550                Berlin                small                Charms for young patients

LONDON/1350              London              Fragment            Recipe book

BERLIN/1350                Berlin                small                Recipe book

CHESTER B./1200            London              Unfinished            Oral diseases



Pahor, A L (1992b), 'Ear, Nose and Throat in Ancient Egypt' Journal of Laryngology and Otology, 106: 677-687, 773-779, 863-873.


See [B_390; KESKINTO; v4]

(as per F. Tonic; EEF; 011603) * An article co-written by neurosurgeon Gonzalo Sanchez, MD and Egyptologist Tamara L. Siuda, MA entitled "Ebers Papyrus Case #873:

A Probable Case of Neurofibromatosis I" appears in the December 2002 issue (Volume 55 No. 12) of the South Dakota Journal of Medicine (ISSN 0038-3317).  This paper was originally presented at the 2000 Annual Meeting of the American Research Center in Egypt in Berkeley, CA.


See [B_580,HOUSE] “Ancient Egyptian Medicine.”
By John F. Nunn; 1996; University of Oklahoma Press.
Excellent references throughout and bibliography.


Filed under [B_580] see this article:
“Minoan Deities in an Egyptian Medical Text.”
By Peter W. Haider, 2004.
References and Notes:
See W. Wreszinski, Der Londoner Medezinische Papyrus (B.M. 10059) und der Papyrus Hearst (1912)


Re. B.M. 10059:
See Chapter 13, incantations 27-30 in Hieratic/Phonetic/Semitic forms.
See Chapter 14, incantation 31 in Hieratic/Phonetic/Nubian? forms.
See Chapters 15-16, incantations 32-33 in Hieratic/Phonetic/Minoan forms.
Razaja/Razija=Lazaja/Lazija [Minoan Deity]
Ameja/Amija [Minoan Deity]


See [New Kingdom] Papyrus Harris no. XII:
Magical sentences in Minoan forms.


Pursue: T.E. Peet, “The Egyptian Writing Board, B.M. 5647,” in Essay in Aegaen Archaeology presented to Sir A. [Arthur] Evans (1927). Pages 90-101.


Pursue: J. Chadwick and J.T. Killen and J.-P. Olivier, The Knossos Tablets (1971).


Pursue: E.L. Bennett and J.-P. Olivier, The Pylos Tablets Transcribed, Part I (Inc. Graec. 51, 1973).


(as per EEF; K. Newkirk; 102005)
Kahun Gynecological Papyrus is online from Etana Books, in two
volumes, text & plates, at the following URLS :


(as per EEF; J. Kyffin; 101905)
<snip> an online translation and discussion of a medical (gynec.?) papyrus on that site, by Stephen Quirke.
Note of moderator:

MEDINET-HABU: ostraca and pylon and inscriptions

[B_060,ALL,OS tafel] CATNYP# *OBZ+++(Duemichen,J. Kaledarischen Opferfest-Listen im Tempel von Medinet-Hahn), "Die Kalendarischen Opferfest-Listen im Tempel von Medinet-Habu: nach dem am vordersten Pylon des Tempels aufgefunden Bruchstucken desunter Ramses II. abgefassten Originals und der unter Ramses III. an der sudlichen Aussenwand seines Memnoniums eingemeisselten Copie/ zusammengestellt und mit Uebersetzung und Erlaeuterungen hrsg. von Johannes Dumlichen.". Liepzig, 1881. AKA Medinet-abu.

Tafel III, VIII = math!

*Tafel IX shows 1, 2, and 5 times 365.

Calendrical math.

Johannes Dumlichen [1833-1894]


Copies ordered 9/17/02 and got a job offer while working!

Copies retrieved on 9/18/02.

[B_084,rvw] CATNYP# *OAC p.v.267, "Medinet-Habu demotic ostracon Richard Anthony Parker...", Chicago 1940.


(as per T.E. Peet, [B_041b]) see ABBOTT and see work by LEPSIUS on inscribed rock at Medinat Habu.


[W_045,rvw] WATSON# 533.5 St3. "Coptic ostraca from Medinet Habu / by Elizabeth Stefanski and Miriam Lichtheim." Chicago, 1952.


See Lichtheim.


[W_046,rvw] WATSON# 533.5 L61. "Demotic ostraca from Medinet Habu", Chicago , 1957.


See this link!


Edgerton, W. F. and Wilson, J. A. The Historical Records of Ramses III: The Texts in Medinet Habu Volumes I and II. Studies in Ancient Oriental Civilization [SOAC] 12. Chicago: University of Chicago Press, 1936.



MEDINET-MADI: (Greek) ostraca

O. Medin. Madi.: (Greek; ~200 AD)



MEGIDDO: ancient (Israeli) city of

The root of the word Armageddon?


(as per PM) AKA Tell el-Mutsellim.

See Megiddo Ivories; AJA 42 (1938), p. 334-5.


Three names for one town:

Armageddon is the mythical place of the Book of Revelations; Megiddo is mentioned in the Old Testament. Itis also the region where Thutmosis III won a decisive battle.

[new] info:


(as per EEF; A. Dailey; 093003)
According to Ahituv, Canaanite Toponyms in Ancient Egyptian
Documents (Leiden 1984), MEGIDDO is for the first time mentioned
(as MkT, Makida) in Egyptian texts during the reign of Tuthmosis
III. Is this still valid, or have since then older references been


(as per EEF; 102303)
…And MEGIDDO Stratum VI is the key.
Until recently, most scholars dated Stratum VI to the period just before the time of David, making him a candidate for its destruction; a later stratum would then represent the town of David and Solomon. However, in a series of articles,1 as well as in a recent interview in this magazine,* the head of Tel Aviv University’s Institute of Archaeology, Israel Finkelstein, has argued forcefully that Megiddo Stratum VI should be dated to the period of David and Solomon (otherwise known as the United Monarchy). Stratum VI was destroyed, he contends, by the Egyptian Pharaoh Sheshonq I, the Shishak of the Bible (1 Kings 14:25-26; 2 Chronicles 12:2-9). All scholars agree that Sheshonq/Shishak cut a devastating swath through Israel in about 925 B.C.E. A list of towns he conquered and destroyed is inscribed in a poorly preserved hieroglyphic inscription in the temple of Amun-Re at Karnak. More than 50 towns are named, including MEGIDDO
…Ancient MEGIDDO (Tell el-Mutesellim) sits at a strategic point along the corridor that the Levant forms between Egypt and Mesopotamia, where for millenia economic goods, peoples and ideas have passed. It is located at the entrance to the Wadi ’Arah, a key pass through the Mount Carmel Range that obstructs the north-south trunk route traversing the region.
In the 15th century B.C.E., Pharaoh Thutmosis III, the great empire builder of New Kingdom Egypt, campaigned north to subdue a coalition of rebellious principalities led by the city of Kadesh, on the Orontes River in modern Syria. His major obstacle was MEGIDDO, which had joined the Kadesh coalition. “The capture of Megiddo is as the capturing of a thousand cities,” the pharaoh said. He was successful, but only after a protracted siege of the defiant town. Over the centuries, MEGIDDO witnessed the passing of numerous invading armies and military campaigns, securing for itself a prominent place in the historical memory of the region, and earning it the apocalyptic designation as the scene of the final conflagration, the Armageddon of the Bible….



MEHY: stele

(as per K. Weeks) Pursue biography of Mehy and Ramses II.


(as per EEF) see this link to an August 15 2000 post thread from Peter Feinman.


(as per P. Feinman) see "La Stele de L'an 400 Retrouvee" by Pierre Montet, 1931.

This Stele originally stood at Khata'Na Qantir.


Review GENESIS 50:1-11.



MEIDUM: (AE; OK) pyramid at settlement of

Investigate cubit markings and construction date.

Also investigate ABU RAWASH.



MEKUTRA: AE papyri

Viewed at the MET, 4/24/02.

Found at THEBES.

11th Dynasty; ~2009-1991 BCE.

Hieratic math content.




MELANGES: title of works

[B_085,rvw] CATNYP# *OBQ+ 73-2731 t.107, "Itineraires d'Egypte : melanges offerts au pere Maurice Martin s.j. / reunis par Christian Decobert." Cairo 1992.

History and Church History.


[W_006,rvw] WATSON# 520 Et82 v13. "Melanges, Jacques Jean Clere." France, 1991.



[B_195,rvw,cubit,return to copy] CATNYP# *OBKG (Chabas, F. J. Melanges Egyptologiques), “Melanges Egyptologiques”, Paris, France Sept. 1873.

[First published in 1862].

Two volumes bound as one.

NYPL has 3rd series published 1870-1873. (Chalon-sur-Saone)

Available also at the Wilbour Library.

The second volume of this set has CUBIT stuff.



MEMNON: (AE, MK) colossus, graffitti

Near the Ramesseum and VOK.


14th Century BCE [Amenophis] Statues near Ramesseum & KV.

The [~1 BCE] quake caused cracks to develop in the Colossi, which ever after began “singing” when the sun rose. This led the Greeks to deem them the Oracle of Memnon (an Ethiopian king in Greek mythology), to which they and later the Romans made pilgrimages. When the Roman emperor Septimius Severus restored the statues in hopes of gaining favor with Memnon, they ceased speaking their oracles.



MEMPHIS: (AE) town




MENANDER: codex; Greek playwright

(as per E. G. Turner) This Greek codex from ~500 CE.

This codex was included in the archive of Dioscorus of Aphrodito.

See Comedia Florentina in P.S.I. [PSI] 126.

See P. Bodmer IV.


p. 35 of [B_517], has [no catnyp] very similar alt:

[B_519,rvw] CATNYP# JFD 01-5242

“Plays and Fragments / Menander ; with an introduction by Norma Miller.”

London, 1987.

Available from OXBOW catalog [B_332 alt]



MENDOZA: (Aztec) codex

See [B_359]; See also Dresden (Mayan) Codex.

Arithmetical content. Accounts.



See also RYLANDS; [B_093]



MERENPTAH: (AE; Hieroglyphic) Victory Stele of,

circa 1207 BCE


(as per T.E. Peet, [B_041b]) Coregent Son of Ramses II who ruled as Pharaoh 9 years after his death.


(as per Kenneth R. Weeks) Ramses II's 30th son and the fourth son by Queen Isisnofret (his 2nd principal wife).

Merenptah was buried in KV8 (19th dynasty).

Ramses II buried in KV5.

Stele contains earliest non-biblical reference to people of Israel

(in Canaan).


(as per EEF; G. E. Kadish) … you might want to consult Kent

Weeks' recent publication: : KV 5 A Preliminary Report on the Excavation of the Tomb of the Sons of Rameses II in the Valley of the Kings (AUC Press, 2000). It's vol. II of the publications of the Theban Mapping Project.


[W_047=B_125,rvw] WATSON# 533.5 W36., CATNYP# *OBX+93-2475 "Gottergericht und "Heiliger" Krieg im Alten Agypten : die Inschriften des Merenptah zum Libyerkrieg des Jahres 5 / von Thomas von der Way."

Heidelberger, 1992. See plates.


[W_048,rvw] WATSON# 520.5 So8. "Les monuments du roi Merenptah / par Hourig Sourouzian." 1989.


[W_049,rvw] WATSON# 536 B642 v16. "Untersuchungen im Totentempel des Merenptah in Theben / unter der Leitung von Horst Jaritz", Stuttgart, 1997.


(as per T.E. Peet,[B_181], p. 109) Quoted tr. of victory stele:

“Canaan is captured with every evil circumstance (?). Askalon is carried captive. Gezer is taken. Yenoam is brought to nought. Israel is destroyed, its seed is not. Syria has become as the widows of Egypt. All the lands together are at peace.”

See also [B_228], JEWS for alternate tr.

(as per S. Katary, [B_100])

Merenptah is mentioned often in P. Wilbour. [7?]


As per BASNY lecture at Taipei Noodle House, 2nd Avenue by 52nd street NYC:

(Upstairs dining room) hosted by BASNY President Gary Greenberg on January 21, 2003.

My notes and the handout provided on file with [B_227]

Merneptah’s Israel in the time of the sea peoples.”

Lecturer, Dr. Peter Feinman of the AIA, describes the “Song of Deborah” as one of the two oldest Biblical songs. The other is the Song of the Sea.

Here a possible connection was made to the Sisera [whose head was crushed/spiked by Deborah. Sisera may be equivalent for Shasu (Bedouins).

He suggests that this song is diametrically opposed to the structure of the AE barks of many Pharaohs and that this suggests a strong AE influence over the people who wrote it.


Gary Greenberg and Peter Feinman noted that no further references to Israel occur outside of Israeli

territory until the Assyrian records of ~7-800 or possibly 900 BCE.

No other AE references to Israel occur AT ALL!



MERSENNE: (French) Mathematician; primes



GIMPS: Yields newest [2001] 39th M. Prime!

2^13,466,917-1 [over 4 million digits!]



MERTON: (Greek) papyri; collection

(as per E. G. Turner) P. Merton = The Greek papyri in the collection of Wilfred Merton.


Vol i, ed. H. I. Bell and C. H. Roberts, London, 1948.


Vol ii, ed. B. R. Rees, H. I. Bell, J. W. B. Barns, Dublin, 1959.


P.Mert.: A Descriptive Catalogue of the Greek Papyri in the Collection of Wilfred Merton

P.Mert. 1.4. Letter from Aristomachos: (Greek; from Philadelphia?)



MESHA: (Moabitic) Stela; King of the Moabites

See UHN: p. 212: Stela of king Mesha of Moabites 842 BCE mentions YAHWEH.


Stele; 900 bce

MESOAMERICAN: manuscripts and codices




Mesoamerica, Pre-Columbian, §VI, 3: Manuscripts: Regional traditions

Anonimo Magliabechiano Codex see Codex Magliabechiano

Atlantic Codex (Milan, Bib. Ambrosiana)


(Florence, Bibl. Naz., Bench Rare 50)


Leoni: (2) Pompeo Leoni

Pacioli, Luca


Aubin Manuscript 20 (Paris, Bib. N., MS. Mexicain 20)

Mesoamerica, Pre-Columbian, §II, 4(iii): Post-Classic period: Southern Highlands

Mesoamerica, Pre-Columbian, §VI, 1: Manuscripts: Introduction

From the borgia group: see


Aubin Manuscript #20

Skin folded in four sections, painted on one side.
51 by 91 cm.

Also known as Fonds Mexicaines 20 or Pintura No. 20 de la Colección Goupil Aubin.


Barberini Codex (untraced)

Barberini Codex (The Badianus Manuscript: An Aztec Herbal of 1552), pages 34-35 (for hiccups and for cough)

A small manuscript in the Vatican Library, bound in 16th-century crimson velvet, contains the earliest-known treatise on Mexican medicinal plants and native remedies. The Barberini is an herbal, documenting the pharmacological treatment of diseases. There were no Latin equivalents for most plant names, and so the translator had no choice but to record the Aztec names.


Azcatitlan Codex, folio 23

The first known reference to this Codex appears in the catalog of the Indian historical museum of Lorenzo Boturini Benaduci (1702-1755). There are no documented references from the year 1791 onwards until 1830, when Joseph Marius Alexis Aubin (1802-1891), director of the École normale superièure de Paris, traveled to Mexico on a research trip and acquired the manuscript. In 1840 he returned to France with his library, and in 1889 he sold his collection to Eugene Goupil. Following Goupil's death, his wife donated the collection to the Bibliothèque Nationale in 1898.

Sangallo, da: (1) Giuliano da Sangallo, §1(i): Early career, before c 1485

Bernulphus Codex (Utrecht, Catharijneconvent)

Ottonian art, §IV, 2(ii)(b): Manuscript painting, after c 1025

Biduini Codex (Koblenz, Landeshauptarchv)

Chronicles and histories, manuscript, §3: Medieval

Bocskay Schriftmusterbuch (Vienna, Kunsthistoriches Museum, Bocskay Codex)

Habsburg, §I: (10) Rudolf II, §2: Patronage

Boxer Codex (untraced)

manuscript dated 1590, and later acquired by Charles R. Boxer (hence known as the Boxer Codex), includes illustrations of these resplendently tattooed peoples


… The sixteenth century Spanish conquistadores called them pintados, “painted people.” Natives of the Western Visayan islands, these pintados were among the first local peoples to encounter the white man. Thus did they enter the European record. An anonymous manuscript dated 1590, and later acquired by Charles R. Boxer (hence known as the Boxer Codex), includes illustrations of these resplendently tattooed peoples. It later became clear that the body marks were not painted on, as the Spanish description suggested, but were applied via the tattooing practice of puncturing the dermis and inserting pigment to create an indelible design.

Brunei, §5: Coins

Carcassonne Codex (untraced)

NO GOOGLE: Carcassonne Codex!


Calvo, Marco Fabio

Codex Aubin (London, BM, Add. MS. 312)

Codex Aubin, (also called Codice de 1576) which is a Nahuatl text illustrated with marginal images painted in colour.  On page 117 of the original there is a drawing of an Indian with large drops of blood flowing from the nose. The accompanying text in Nahuatl speaks of tribute payments made on “today, Saturday the 18 of August” and adds “… and also in August the sickness continued.  Blood came out of our noses. Only in our houses from did the priests take our confessions and they helped us to eat. And the doctors cared for us.  And when the church bells rang they did not sound for the buried, for we were abandoned in the church.” See Charles E Dibble (translator), Historia de la nación mexicana: reproducción a todo color del Codice de 1576 (Codice Aubin),. Madrid, Ediciones José Porrua Turanzas, 1963. (The translation is from Nahuatl into Spanish, the English passages above are our translation of Dibble's Spanish transcription.)


Throne, §V: Pre-Columbian Americas

Codex B (Paris, Inst. France)

Mesoamerica, Pre-Columbian, §X, 2: Museums, exhibitions and collections

Codex Borbonicus (Paris, Bib. Assemblée N., Y. 120)

Aztec, §4: Painting

Mesoamerica, Pre-Columbian, §VI, 2: Manuscripts: Materials and techniques

Mesoamerica, Pre-Columbian, §IX, 7(ii): Musical instruments: Types

Codex Borgia (Rome, Vatican, Bib. Apostolica, MS. Borg. Mess. 1)

Mesoamerica, Pre-Columbian, §I, 4(ii): Religion and iconography: Cosmologies

Mesoamerica, Pre-Columbian, §I, 4(iii): Religion and iconography: Deities and their attributes


Codex Boturini (Mexico City, Bib. N. Antropol. & Hist., MSS 35-38)

Narrative art, §IV: Pre-Columbian Americas

Codex Calixtinus (Santiago de Compostela, Archvs Catedral, Cod. Calixt. Libert 5)


See also

for ordering codex images and tr.



MESOPOTAMIAN MATHEMATICS: also sprinkled throughout

3.1. Same as 1.1.

3.2. Gandz, Solomon. “The Origin and Development of the Quadratic Equations in Babylonian, Greek, and Early Arabic Algebra”. Osiris (1937), 405–557.

3.3. Høyrup, Jens. “Algebra and naive geometry. An investigation of some basic aspects of Old Babylonian mathematical thought”. Altorientalische Forschungen 17 (1990), 27-69, 262- 354.

3.4. Høyrup, Jens. “Mathematics, algebra, and geometry”. In The Anchor Bible Dictionary. Vol. IV. Edited by D. N. Freedman. New York, etc.: Doubleday, 1992, 602–612.

3.5. Friberg, J. “Numbers and Counting in the Ancient Near East”. In The Anchor Bible Dictionary. Vol. IV. Edited by D. N. Freedman. New York, etc.: Doubleday, 1992, 1139-1146.

See TORAH; [B_267,JH,8.5] CATNYP# *P-*PDD 92-4110

3.6. Nemet -Nejat, Karen Rhea. Cuneiform Mathematical Texts as a Reflection of Everyday Life in Mesopotamia. (American Oriental Series). Vol. 75. New Haven, CT.: American Oriental Society, 1993.

3.7. Robson, Eleanor. Review of K. R. Nemet -Nejat – Cuneiform Mathematical Texts as a Reflection of Everyday Life in Mesopotamia. Bibliotheca Orientalis 52 (1995), 424-432.

3.8. Høyrup, Jens. In Measure, Number, and Weight. Studies in Mathematics and Culture. New York: State University of New York Press, 1994.

3.9. Caveing, Maurice. La constitution du type mathématique de l’idéalité dans la pensée grecque. Essai sur le savoir mathématique dans la Mésopotamie et l’Egypte anciennes. Presses Universitaires de Lille, 1994.

3.10. Høyrup, Jens. “Changing trends in the historiography of Mesopotamian mathematics: An insider’s view”. History of Science 34 (1996), 1-32.

3.11. Powell, Marvin A., Jr. “The Antecedents of Old Babylonian Place Notation and the Early History of Babylonian Mathema ics”. Historia Mathematica (1976), 417–439.

3.12. Høyrup, Jens. “Investigations of an Early Sumerian division problem”. Historia Mathematica 9 (1982), 19-36.

3.13. Whiting, Robert M. “More evidence for sexagesimal calculations in the Third Millennium B.C.” Zeitschrift fur Assyriologie 74 (1984), 59-66.

3.14. Friberg, J. “The early roots of Babylonian mathematics : Three remarkable texts from ancient Ebla”. Vicino Oriente 6 (1986), 3-25.

3.15. Thureau-Dangin, François. Textes mathématiques babyloniens. (Ex Oriente Lux, I.) Leiden: J. Brill, 1938.

3.16. Neugebauer, Otto, and Abraham Joseph Sachs. Mathematical Cuneiform Texts. New Haven, Conn.: American Oriental Society and American Schools of Oriental Research, 1945.

3.17-19. Sachs, Abraham Joseph. “Babylonian Mathematical Texts. I. Reciprocals of Regular Sexagesimal Numbers”. Journal of Cuneiform Studies 1 (1947), 219–240; “Babylonian Mathematical Texts. II. Approximations of Reciprocals of Irregular Numbers in an Old-Babylonian Text”; “Babylonian Mathematical Texts. III. The Problem of Finding the Cube Root of a Number”. Journal of Cuneiform Studies 6 (1952), 151–156.

3.20. Gandz, Solomon. “Studies in Babylonian Mathematics. I. Indeterminate Analysis in Babylonian Mathematics”. Osiris 8 (1948), 12–40.

3.21. Bruins, Evert M., and Marguerite Rutten. Textes mathématiques de Suse. (Mémoires de la Mission Archéologique en Iran, XXXIV.) Paris: P. Geuthner, 1961.= [B_612,OS,IMG] See SUSA.

3.22. Friberg, J. “Methods and Traditions of Babylonian Mathematics. I: Plimpton 322, Pythagorean Triples, and the Babylonian Triangle Parameter Equations”. Historia Mathematica 8 (1981), 277– 318.

3.23. Friberg, J. “Methods and Traditions of Babylonian Mathematics. II. An Old Babylonian Catalogue Text with Equations for Squares and Circles”. Journal of Cuneiform Studies (1981), 57–64.

3.24. Neugebauer, Otto, and Abraham Sachs. “Mathematical and metrological texts”. Journal of Cuneiform Studies 36 no. 2 (1984), 243–251.

3.25. Muroi, Kazuo. “Inheritance Problems of Babylonian Mathematics”. Historia Scientiarum 34 (1988), 11-19.

3.26. Idem, “Extraction of Cube Roots in Babylonian Mathematics”. Centaurus 31 (1989), 181-188.

3.27. Idem, “Interest Calculations of Babylonian Mathematics: New interpretations of VAT 8521 and 8528”. Historia Scientiarum 39 (1990), 29- 34.

3.28. Idem, “The Expressions of Zero and of Squaring in the Babylonian Mathematical Text VAT 7537”. Historia Scientiarum (2) 1 (1991), 59-62.

3.29. Idem,  “Small Canal Problems of Babylonian Mathematics”. Historia Scientiarum (2) 1 (1992), 173 –180.

3.30. Idem,  “Reexamination of Susa Mathematical Text No. 3: Alleged value pi = 3 1/8”. Historia Scientiarum (2) 2 (1992), 45-49.

3.31. Idem, “Reexamination of the First Problem of the Susa Mathematical Text No. 9.” Historia Scientiarum (2) (1994), 231-233.

3.32. Idem, “Two Harvest problems of Babylonian Mathematics”. Historia Scientiarum (2) 5 (1996), 249-254.

3.33. Idem, “An Enigmatic Sentence in the Old Babylonian Table of Exponents and Logarithms”. Historia Scientiarum (2) 6 (1997), 229-230.

3.34. Idem, “A Circular Field Problem in the Late Babylonian Metrological–Mathematical Text W 23291-x”. Ganita Bharati 19 (1997), 86-90.

3.35. Idem,  “Expressions of a Unit in Babylonian Mathematics”. Acta Sumerologica (Japan) 20 (1998), 121-125.

3.36. Idem, “Early Old Babylonian Mathematical Problems Written in Sumerian”. Historia Scientiarum (7) (1998), 199-203.

3.37. Brack-Bernsen, Lis, and Olaf Schmidt. “Bisectable trapezia in Babylonian mathematics”. Centaurus 33 (1990), 1-38.

3.38. Høyrup, Jens. “‘Remarkable numbers’ in Old Babylonian mathematical texts: A note on the psychology of numbers”. Journal of Near Eastern Studies 52 (1993), 281-286.

3.39. Høyrup, Jens. “On subtractive operations, subtractive numbers, and purportedly negative numbers in Old Babylonian mathematics”. Zeitschrift fur Assyriologie 83 (1993), 42-60.

3.40. Nemet -Nejat, Karen R. “Systems for learning mathematics in Mesopotamian scribal schools”. Journal for Near Eastern Studies 4 (1995), 241-260.

3.41. Fowler, David, and Eleanor Robson. “Square root approximations in Old Babylonian mathematics: YBC 7289 in context”. Historia Mathematica 25 (1998), 366– 378.

3.42. De Odorico, Marco. The Use of Numbers and Quantifications in the Assyrian Royal Inscriptions. State Archives of Assyria Studies, 3, 1995.

3.43 Van der Waerden, B.L. Science Awakening, I. 2nd ed. Leyden: Noordhoff Interna ional Publishers and New York: Oxford University Press, 1961. [Chapter 3; worth 1 paper]


All the above and more via this link:


MESU BETESH: (OK; AE) obscure reference

(as per E.A. Budge) See BOTD chapter XV.

"Write for thee Thoth [and] Maat day every.

Thine enemy [is] given to the fire, the evil one hath fallen;

his arms [are] bound, removed hath Ra his legs;

the sons of impotent revolt never [again] shall they rise up!"

AKA Children of unsuccessful revolt.

AKA The attendant fiends of the enemy of Ra.


See ANI; B.M. 10471



METALS: wrestled from caves like Philosophy


(as per EEF; S. Bojtos; 121002)

See Amarna letter EA 35 which talks about copper being sent

from Cyprus to Egypt.


(as per EEF; B. Yare; 121002)

STRABO (as reported in Budge's /The Egyptian Sudan/ ) reports copper

mines at or near Meröe. Budge also mentions copper mines to the south of Dâr Fûr between Kossinga and Hufrat As-nahâs. He also states: "COPPER is found at Hufrat an-Nahâs, in the north-west of the Bahr al-Ghazâl Province, and in the mountains near Sawâkin and in the Peninsula of Sinai; none of the mines have been properly worked yet."

Speaking of copper from Sinai in the time of Rameses III, he reports

that "To the same Red Sea port (near modern Kusêr) the copper from the

mines in the Sinaïtic Peninsula was brought, and the metal, in ingots,

was carried across the Eastern Desert into Egypt on the backs of asses."

This suggests that the copper was smelted before it reached Egypt.

There are a number of references to copper and copper mines in

Breasted, ARE, including mines in Atika and Sinai.




(as per EEF; S. Whittet ; 052402)

Re: descriptions or depictions of making bronze in AE.


Nibbi, Alessandra. Tin from the Eastern Desert. GM 19 (1976): 49-50.

other mentions of Tin deposits in Egypt's eastern desert associated with the gold mines.


(as per EEF; F. Yurco ; 052402)

This Anatolian mine of tin as I recall from the reports on it was in

operation only until about 2000 B.C.E. after which time it was played out.

<snip> thus it could have supplied Egypt and Mesopotamia for bronze making.


(as per EEF; A. Eyma ; 052402)

Yes, but the additional puzzle is: what  was the source during the

millenium between the 3rd mill. (Anatolia) and the1st mill. (Spain etc).]


(as per EEF; J. Picton ; 052402)

Just a thought-

trade in tin was 'big business' in the late 3rd and early 2nd

millennium, recorded in a collection of tablets found at Kanesh in

Anatolia. However, the tin was coming FROM the city of Assur in

northern Mesopotamia, and the assumption is that they were

acquiring it from further east (perhaps in conjunction with lapis lazuli?).


Huge donkey caravans carried the tin and textiles to Anatolia via a

series of caravan cities which grew out of the trade, and were exchanged

in Anatolia for silver and copper. The Assur merchants were also

instrumental in various trading outposts in Anatolia acting as

intermediaries for trade in other goods.


A lot of work has been done on this and I would be happy to supply

references. However, there is no record of trading it to Egypt although

I wouldn't assume that these entrepreneurs didn't think of it ( or do it!).


On the connected subject of trade in antiquity, look at the Uruk 'world-

system' of the 5th millennium trading from Anatolia to Iran and down

the Arabian Gulf, and possibly further east. Not to mention the Ubaid

period which is even earlier, when seafarers were trading down the Gulf

as far as Oman (reed-impressed Bitumen from boat caulking has been

found in Oman, and the Bitumen is sourced in Mesopotamia).





Asem in Ancient Egyptian/Coptic

See Dbn [Deben] in RMP problems; see RHIND

Henri Stierlin, The Gold of the Pharaohs, Terrail, Paris, 1997. Pb.,

224 pp., col. ills. ISBN: 2879391172, price: USD 27.50


Hans Wolfgang Müller, Eberhard Thiem, Gold of the Pharaohs, Cornell

University Press, Ithaca / London, 1999. Hardcover, 256 pp., col. ills.

ISBN: 0801437253, price: USD 60




(as per D. Hall)

A scholar of Israeli archaeology indicated the Philistine (Peleset)

settlements after Ramesses III had iron making facilities, although I

have not seen the studies.  The Sea Peoples had migrated through

Anatolia where iron making technology was known and then continued

south towards Egypt.





“The earlier occurrence of zinc in man - made artifacts is in the

form of the copper alloy known as brass.

Ever since the discovery of copper and the alloying elements

of tin, arsenic, lead, etc., different materials,

including zinc, were used to alloy and harden copper.


The earliest method of making brass was possibly the cementation

process in which finely divided copper fragments were intimately mixed

with roasted zinc ore (oxide) and reducing agent, such as charcoal,

and heated to 1000 C in a sealed crucible.


Zinc vapour formed, dissolved into the copper fragments yielding a

poor quality brass, zinc percentage of which could not be easily



Fusion of zinc with copper increases the strength, hardness and toughness

of the latter.

When the alloy is composed of 10-18% zinc, it has a pleasing golden

yellow colour.  It can also take very high polish and glitter like gold. For this property, brass has been

widely used for casting statuary, covering temple roofs, fabricating vessels, etc.

Reduction of zinc oxide around 1000 C is crucially important : below

950 C no zinc is produced. Zinc is obtained in the vapour form at this

temperature, since its b.p. is 913 C.

With trace of oxygen, the zinc vapour would be reoxidised and hence

the successful operations in the past must have been done in closed


If the temperature were higher than 1083o C during brass-making,

then copper would melt and flow down to the bottom of the crucible

forming a puddle there, exposing a very small

surface area of the metal for alloy formation.”


See VEDAS; RGVEDA [fire altars/smelting]

METHEN: (OK; AE) inscriptions

(as per T.E. Peet) "Land measures... in full development"


(as per J. Legon) A Sakkarra tomb of mTn (Methen).

Land measures (math), Early 4th Dynasty, (_LD_II, 3-7).

See also PALERMO.



METROLOGY: The study of measure



See TORAH, Deuteronomy 13-16, honest weights and measures.


(as per AEB 81.1169) Petruso, Karl M., Early Weights and Weighing in Egypt and the Indus Valley, Bulletin Museum of Fine Arts, Boston 79 (1981), 44-51. See MINOS.


(as per AEB 85.1319) Rawlins, Dennis, Ancient Geodesy: Achievement and Corruption, Vistas in Astronomy, Oxford 28 (1985), 255-268. A review of the accurate latitude placement? of some AE Temples.

(as per M. St. John)

A minute of longitude (practically a constant) =  1.85 km (1.15625 miles) so that from my table of geographic positions of these pyramids I can give you the distances between them:


Saqqara  (at least 15 pyramids at this site)

5.55 kms (3.47 miles) to

Dashur (at least 7 pyramids at this site)

5.55 kms (3.47 miles) to

Mazghuna (at least 2 pyramids at this site)

20.35 kms (20.35 miles) to

el-Lisht (at least 2 pyramids at this site)


If we exclude Saqqara then each of the other sites contain pyramids dated to 12/13th Dynasties i.e. in the 330 or so years between 1985 and 1650 BC. This does not satisfactorily explain ALL the data, but the edge of desert, i.e. just out of reach of floods, holds for each and every pyramid ever built.


(as per AEB 85.1323) Cour-Marty, M., La collection de poids du Musee du Caire revisitee, RdE 36 (1985), 189-200 (kdt fraction standard). Work on weights and Measures [MATH].


(as per G. Nygaard) See this interesting link.


(as per G. Oaten) See this remarkable link.


I suggest you review Petrie's survey of Gizeh (Giza). See Giza and Gizeh.

See [B_130] below.


[B_126,rvw] CATNYP# *OBLF (Barnard, F.A.P., Imaginary ..),

“The imaginary metrological system of the Great Pyramid of Gizeh”,

NY, 1884. See Giza. Also available on microform.


[B_128,rvw] CATNYP# *OBLF (Edgar, J. Great pyramid passages…),

“The Great Pyramid passages and chambers…”,

London, 1910. A metrological study.


[B_129,rvw] CATNYP# *OBL+++ (Perring, J.S., Pyramids of Gizeh),

“The pyramids of Gizeh, from actual survey and admeasurement, by J. E. [!] Perring. Illustrated by notes and references to the several plans, with sketches taken on the spot by E. J. Andrews.”, London, 1839-42. See images.



CATNYP# *OBLF (Petrie, W.M.F. Pyramids and temples of Gizeh),

“The pyramids and temples of Gizeh”. London, 1883.

See Plates.



CATNYP# *OBLF 95-4291 reprint of above [B_130].

London, 1990.

See update by Dr. Zahi Hawass.

See all the carefully prepared measurements!

Note the varied lengths of sides at the Great Pyramid.

See a detailed study of the Granite temple (by the Sphinx).


(as per W. Knorr) Seek works of Hero of Alexandria ~ 50 CE.





(as per S. Katary, [B_100]) One Aroura ~ 2/3 an acre.


(as per L. Bailey) See Edward Castle’s dissertation on Metrology

Not yet published, pursue at UMI; Bell & Howell?


[B_210,8.5,SIBL] CATNYP# VBDB (Hussey, R. Essay on the ancient weights and money) Hussey, Robert, (1801-1856).

“An essay on the ancient weights and money, and the Roman and Greek liquid measures, with an appendix on the Roman and Greek foot. By the Rev. Robert Hussey…”

Oxford, 1836.

This found via a reference in [B_149]. See Lepsius.

Little info on AE Cubits but an interesting metrological collection.

One footnote on page 235 specifies a red stone Egyptian Cubit at Turin measuring ~20.5 inches.


[B_211,8.5,CUBIT] CATNYP# VBDC (Fenner von Fenneberg, L. Untersuchungen uber die Langen) Fenner von Fenneberg, Ludwig.

“Untersuchungen uber die Langen- Feld- und Wegemaasse der Volker des Altherthums, insbesondere, der Griechen und der Juden / von Ludwig Fenner von Fenneberg.”

Berlin, 1859.

At the Science Library. Also at Wilbour.

See page 57 for CUBIT analysis.

This found via a reference in [B_149]. See Lepsius.

*This may be a pseudonym for ___?


[B_219,cvr only,rvw]

CATNYP# 3-VBDB (Boeckh, A. Metrologische Untersuchungen uber Gewichte)

“Metrologische Untersuchungen uber Gewichte, munzfusse und masse des altherthums in ihrem zusammenhange, von August Bockh.”

Berlin, Veit, 1838.

August Bockh [Boeckh], 1785-1867.

At the Science Library.

This found via a reference in [B_149]. See Lepsius.


[B_232,return to it again, NO COPY,SIBL] CATNYP# JSD 73-374

“Metrologicorum scriptorum reliquiae, collegit, recensuit, partim nunc primum edidit Fridericus Hultsch. Editio stereotypa editionis annorum 1864/1866.”

Stutgart, 1971.

Author: Friedrich Otto Hultsch, 1833-1906.

Note: Cover Title=Scriptores Metrologici.

Volume 1: Quo scriptorum Graecorum et Romanorum Teubneriana.

[Scriptores Graeci]

Volume 2: Quo scriptores Romani et indices continentur.

At the Science Library.

Poetic [Greek-math] stuff [in Latin].


[B_234a,8.5,NO IMG]

CATNYP# *OBM+1809 (France, Commission des Monuments d’Egypte)

“Description de l’Egypte, ou, Recueil de observations et des recherches qui ont ete faites en Egypte pendant l’expedition de l’armee francaise, publie par les ordres de Sa Majeste l’empereur Napoleon le Grand.”

Paris, 1809-1828.

See copies of Girard’s Nilometer work.

Tome premier.

Article title: Memoire sur le nilometre de ile d'Elephantine et les mesures

(Notes on the Nilometer on the island of Elephantine)

egyptiennes par M. P. S. Girard.

Pub.: Paris, 1809

Pages 1-48 including (pg. 48) chart of historical units converted to meters.

Publisher: De l'Impremerie Imperiale

(by order of Napoleon the Grand)

Found this via NYPLSOI.


[B_234b,rvw] CATNYP# *OBM++ (France, Commission des Monuments d’Egypte. Description de l’Egypte Library has: Text vols.)

As above.


[B_234c,rvw] CATNYP# *OBM+++ (France, Commission des Monuments d’Egypte. Description de l’Egypte)

As above.


[B_HOUSE,W_084=R_006,NO CATNYP] WATSON# 500.9 M46

“Measuring and Weighing in Ancient Times.”

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

Preface reference to an iron Byzantine rod, discovered at Schlomi, Israel, measuring 5 Roman Cubits totalling 2.59 meters in length.

2.59/5=~520mm=Roman Cubit


In the Hittite laws the price of a bull (for ploughing) was 12 silver shekels.

A cow at 5 shekels.

A calf at 3 shekels.


In the code of Hammurabi the salary for a farm laborer is set at 6 “she” [SHEH] of silver per day.


Jeremiah 32: 9-10 tells of a Prophet buying a field for 17 silver shekels.


Genesis 23 tells of Abraham’s purchase of the (Burial) cave of Machpeleh for 400 shekels of silver. (Exhorbitant price)


The ~1800 BCE Archive of Mari (on the Euphrates) contains Royal documents regarding the preparation of valuable metals into crafted works and involving a weighing before and after the work.

The technical term for the variance in weight (the inherent loss due to both processing metals and weighing innaccuracies) was: shiqu(m).


Isaiah 40: 15 has the term as: shahak.

Often translated as “dust in the balance [scale]”


See the Gold (standard) meter in the Louvre.


See Judaen scale weights:

2, 4, 8, 16, 24, and 40 shekels

4 Judaen shekels = 1/2 deben (an AE unit)

10 AE qebets = AE deben

Deben was a quasi-standard heavy ring of refined precious metal.


1 Judaen shekel = 24 gera = 11.38 grains or grams?

1 nesef = 5/6 Judaen shekels

1 pym = 2/3 Judaen shekels

1 beqa= 1/2 shekel

See Samuel 13: 21 (the only use of pym)


See II Samuel 15: Absalom:

Lmlk (to the King) standard.

The holy shekel = 20 gera?

See the Judaean lmlk jars of Hebron, Mamshit, Ziph and Sochoh.


Kikar = Talent = ~25 kilograms=~55 pounds

Maneh= Minah = 50 or 60 shekels.


See I Samuel 1: 24; 25: 18; II Samuel 16: 1

See one nevel of wine


See Samarian ostraca inscribed: laginos (volume)


See Biblical period shards from Tel Khualiefeh (near Eilat).

See Persian period shards from Elephantine (Yev)


See many references from (~1350 BCE) Ugaritic texts to:

Kad = volume = Biblical bat or bath = ~22.5 litres.

Term is Akkadian in origin?: karpatu or kiripu.

One term for many goods



See Western Anatolian volume: Kyprus = wine measure

19.6-22.4 liters = Chian Kyprus

21-22 liters = Lesbian Kyprus

20-25 liters = Samian (wine) Kyprus

19.6-21.1 = Charsonessos (Mendian wine) Kyprus


See four different standard shekels of:




And Mesopotamian metrology


See AE h’qt [HEKAT] = 5.2 litres of olive oil but,

= only 4.5 litres of wine.


See Assyrian sillu = 5.7 litres

Assyrian cubit = 330 mm.= 27 dektiloi [fingers]


See Athenian kotoyle = .272 litres


See Ancient Greek Metretes = 2 bat

See Ancient Greek amphora = 1 metretes = 40 litres

(amphi phoreos = carried by a pair of porters)


Oversized and randomly shaped larger vessels called pithoi from Greek term pithos.

Capacity of pithoi = 5 bat = 110 litres

Which~=6 AE ephet of 19.1 litres.

See this text by Heltzer, Michael.:

“Die organization des hondwerks im ‘Dunklem

Zeitalter’ und im            1 Jahrtausend v.u.z. nostlichen Mittelmeergeheit”, Padova, 1992.

See [B_374,rvw]


Greek name for a measure of kotoyle = .273 ml.

4 choinix = 1 kotoyle (dry)

1 chous = 4 kotyles (liquids)

Mina=mna= ~1/2 kilo (usually?)


See Metronomoi (enforcers of uniform measure)


(as per L. Holland) Hebrew word Caf means palm [of hand] and scale-pan.

Balance comes from bilanx [Latin: two pans]


See the tombstones (4-500 CE) of ZOAR.


See deed from KEFAR BARU dated to [Bar Kokhba] the third year of the freedom of Israel.


Clarify Gittin? Talmud?


See inscriptions in the SUSYA synagogue in (Naveh 1978, No. 76, Hebrew).

Dating from the destruction of the second temple.


See page 55 [Hebrew]

weighing gold (relief) from: tomb of Meruru=ka ~2300 BCE

weighing gold (painting) from: tomb of Amen-em-het ~1950 BCE


(as per the link below):


Chabas, F., Détermination métrique de deux mesures égyptiennes de capacité, Maisonneuve, Paris, 1867.

Chabas, F., Recherches sur les poids, mesures et monnaies des anciens égyptiens, Imprimerie nationale, Paris, 1876.

Cour-Marty, M.A., Les Textes des Pyramides témoignent du souci de normalisation des anciens égyptiens, N.1, pp. 123-140, Hommages à Jean Leclant, IFAO, Le Caire, 1994.

Ebers, G., Papyrus Ebers, Die maasse und das kapitel über die augenkrankheiten, Hirzel, Leipzig, 1889.

Jomard, E., Mémoire sur le système métrique des anciens égyptiens, contenant des recherches sur leurs connaissances géométriques et sur les mesures des autres peuples de l'Antiquité, Imprimerie royales, Paris, 1817.

Letronne, A.J. et Vincent, A.J.H., Recherches critiques, historiques et géographiques sur les fragments d'Héron d'Alexandrie ou du système métrique égyptien, Imprimerie nationale, Paris, 1851.


[B_374,rvw] CATNYP# *ODC 96-2805

“Die organization des handwerks im ‘Dunklem Zeitalter’ und im 1 Jahrtausend v.u.Z. im ostlichem Mittelmeergebeit/ Michael Heltzer.” Padova, 1992.


See MINOS below:


See Anglo-Saxon Metrology link below:


1. NIST Special Publication 811, 1995 Edition

2. CRC Handbook of Chemistry and Physics 70th edition

3. Oxford English Dictionary

4. Websters New Universal Unabridged Dictionary

5. Units of Measure by Stephen Dresner

6. A Dictionary of English Weights and Measures by Ronald Zupko

7. British Weights and Measures by Ronald Zupko

8. Realm of Measure by Isaac Asimov

9. United States standards of weights and measures, their

creation and creators by Arthur H. Frazier.

10. French weights and measures before the Revolution: a

dictionary of provincial and local units by Ronald Zupko

11. Weights and Measures: their ancient origins and their

development in Great Britain up to AD 1855 by FG Skinner

12. The World of Measurements by H. Arthur Klein

13. For Good Measure by William Johnstone

14. NTC's Encyclopedia of International Weights and Measures

by William Johnstone

15. Sizes by John Lord

16. Sizesaurus by Stephen Strauss

17. CODATA Recommended Values of Physical Constants available at

18. How Many?  A Dictionary of Units of Measurement.  Available at


All of the above [1-18] via this link:


See also NEWTON; Sir John Greaves. See BOECKH

See FAYUM; [B_075=O_002]

Greek bath unit=loutrun=5.81 gal apx=22 liters


(as per EEF; N. Doyle; 041204)
A couple of years ago I wrote a paper (currently unpublished) on
Egyptian zoomorphic balance pan weights. These [references to works on ancient weights] will likely be helpful, with bibliographies leading to more specific material:


Bleiberg, E. 2001. Prices and payment. In The Oxford Encyclopedia of
Ancient Egypt, 3 vols. (ed. D.B. Redford). Oxford: Oxford University
Press, vol. 3, p. 65-68.


Cour-Marty, M.-A. 1990. Les poids égyptiens, de précieux jalons
archéologiques. Cahier de Recherches de l'Institut de Papyrologie et
d'Ègyptologie de Lille 12: 17-56


Doll, S.K. 1982. Weights and measures. In Egypt's Golden Age: The
Art of Living in the New Kingdom, 1558-1085 BC (ed. E. Brovarski, S.K. Doll,
R.E. Freed). Boston: Boston Museum of Fine Arts, pp. 58-62.


Grandet, P. 2001. Weights and measures. In The Oxford Encyclopedia
of Ancient Egypt, 3 vols. (ed. D.B. Redford). Oxford: Oxford University
Press, vol. 3, pp. 493-95.


Petrie, W.M.F. 1926. Weights and Measures. London: Egypt Exploration


Petruso, K. 1981. Early weights and weighing in Egypt and the Indus
Valley. Museum of Fine Arts (Boston) Bulletin 79: 44-51.


Pulak, C.M. 1996. "Analysis of the Weight Assemblages from the Late
Bronze Age Shipwrecks at Uluburun and Cape Gelidonya, Turkey." Dissertation,
Texas A&M University


(as per personal correspondence; G. Westwood; 050004)





(as per A.H. Gardiner) similar to P. Turin.


[W_034,rvw] WATSON# 108.1N48 M58 n.s., v. 9, no. 8 (April, 1951) article in MMA Bulletin, Scott, Nora

Elizabeth, "The Metternich Stela".



MEYER: (Greek) papyri and ostraca

(as per E. G. Turner) P. Meyer = Greichische Texte aus Agypten: i, Papyri des Neutestamentlichen Seminars der Universitat Berlin, ii, Ostraka der Sammlung Deissmann, ed. P. M. Meyer, Berlin, 1916.


P.Meyer 1. Gesuch von Katökenreitern an das Königspaar:

(Greek; 144 bce; Arsinoite)



MIBTAHIAH: (Aramaic) archive of

(as per Y. Muffs) See [W_012], ELEPHANTINE.

Pursue these texts:

J. Euting, “Notice sur un papyrus egypto-arameen,” MAI, II (1903), pp. 297 ff. [publishing of a related Aramaic deed].



CATNYP# *ODF+++(Sayce, A. H. Aramaic Papyri Discovered at Assuan)

A. H. Sayce and A. E. Crowley, Aramaic Papyri Discovered at Assuan [ASWAN], / ed. By A. H. Sayce, with the assistance of A. E. Cowley, and with appendices by W. Spiegelberg and Seymour De Ricci. (London, 1906).

Arthur Ernest Cowley.



MICHAELIDAE: (Greek and Latin) papyri

(as per ZPE; D. Fowler) Seek P. Michael. 62, a Greek ~600 CE. set of (math) problems and tables.

Seek “A mathematical tablet”,

Aegyptus [B_371] 33 (1953) 222-40.


[B_371,rvw] CATNYP# *OBH (Aegyptus)

Milan, 1920-1952, 1972-


[B_372,rvw] CATNYP# *OBI 76-1333

“Index of articles volumes 1-50 of Aegyptus 1920-1970 / S. M. E. van Lith.” Amsterdam, 1974.


(as per Duke Univ.)

Papyri Michaelidae, being a Catalogue of Greek and Latin Papyri, Tablets and Ostraca in the Library of Mr G.A. Michailidis of Cairo, ed. D.S. Crawford. Aberdeen 1955. Nos. 1-60 papyri, 61-62 wooden tablets, 63-129 ostraca. For the dispersal of this collection , see ZPE 100 (1994) 223-6 (S. Clackson); Emerita. Rivista de linguistica y filologia classica 64 (1996) 289 (S. Daris). [o.e. AUP]


(as per E. G. Turner) P. Michael. = The Greek Papyri in the collection of Mr. G. A. Michailidis, ed. D. S. Crawford, London, 1955.


P.Michael. 7. Private letter, Lysimachos to Sôsios:

(Greek; 147 bce)



CATNYP# *OBKQ (Michailidis, G. A. Papyri Michaelidae)

BOBST# PA3303.M5 C7

“Papyri Michaelidae, being a Catalogue of Greek and Latin Papyri, Tablets and Ostraca in the Library of

Mr G.A. Michailidis of Cairo. Edited with translations and notes by D.S. Crawford.”

Aberdeen, 1955.

See BOBST Archive: O 1

Largely a collection of correspondence with some metrology and math.

See p. 131 for item #62:

Byzantine Division tables and arithmetical problems, which includes tables for 1/3; 1/2;

2/3’s and may have included 1/4. Also with calculations of interest; profit.




MICHIGAN: (University; Greek) papyri and ostraca

(as per Otto Neugebauer, W_024, HEIDELBERG) Seek P# 151, Greek Astronomy (math?).


See this link to the University of Michigan Papyrus Collection.


(as per AEB 81.1147) Bruins, Evert M., Reductible and Trivial Decompisitions Concerning Egyptian Mathematics, Janus, Amsterdam 68, (1981), 281-297.

Re: Mich. XV, Inv. No. 5563a.


[B_373,rvw,SIBL] CATNYP# *VBA p.v. 1502 [and 1509]

“Nouvelles decouvertes sur les mathematiques babyloniennes; conference faite au Palais de la decouverte le 1er decembre 1951.”

By Evert M. Bruins., Alencon, 1952.

See MCT.


Milan, 1920-1952, 1972-


(as per ZPE; D. Fowler) Seek P. Mich iii 145-7 and xv 686 for;

(math) multiplication and division tables.

See also O. Mich. [inv.] 9733. See ZPE 18, 1975.

See also P. Mich. iii 134. Math.


[B_040, IMG] CATNYP (for HM9 below)# JSP 76-614 (as per M. Gardner) The Akhmim Papyrus, a Hellene 500 AD to 800 AD papyrus, found along the Nile, was cited by Wilbur Knorr, Stanford History of Science Department, in:

Historia Mathematica, HM 9, 1982, pp.133-171 "Fraction in Ancient Egypt and Greece.", Toronto, International Commission on the History of Mathematics.

(The HM text is not available except at NYPL Science Library).

Above text also includes images of:

P. Michigan 145; n/23 and n/29 tables.

P. Michigan iii 146; n/(7-10) tables.


(as per E. G. Turner) Seek ostraca from Karanis from the University of

Michigan collection.

See O. Mich. = Greek Ostraca in the University of Michigan Collection, ed. L. Amundsen, Ann Arbor, 1935. See below 2 editions by H. C. Youtie and O. M. Pearl with ostraca.


(as per E. G. Turner) P. Mich. = Papyri in the University of Michigan Collection, ed. C. C. Edgar, A. E. R. Boak, J. G. Winter, and others, Ann Arbor, 1931-47. 8 volumes in 1965, each with its own subtitle. The numerical sequence was not established till vol. iii. Vol I, Zenon Papyri, by C. C. Edgar, is often referred to as P. Mich. Zen.


Vol i, Zenon Papyri, Nos. 1-120, ed. C. C. Edgar, 1931.

Vol ii, Papyri from Tebtunis, Nos. 121-8, ed. A. E. R. Boak, 1933.

Vol iii, Miscellaneous Papyri, Nos. 131-221, ed. J. G. Winter and others, 1936.

Vol iv, pt. I, Tax Rolls from Karanis, Nos. 223-5, ed. H. C. Youtie 1936.

Vol iv, pt. II, Text Nos. 357-63 and Indexes, ed. H. C. Youtie and O. M. Pearl, 1939. [ostraca]

Vol v, Papyri from Tebtunis, pt ii, Nos. 226-356, ed. E. M. Husselman, A. E. R. Boak, and W. F. Edgerton, 1944.

Vol vi, Papyri and Ostraca from Karanis, Nos. 364-428, ed. H. C. Youtie and O. M. Pearl, 1944. [ostraca]

Vol vii, Latin Papyri, Nos. 167-8, 429-63, ed. H. A. Sanders, with contributions by James E. Dunlap, 1947.

Vol viii, Papyri and Ostraca from Karanis, Second Series, Nos. 464-521, ed. J. G. Winter and H. C. Youtie, 1951.


(as per E. G. Turner) P. Mich. i, = P. Mich. Zen.


O. Mich.: (Greek; 235-4 bce)


P.Mich. 1.1. Fragment of an Account: (Greek; 259 bce; Philadelphia)

Small accounts; math; drachmas.


P.Mich.Aphrod.: Settling a Dispute: Toward a Legal Anthropology of Late Antique Egypt

P.Mich.Aphrod. 1: (Greek; AD 547; Aphroditopolis)


P.Mich.Mchl: A Critical Edition of Select Michigan Papyri

(Greek; AD155 ; from Karanis)

Minor math content.


See ZENON.;sid=3325423da0ee491b0fcc02f4a7a434e2;rgn1=apis_all;med=1;size=50;c=apis;lasttype=boolean;view=entry;lastview=reslist;subview=detail;cc=apis;entryid=x-2701;viewid=621_A.BMP;start=1;resnum=

CATNYP# *OAC (Isis) 1923
“Michigan Mathematical Papyrus No. 621.”
Isis, Volume 5, No. 1, 1923, pages 20-25.

Analysis of Greek unit fractions similar to Achmim Greek papyri.


MILANESI: (Greek) papyri from the Catholic University of Milan

(as per E. G. Turner) P. Mil. = Papyri Milanesi, vol. i, fasc. I, ed. A. Calderini; fasc. II, ed. S. Davis, Milan, 1928, 1966.


P. Mil. R. Univ. = Papiri della R. Universita di Milano, vol. primo, by A. Vogliano, Milan, 1937. Sometimes called P. Primi or P. R. U. M. to distinguish this from the other Milanese series. Reprint 1966. [PRUM]


P. Mil. Vogliano = Papiri della Universita degli Studi di Milano (continuation of P. Mil. R. Univ.).


P. Mil. Vogliano ii, Milan, 1961 (many collaborators).

Vol. iii, Milan, 1965 (I. Cazzaniga, M. Vandoni and others).

(P Mil Vogl.=Sappho fragment=L&P frg. 98)


Pursue active tr. project on Greek P. Bon.


P.Mil. 1.2rptripl. Sale of a sixth of a palm grove

(Greek; 104 bce; from Pathyris)

Minor math content.


P. Mil. Congr.


P.Mil.Vogl. 1.23. Division of inheritance: (Greek; AD 108; Tebtynis)

No math.


See HIBEH;  [O_008,8.5,IMG]


CATNYP# L-11 4057 Library has: [Vol.]1, [pt.2]

BOBST# PA3339 .M65

“Papiri Milanesi (P. Med.).”

Milan, 1928.

Studies from the series “Aegyptus (Milano).” [by Sergio Daris] include Greek Papyri.

See plates.


P. Mil. R. Univ. = Papiri della R. Universita di Milano, vol. primo, by A. Vogliano, Milan, 1937. Sometimes called P. Primi or P. R. U. M. to distinguish this from the other Milanese series. Reprint 1966. [PRUM]


CATNYP# *OBKQ+ (Milan (City.) Università. Papiri) Vol. 1-7.

“Papiri della R. Università di Milano…”



BOBST# PA3310 .M5 v.6 c.1


“Papiri [Greek] della Università degli studi di Milano volume sesto (P. Mil. Vogliano 258-300) / Edito da Claudio Gallazzi [and] Mariangela Vandoni con la collaborazione di Antonio Aloni; Fabrizio Conca; Dario del Corno; Alessandra Gavezzotti Gara; Robert Hubner.”

Milan, 1977.


MILESIAN: (Greek) accounting

See UHN: 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


See UHN: p. 220 note on Milesian Accounts:

Digamma=stigma=old semitic vov=6

koppa=qoppa=old semitic quf=90

san=sampi=semitic tsade=900


See HIBEH; Values noted in HIBEH parapegmata include (stigma and qoppa only)


MILITARY: intelligence

1. "Philo, from the Greek colony of Byzantium, was active in Alexandria

and Rhodos about 200 B.C. He is famous as one of the earliest teachers

of military engineering, and is known to have written technical and

scientific works, including one on fluid mechanics."


2. Now at the CAIRO Museum. "the [PIANKHY] stela, being the

report about a military intervention, contains rich information on

military matters, unique for the 8th century B.C. This concerns the

military organization, its social status, and questions of ethnic



3. GEBEL-BARKAL: monuments.  See [Karl Richard AKA Justus]

Lepsius, fragment of stela, an account of a military expedition. In

Berlin Museum (#1068). See work by Erman in ZAS 29, pp. 126-7.


4. See JEA 39, (1953), "Egyptian Military Organisation", pp. 32-47.


5. See: CATNYP# *OBT 92-4385 "Egypt, Canaan, and Israel in ancient

times / Donald B. Redford" Princeton, NJ, 1992. Includes analysis of AE

 military and political campaigns including the battle of Kadesh.


6. For a discussion of Jewish Mercenaries in antiquity, cf. P.


Jewish Military Colonies [in Hebrew] (Tel Aviv, 1948).


7. CATNYP# JFE 00-15142 "Columbia papyri IX : the Vestis militaris

codex / edited with commentary by Jennifer A. Sheridan.." Atlanta,

Georgia, 1998. =From the series: ASP Volume 39. On Roman Military



8. See the Lachish letters, dated at approximately 590 B.C.,

consist largely of military communications.


(as per D. Lorton; EEF; 123102)

available from University Microfilms [UMI]:


_War in Ancient Egypt_, 1995

UMI Number: 9617620


See also: 'Fighting Pharaohs: Weapons & Warfare in Ancient Egypt' by

Robert B. Partridge;  c350 pages / 402 b&w illustrations,

ISBN 0954349733 (Hb)/0954349725.


MILL: (AE) papyrus



WATSONLINE Yields nothing.


(as per H. Goedicke, Berlin 3024) Seek P. Mill II, 5

(regarding an assassination.)





MILLINGEN: (AE) papyrus

(as per Y. Koenig) The Millingen Papyrus in ZAS 34, P. 41,

Story of Sinuhe.P. 41. See SINUHE.


WATSONLINE Yields nothing.


(as per LEX) = P. Berlin 3019.


(as per ZAS) The Millingen P. = The Teaching of Amenemhat.

The Millingen Papyrus in ZAS 34, P. 35-51.



MILO GARDNER: Cryptanalyst and Math Historian
He who introduced me to the RMP [in 1997].
Search this site for his name.
See also:

MINOR: (Greek) ostraca of various minor collections

O. Minor A1: (Greek; AD 49; from THEBES)



MINOS: (Minoan culture; Linear A; Linear B…)

See HPM.

(as per M. Gardner) See work by Emmett Bennett, a U. of Wisconsin Minoan specialist, trying to read the Egyptian fractions contained in Linear A:

“Minos and Minyas: Writing Aegean measures,”

published in an Austrian journal:

Akademie der Wissenschaften, Wien [Vienna] 1999.


(as per M. Gardner) Explore link below by Prof. Karl M. Petruso (of the University of Texas at Arlington):


(as per AEB 81.1169) Petruso, Karl M., Early Weights and Weighing in Egypt and the Indus Valley, Bulletin Museum of Fine Arts, Boston 79 (1981), 44-51. See METROLOGY.


(as per K. Petruso; re: [B_HOUSE,R_006,NO CATNYP] “Measuring and Weighing in Ancient Times.”

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

“I reviewed the Hecht Museum publication in the London Times Higher

Education Supplement, no. 1522 (Jan. 25, 2002), p. 32.”

Prof. Karl M. Petruso, Anthropology, UT Arlington


(as per K. Petruso) Pursue the work of John Neal on historical Metrology [NO CATNYP].



MISHNAH KELIM: (detailed Hebrew purification rituals and metrology)

from the TALMUD

See Hebrew Cubits. Eruvin.



M.I.T.: university



MITHRAS: (Greek) liturgy

(as per E. G. Turner) From the collection of Consul Anastasi.


The Mithras Liturgy is part of the great magical codex of Paris (Papyrus 574 of the Bibliotheque Nationale). Presumably compiled in the early fourth century C.E., this codex contains a variety of tractates, hymns, recipes, and prescriptions, which were apparently collected for use in the working library of an Egyptian magician. Lines 475- 834 of this codex constitute the Mithras Liturgy; these boundaries for the Liturgy are suggested by the continuity of thought within the Liturgy, by the punctuation utilized by the scribe, and by the apparent transition to a different section (lines 835-849: astrological calculations). Interestingly, lines 467-474 parallel lines 821-823 and 830-834: thus the Mithras Liturgy is placed between two closely related versions of spells utilizing lines from Homer.



MMA: The Metropolitan Museum of Art; The Met., collections

See also WATSON.{7ACE74CF-428D-11D4-937C-00902786BF44}



MNAJDRA: Ancient Temple

[Of obscure origin and unusual construction and layout]




MNEMOTRIX: searchtool for more Near East goodies



MOABITE: (Phoenician) stone; stelae



(as per W. Muss-Arnolt) See work by J. Oppert.


“…ancient slab of stone erected in850 B.C. by King Mesha of Moab; it contains a long inscription commemorating a victory in his revolt against Israel. It was discovered at Dibon, Jordan (1868), by F. A. Klein, a German clergyman. Although it was later broken when Klein tried to purchase it from the Arabs, most of the fragments were recovered. They are in the Louvre. The language of the Moabites is a Phoenician dialect that represents an early form of Hebrew.”


"As for Omri, king of Israel, he humbled Moab many years....and his son [Ahab] followed him."





Building codes nyc:



MODIUS: castrensis

See [B_390; KESKINTO]


Sur le <<modius castrensis>>. Copies of pages 464-5 only.

Modius castrensis versus Modius Ordinaire may be resolved in:

Greichische und romische Metrologie, by Freidrich Hultsch, 1882.

Sextarius castrensis [?]


Task one:
Define Modius Castrensis; Modius Ordinaire

MOELLER: (Author)

Georg Hermann Moeller 1843-?


(as per everybody) See Moeller’s “Hieratische Palaogrophie”,

Liepzig, 1927, three volumes.

[B_308,IMG,8.5] CATNYP# *OBR++(Moeller, G. Hieratische Palaographie)

“Hieratische paläographie. Die aegyptische buchschrift in ihrer entwicklung von der fünften dynastie bis zur römischen kaiserzeit.”


Review number forms and variants. No mathematics.

See Volume 3.

Thanks to E. Garner for the copies from volume III.


G. Möller, Hieratische Lesestücke, II (1909), pp. 1-6, 28, 39.



MOMIES: tablets

T.Mom.Louvre: Catalogue des étiquettes de momies du Musée du Louvre

T.Mom.Louvre 1: (Greek; from Bompae)



MONAC.: (Greek) papyri

(as per E. G. Turner) P. Monac. = Veroffentlichungen aus der Papyrussammlung der K. Hof- und Staatsbibliothek zu Munchen: Byzantine Papyri, ed. A. Heisenberg and L. Wenger, Leipzig-Berlin, 1914.



MONSTERS: ooh scary






See GILGAMESH; [B_532,alt,HOUSE]

See HAWARA; killed by GILGAMESH with the aid of his special friend ENKIDU.

(as per EEF; C. Graves Brown; 082603) Bes:
For the [AE] female [MONSTER/GOD] Bes see also Bosse-Griffiths, K., 1977.
'A Beset Amulet from the Amarna Period' in the Journal of Egyptian Archaeology' Vol 63.
The collar can be viewed with a low resolution image at:

See also:
Henry G. Fischer, "The Ancient Egyptian Attitude Towards the
Monsters and Demons in the Ancient and Medieval Worlds. Papers
Presented in Honor of Edith Porada. ed. by A.E. Farkas et al. (Mainz, 1987).


(as per M. Tilgner EEF; 012005)
This passage is translated in J.F. Borghouts, Ancient Egyptian Magical
Texts, Leiden, 1978, pp. 86-87 (text no. 125 = BM 10052, rt. 6, 4-9):
"(A curse against the crocodile Maga)
... Backwards, Maga, son of Seth! ... The finger of the 77 gods is in
your eyes while you are bound to the great landing-pole (nay.t) of Osiris,
while you are bound to the four posts (sxn.t) of Upper Egyptian greenstone
which are at the prow of the bark of Re'..."


MONUMENTS: (neolithic images) of human achievement



MOOK: papyrus

(as per Peet, [B_041b], ABBOTT) see Papyrus Mook in ZAS.

Go to ZAS I xiii.106, I.5.



MORGENBLATT: fur gebildete leser.

[MORNING PAPER: for educated readers]



AKA MORGENBLATT fur gebildete stande.

Supplements included:

(art journal) Kunstblatt

(smart journal) Intelligenz-blatt



MOSCOW or MOSKAU: (AE; Hieratic; math) papyri

Visit the Moscow (Pushkin) Museum.

Seek P. #4576.


I have a link to a partial tr. and hieratic image of the MOSCOW Papyrus,

from St. Andrews.


Acquired by V.B. Golenischev or Golenischeff and housed in the Moscow Museum of Fine Arts (as of 1923). Published by Professor Strouwe [Struve] or Professor Turaiev by 1930. See [W_050]


[B_017a, 8.5,NO IMG] CATNYP# OBH+ JEA, "Four Geometrical Problems from the Moscow Mathematical Papyrus", Journal of Egyptian Archaeology Volume 15, Nov. 1929, pp 167-184, by Battiscombe Gunn and T. Eric Peet.

(as per T.E. Peet) see Pap. PETROGRAD 1116A recto.

JEA is also at Watson Library, MMA, NY.


[B_017a.2, 8.5’s,NO IMG] CATNYP# OBH+ JEA,

Journal of Egyptian Archaeology Volume 12, 1923

pp 123-137ff, by Battiscombe Gunn and T. Eric Peet. “Recent Publications”

showing and abridged intro to [B_092]

A detailed analysis of the contents of [B_092].

References to Spiegelberg’s “Kopt. Handworterbuch.”


Reference to K. Sethe’s; Northampton

“Report on some Excavations in the Theban Necropolis.”


References to T. Deveria’s:

Memoires et Fragments (Bibliotheque Egyptologique)


[B_017b,8.5,NO IMG,LB] CATNYP as above, See Vol. XVI, p. 242-9, 1930 for Kurt Vogel. See also [B_303]


[B_033,PIX,r05.2] CATNYP# *OBR+++(Leningrad, E. Papyrus hieratiques) "Les papyrus hieratiques nono 1115, 1116a et 1116b de l'Ermitage imperial a St. Petersbourg", by Gosudarstvennyi Ermitazh (Russia), 1913.

This book must be photographed.


[B_028,HOUSE] CATNYP# JFM 95-854 (see volumes two and three) "Ancient Egyptian Science: a source book" by Clagett, Marshall, 1989.

This is critical to any study of the MMP or Rhind P. or Berlin P 6619 (square roots) or Kahun IV. Images of all are included.

Volume three shows references to AE math analysis by Eisenlohr and Guillemot and Nims and Schiaparelli


(as per L. Bailey)

[B_341,8.5,IMG] CATNYP# OEA (Quellen und Studien zur Geschichte der Mathematik) Bd. 1 – bd. 4.

“Quellen und Studien [sources and studies of the history of Mathematics] zur Geschichte der Mathematik. Abteilung A; Quellen.”

Berlin : Verlag von Julius Springer, 1930.

vol. 1. Otto Neugebauer, J. Stenzel, and O. Toeplitz, editors.

P. 113-119: Von J. J. Perepelkin in Leningrad:

“Die Aufgabe Nr. 62 des mathematischen Papyrus Rhind.”

Gold, Silver, and Lead Deben (rings).

P. 113-119: By Dr. Bibhutibhusan Datta, Univ. Calcutta.

“Origin and History of the Hindu names for Geometry.”

Harpedonaptai sounds Hindi?

P. 300-380: Von O. Neugebauer, Gottingen.

“Arithmetik und Rechentechnik der Agypter.”

(K. Sethe in Verehrung und Dankbarkeit.)

See Berlin P. #6619.

See Cairo wood tablets CG 25367-8

See Kahun P.

See Rhind P.

Amazing detailed analysis of 2n table.

P. 413-450: Von O. Neugebauer, Gottingen.

“Die Geometrie der agyptischen mathematischen Texte.”

See Kahun P. LV.4

See Berlin P. #6619.

See MMP.

See p. 441 for details on the obelisk problem from P. Anastasi I, 14, 8-16, 5.

See also:

P. Anastasi I, 14, 2-14, 8.

P. Anastasi I, 16, 6-17, 3.

Showing partial images of the above.

(as per S. Lorber; W. Knorr) See work by B. L. Van der Waarden in:

“Die Entstehung [the emergence] der agyptischen Bruchrechnung.

Quellen und Studien”, B4, 359-382., See [B_341,rvw again!]


[W_050,rvw] WATSON# 533.6 St8. "Mathematischer Papyrus des Staatlichen Museums der schonen Kunste in Moskau / herausgegeben und kommentiert von W. W. Struve ; unter benutzung einer heiroglyphischen Transkription von B. Turajeff ; mit 15 Textfiguren und 10 Tafeln. Berlin, 1930.

(also with Turajeff or Turaiev or Touraieff) NO CATNYP.


(as per AEB 95.1152) Rampelberg, Doris, Les Egyptiens anciens s'etaient-ils trompes...Calculation of triangles.


(as per AEB 95.1155) Robins, Gay, Mathematics, Astronomy, and Calendars in Pharaonic Egypt, in: Civilizations of the Ancient Near East, III, 1799-1813.


(as per AEB 87.1010) Couchoud, Sylvia, Le nombre pi et les surfaces rondes dans l'Egypte pharaonic du Moyen Empire, SAK 14 (1987), 35-42.

Pi ~ sqrt10. Seek other work by S. Couchoud, see ANASTASI.

See [B_114], MOSCOW.

See also Pi.

See also

1.11. Couchoud, Sylvia. Mathématiques égyptiennes. Recherches sur les connaissances mathématiques de l’Egypte pharaonique. Paris: Le Léopard d’Or. 1993.


(as per LEX) see P. Moskau 4657, work by CAMINOS, literary fragment.



MOSE: (AE; Hieroglyph) inscriptions of

(as per S. Katary, [B_100]) 

The inscription of Mose [not Moses]

See “The Memphite Tomb-Chapel of Mose”, by G. A. Gaballa,

Warminster, 1977.

Mention of land acquisition/holdings.

Possible math content.



MOUTH: (AE) ceremony of the opening of the

(as per EEF, Gilberto Modonesi)

The shadow as black body is also present in Valley of the Kings in the

tomb of the  king Seti I (n.17 ), at the bottom of the text of scene X of the

Opening of the Mouth Ritual. Reference: E. Hornung, The Tomb of Pharaoh

Seti I - Das Grab Sethos' I, Artemis Verlag, Zurich und Munchen, 1991,

p. 166, fig. 102.



MOVIEFONE: service


M.P.E.R.: (Greek; math) papyri

(as per ZPE; D. Fowler) Seek many Greek math tables.

See Erzerhog-Rainer, MPER.


(as per E. G. Turner) P. Mitteilungen Wien, see MPER.



MUNCHEN: (Greek) papyri


See HIBEH; [O_008,8.5,IMG]



MUNCHNER: (Greek) papyri; ostraca

See [B_042] ABBOTT.


P.Münch.: Die Papyri der Bayerischen Staatsbibliothek München

P.Muench. 1.1. Settlement: (Greek; 574 AD; Syene)



MUNICH: institute; collections



MURASUS: (cuneiform) archive of

See NIPPUR [B_379]



MURRABAT: (Greek) papyri; legal deeds from Nero’s reign


(as per H. Misgav)

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

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

See Murrabat 18.




See DJD.

P.Mur.: Discoveries in the Judaean Desert



MUSIC: is math


See WEAPONS; [B_506c]


See [B_390; KESKINTO; v3]



MUT-HETEP: (AE) funerary papyri of

(as per E.A. Budge) See BOTD.

See P. British Museum 10,010.



MYTHUS: papyrus

(as per AEMT) Seek Demotic P. Mythus at Leiden.





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