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Last updated 12/25/05

 

 

 

See images and analysis of ancient mathematical objects: IMAGE GRID

 

KAHUN: (AE; Hieratic) papyri

Hieratic Mathematical Papyrus (Dynasty [XI-] XIV).

 

Follow this link to a fragment (Kahun IV, 3, An Arithmetic Progression) with some linear progression/number theory notes by John Legon.

See same in DE 24 (1992).

http://www.legon.demon.co.uk/kahun.htm

 

Found in 1889 by (Professor) Sir William Matthew Flinders Petrie and

Published with images by Francis Llewellyn Griffith in:

[B_004,glyph tr.,IMG,notes filed with]  CATNYP# OBR+Griffith.

"The Petrie Papyri: Hieratic Papyri from Kahun and Gurob",

London 1898.

See Kahun LV.4

40 x 3 = 120

1/10 x 120 = 12

1 divided by (3/4) = 4/3

4/3 x 12 = 16

square root of 16 = 4

3/4 x 4 = 3

[Answer] 10 of 4 x 3 rectangles/bandages?

 

Find the 3,4,5 triangle! Reciprocals and ratios!

Find awareness of f(x): [((3/4)(sqrt2))^2]=(9/8)=1.125!

Find the circle! [interpret considering AE Pi]:

Consider 16 unit squares forming a larger square.

Consider the diagonal.

Diagonal=4(sqrt2)

3/4 of this diagonal=

(12(sqrt2))/(4)=3(sqrt2)=4.2426=~17/4=~4 1/4.

 

Note .75(sqrt2)=1.06066

[Note (1.06066)^2=1.124999=~9/8]

The difference of two perfect squares may be lurking here.

A square of sides =1.125 has an area of 1.125^2=1.265625

A square of sides =1.000 has an area of 1.000^2=1.000000

1.265625/(1)= 1.265625 and guess what! See it with my eyes.

The area of the largest possible inscribed circle within a square with sides = 1.125 would have its area determined via:

Circle Area=((8/9)diameter)^2

Interpreted AE Pi=256/81=~3.160493

Voila, a squared circle!

How close were they?

A circle as above, diameter=1.125,

Make the modern determination via the obvious formula.

 

Now, using Pi as 256/81, find how very close they were.

 

NO CATNYP, M. Cantor "Die Mathematischen Papyrus fragmente von Kahun" 1898, OLZ Volume 1 #10, 306-8.

 

Also mentioned without image in:

[B_003,IGNR] (CATNYP# OBM+Petrie) "Illahun, Kahun and Gurob :1889-1890", by Petrie with chapters by Professor Sayce.

 

Follow these links to S. Fryer's hieratic samples from Kahun.

http://home.prcn.org/~sfryer/kahun_letter2.html

and,

http://home.prcn.org/~sfryer/Hieratic/Samples/Neni1.htm

 

(as per A.H. Gardiner) Gurob AKA Ghurab, which is near Hawara.

 

(as per AEB 96.0955) See gynaecological P. Kahun.

 

See Kahun 8? Math.

 

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

See Papyrus Kahun II, I (MK; XII dynasty, 2000-1788 BCE.)

Legal content. See DJE I, pp. II ff., *13.

 

(See preliminary tr. by L. Bailey of Kahun LV.4)

 

See BUTO; reference from [B_406] to:

“Die chronologische Fixierung der agyptischen Mittleren Reich nach dem Tempelarchiv von Illahun.”

[Chronological adjustments of the MK]

See also CALENDAR.

 

(my analysis 051502):

Hieroglyph tr. of the Kahun fragment [IV.2].

From Clagett's V.3. [B_028]

 

This is a 2/3 through 2/21 fragment (only) for 2/odd numbers.

 

My modern style tr. follows in the same order as the hieratic fragment.

 

[answer]           preceeds                                               [question]

[unbolded items demonstrate workings]

 

2   2/3                                                                                       3

 

1/3  1/15  2/3  1  1/3                                                                   5

 

1/4  1/28  1/4  1/2  1  1/4                                                            7

 

1/2  1/18  1/2  1  1/6                                                                   9

 

1/6  1/66  1/6  2/3  1  1/6                                                            11

 

1/8  1/104  1/4  1/52  1/8  1/2  1  1/8                                13

 

1/2  1/30  1/2  1  1/10                                                     15

 

1/4  1/68  1/3  1/51  1/12  1/3  1  1/12                              17

[note: 17*12=204; 204/68=3; 204/51=4; 204/12=17]

 

*[1/6]  1/114  1/4  1/76  1/12  1/2  1  1/12                         19

[note: 19*12=228; 228/114=2; 228/76=3; 228/12=19]

[note: the bracketed  *[1/6]  does not exist on the papyrus fragment!]

 

1/2  1/42  1/2  1  1/14                                                     21

 

Although I have formatted this to bring attention to specific fractions, the hieratic does not include any

such distinctions except that some of the “workings” symbols are horus-eye parts.

 

See EL-LAHUN; LAHUN

 

http://members.aol.com/brucefriedmandcg/page26.html

 

http://www.cwru.edu/UL/preserve/Etana/papyri_kahun_gurob_text/ chapter4.pdf

For the text to [B_004]

See pages 15-18. Re: Math

(As per M. Silver; EEF; 021604)
Papyrus Kahun 13 which seems to deal with debts mentions the word wAwA.
In an article published in 1973 Ray offered the suggestion that this
term means "interest". <snip>

Images of the crucial plate #8 from text:
http://www.cwru.edu/univlib/preserve/Etana/papyri_kahun_gurob_plates/plate8.pdf

 

 

KAIRO: See CAIRO

 

 

KAMARA; KATSESHNI: See NAVILLE.

 

 

KARANIS: (Greek) papyri

(as per E. G. Turner) AKA Kom Aushim.

See GOODSPEED; Michigan.

 

P. Karanis Goodsp.: Papyri from Karanis.

P.Kar.Goodsp. 1.: (Greek; AD 158; from Karanis)

http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0142

Karanis=Karanidos

See NYU; [B_452=O_020,8.5,IMG]

Seek information of Julius Septimius Sabinus (~300 CE, Censitor)

 

See Soknopaiu Nesos.

[O_060,rvw]

NO CATNYP

BOBST# PA3352 .W52 Oversize

Karanis and Soknopaiu Nesos, studien zur geschichte antiker cultur-und personenverhaltnisse. Von Dr. Carl Wessely.”

Wien, 1902.

Translations of Greek papyri by:

Carl Wessely, 1860-1931.

 

[B_456=O_025,8.5,IMG]

CATNYP# STG (Michigan. University. University of Michigan Studies, Humanistic Series. V. 42-43)

BOBST# PA3305 .M5 v.4

“Tax rolls from KARANIS; edited by Herbert Chayyim Youtie, with the collaboration of Verne Brinson

Schuman and Orsamus Merrill Pearl.”

Ann Arbor, Mich., 1936-.

See BOBST Archive: O 1

Includes a collection of tax accounts

Roll 223: P. Cairo 57187

Roll 224: P. Mich Inv. 3159; 4171; 4910; P. Iand. VII, 141 [over 6400 lines]

*JANDA papyrus identified as a missing portion of this roll.

Roll 225: P. Mich Inv. 4172

“The 1st of three rolls unearthed at Kom Aushim (Karanis) by sebbakhin in 1924…”

“the 3 rolls together provided an unusually complete account of the daily collection of money taxes at

Karanis during 3 consecutive years in the second half of the second century A. D.” i.e. 150-200 CE

Lists of names; estates and payments received or due. Math. Accounts.

[Note about 100 years before Tetricus and his son the young prince Tetricus II abdicated Gaul to Aurelian.]

 

See YOUTIE; AURELIUS ISODORUS

[B_469=O_039,IGNR]

CATNYP# STG (Michigan. University. University of Michigan studies, Humanistic series. v.47)

BOBST# PA3305 .M5 vol.6

“Papyri and ostraca from Karanis <by> Youtie and Pearl.”

In the Humanistic Series [XLVII] of “Michigan Papyri.”

Edited and prepared by Herbert Chaim Youtie, 1904-?

Michigan, 1944 [-1951].

Translations of Greek papyri, No plates.

 

See also Giss.; Cairo; Chicago; Columbia:

 

KARATEPE: (Semitic, Phoenician) inscriptions; statues

commemorative inscriptions in Northwest Semitic, such as the example found at Karatepe, Cilicia (in Turkey) in 1947.

From,

http://www.flavinscorner.com/4-6-01.htm

See Dr. Gordon; PARAÍBA

 

DNWSI promotion:

In the Karatepe inscription, for example (KAI 26 ii 7-8, 13; cited in DNWSI, p. 473), Azitiwada recounts several reasons why a Cilician city ought to be named after him. One of these reasons is his ability to give its inhabitants a "pleasant dwelling" (<sem>$bt n(mt</sem>). DNWSI, citing this reference under the root <sem>y$b</sem>, lists the possibility that the Phoenician term should be derived from <sem>$bt</sem>, "to cease, rest," as well as <sem>y$b</sem>, "to sit, reside." In other words, <sem>$bt</sem> at Karatepe poses the same morphological and semantic ambiguities in its context as does htb#$ in Ruth 2:7. Seeing polysemantic ambivalence at Karatepe therefore better helps explain the versional options and strengthens the possibility that polysemantic variability might also be occurring in Ruth 2:7.

http://rosetta.reltech.org/TC/vol01/HoftijzerJongeling1996rev.html

 

KARATEPE: (Phoenician) inscribed statues:

On the back of the figure extending to below the waist was a 20-line Phoenician inscription, and scattered around were fragments of stone carved with hieroglyphics, suggesting the exciting possibility that this might be a bilingual inscription.

The next year (1947) excavations of this Late Hittite fort were led by Bossert and U. Bahadır Alkım. They discovered that the lion carved in relief was not actually a lion, but a bull - an animal held sacred by the Hittites - and that there were two of them. The figure which had stood upon the sacred bulls turned out to be the Storm God. But the bilingual inscription overshadowed all the other finds, and was to throw light on a little known period of Anatolia’s history. Comparison of the two texts, one in Phoenician and one in hieroglyphic Luwian, enabled the latter to be deciphered for the first time.

http://www.atamanhotel.com/karatepe.html

See Phoenicians; TRADE

 

 

KASR KARUN: (Greek; Ptolemaic) Temple at

See FAYUM; [B_075=O_002]

 

KELIM: ritual purifications

See TORAH; MISHNAH; TALMUD; CUBITS; HEBREW CUBITS

Notes from Encyclopaedia Judaica

V. 10 p. 899-900

 

Kelim (vessels) is the first section of the tractate Mishnah Tohorot.

1. Bava Kamma

2. Bava Mezia

3. Bava Batra

 

See Sidrei Tohorot (1873) by R. Gershon Hanokh Leiner

See also TARBIZ 16 (1945) p. 71 ff.

 

KELLEYS ISLAND: (American Indian) pictographs in Ohio, near Lake Erie

From American Indians ~?1200-1600 CE.

 

http://www.ohiohistory.org/places/inscript/

 

 

KELLIS: (Greek) papyri

P. Kell.: Greek Papyri from Kellis.

P. Kell 1.1.: (Greek; AD 293-94 ; from Kellis

http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0143

 

KEMET: full color; quarterly publication/ journal of AE

Inquire for publications to:

KMT Communications, Inc.

P.O. Box 1475, Sebastopol, CA 95473-1475

 

KENYON’S: (Greek) papyri

(as per D. Fowler) See Kenyon’s (Greek) Papyri ii , no. cclxv 40. Math.

 

(as per E. G. Turner) Kenyon, a classical scholar who joined the British Museum in 1889. Pursue the bibliography of F. G. Kenyon, “Egypt Exploration Fund Archaeological Reports”, 1892 and 1893, p 27.

(taken over in 1914 by JEA..; [B_303])

 

(as per F. Hultsch; [B_358a]) See “Kenyon Greek Papyri in the British Museum.”

 

 

KESKINTO: (Greek) astronomical inscription

(as per personal correspondence to; M. Gardner; 102802)

Recent efforts to wrestle with the fragmented remaining phraseology found at Keskinto:

(Note, the numerical conversions from this portion of the inscription were made in the same style of

Milesian Accounting we previously discussed when I figured out the Hibeh i, 27 parapegma).

(Also note, the items in quotes are my desperate attempt to represent the Greek letters with our alphabet in order to follow my references on the copies I sent you earlier.  This is followed by a poor phonetic representation of the Greek with my Brooklyn accent, and finally a definition [as per my helpful friends and Liddell and Scott's Lexicon]).

 

[lost 35 symbols]

" o' "                = owe = the [masculine]

"xuxlos"           = keeklose = circle.

"moirvw"           = mwahrohn = parts.

" tE' "               = tau sigmeh = 300 [+] 60 =360 [degrees?]

"stigmwv"         =steehmohn = points

"Dwx"               = Theta Psi kappa = 9000 [+] 700 [+] 20 = 9720

                           [*27ths of a degree of a circle of 360 degrees]

" h' "                 = eee = the [feminine]

"moipa"             = meerah = parts

"otigmwv"          = steeghmohn = [secondary points or sub-points]

"xS"                 = kappa *stigma [or *digamma] = 27

[end of phrase 1]

 

[lost 12-18 symbols]

"Deo]is"            = Thayoh = God [may actually = monotheism]

"X[a]pistnpiov"   = Kcharee-steeriohn = Thanks-offerings

[end of phrase 2]

 

Read phrase 1 - literally as a string:

[lost 35 symbols]…

"the circle parts 360 points 9720 the parts ['] secondary points 27."

[end of phrase 1]

 

Read phrase 2 - as noted:

[lost 12-18 symbols]

"Thanks-offerings [to] God!"

[end of phrase 2]

 

Milo, all I can scratch my head about is  - why divide a degree into 27ths?

What an unusual choice.

A trinity of trinities.

3^3=27

If harmonized with the Moon or the Cubit or the Sexagesimal system, the degree ought to be divided into some other number of sub-points. Many other numbers would seem more reasonable. Don't you think?

 

(as per personal correspondence; M. Gardner; 102902)

divide 9720 by 60, find: 162

divide 162 by 27, find 6

[same numbers, slightly different perspective, no clue as to why 27 got here.]

Ennead; i.e. Theolological interference?]

Consider this a factor in early keskinto-ish recognition of the precession of the equinoxes

[Why not?]

 

Other Bruce thoughts:

If the solar day (variable length of sunrise to second sunrise) is 9720 parts

Each of our modern minutes (lepta) is 6.75 parts [exactly]

Each of our modern seconds (lepta/60) is 0.1125 parts [exactly]

 

[O_001=Y_001(SYRACUSE!),8.5,TR ONLY,NO IMG]

NO CATNYP. BOBST# PA 27.I7 vol. 12 fasc. 1-3

Y_001=SUMMIT# CN360 I6 v.12 (sent to me as a loan 8/20/02)

The primary source text for analysis of the Keskinto astronomical inscriptions:

and Binding reads: “Inscriptiones Graecae XII 1-3 SVPPLEMENTVM”

Internal cover page heading reads: “Inscriptiones Insvlarum Maris Aegaei Praeter Delvm”

Part one: Rhodi [Island of Rhodes] = Fasciculus I

Fasciculus I = “Inscriptiones Rhodi Chalces Carpathi Cvm Saro Casi Cosilio et Avctoritate Academie

Litterarvm Regiae Borvssicae Edidit Friderichvs Hiller de Gaertringen”

“Berolini Apvd Georgivm Reimervm”

“MDCCCXCV”

[I believe this scholarly Tome was bound with Fasciculus II and Fasciculus III in 1895 [2 years after the 1893 discovery/archeological voyage to Rhodes] and/or 1939.

Item 913: on page 148-149 and its corrigenda referenced to item 913 on page 207!

 

This was harder to find than love.

 

KESKINTO notes and annus vagus considerations filed with [O_001].

 

Melita, help!

Review the block Greek of the rest of [O_001] which interests me for astronomical pursuits.

 

As follows:

KATAPLATOS

 

KA ‘ ASXHMA

KATAMHKO[S]

KATABASOS

RYPOINTOS

RYPOENTOS

ThAI /// ONTOS

Th /// ESTONTOS

 

//////////APOMAI

//////////E ODOI

IOIDOAKOI

TROPIKOI

REPOMAI?

ETCETERA!

 

See link below:

http://www.bbaw.de/forschung/ig/pub.html

See IG; [O_001]

 

See PALMISTRY; PETERHOUSE; CLOCKS; work by Derek Price.

 

http://encyclopedia.astrologer.ru:8005/cgi-bin/guard/V/veliky_god.html

web link above includes reference to KESKINTO

Investigate and translate

See sexagesimal considerations and Sidereal and synodic discussion.

Avtor Prodolzhitel'nost' velikogo goda

Diogen Stoik 6 480 000 let

Kassandr 3 600 000 let

Beros 2 160 000 let

Antioh 1 753 005 let

Nadpis' iz Keskinto 291 400 let [great year of 291,400 solar years]

Orfei 120 000 let

Geraklit (po Aetiyu) 18 000 let

Geraklit (po Cenzorinu) 10 800 let

Gippas 59 let

 

[B_439; 8.5;NO KESKINTO]

CATNYP# BVX (Guerin, V. Voyage dans l’ile de Rhodes et description)

“Voyage dans l’ile de Rhodes et description de cette ile.”

Paris, Durand, 1856.

By Victor Guerin (1821-1891)

Includes folding map and bibliography which does not refer to the KESKINTO inscription.

7/6/02 copied map (1) and cover only – original crumbling and bibliography not useful as I determined the

inscription was discovered after publishing of this text!

 

(as per D. Fowler) See Rhodes, IG xiii(1) 913.

See the (Greek) division of a circle into 360 parts. Sexagesimal math.

See HAMA ii, 590 ff. and 698 ff.

 

14. Astronomical inscription from Keskinto / Rhodos / Greece

"The Large Year takes 291,400 years" (i.e. 200 x 31 x 47 years). Annual details for sidereal and synodic circulation of the planets read:

Merkur:  291400 / 918,700;

Mars:  154,920 / 136,480;

Jupiter 24,500 / 266,900;

Saturn 9,920 / 281,480.

http://www.calendersign.ric.at/english/turnofage1.htm

 

(as per Gallica link below) See: “Comptes rendus hebdomadaires des seances de l’Academie des sciences / Institut de France.” Janvier 1895.

[B_356,IGNR,KESKINTO] CATNYP# *EO 1426 [indexes to title above] must be requested from the NYPL Annex, ughh.

http://gallica.bnf.fr/Fonds_Tables/000/M0003076.htm

Makes mention of this inscription as analyzed by M. Paul Tannery.

 

Note [B_356]; [1895] Gallica article by P. Tannery is the same as that in:

[B_390] V2: “Sur l’inscription astronomique de Keskinto.”

The only Keskinto study I do not have at hand is that by Derek Price.

I have yet to identify the text, if any, Price's study appears in.

 

See also [B_387].

 

[B_387,no img,IGNR,SIBL] CATNYP# JSC 84-25

“Recherches sur l’histoire de l’astronomie ancienne / Paul Tannery.”

Hildesheim ; NY; Georg Olms, 1976.

No significant review of KESKINTO.

 

[B_388,IGNR,SIBL] CATNYP# *ZV-163

“Pour l’histoire de la science hellene [microform], par Paul Tannery. De Thales a Empedocle.” Paris, F. Alcan, 1887.

 

See also Math: prior to 1601.

 

[B_389,IGNR,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.

 

[B_390,8.5,KESKINTO,SIBL] CATNYP# OAL (Tannery, P. Memoires scientifiques) Library has: v. 1-13.

“Memoires scientifiques, publies Par J.-L. Heiberg & H.-G. Zenthen   I   Sciences Exactes Dans

L’Antiquite 1876-1884.” Toulouse, 1912-

Johan Ludvig Heiberg and Hieronymous Georg Zeuthen.

NOTES FROM V1:

PAUL TANNERY

 

MEMOIRES SCIENTIFIQUES

PUBLIES

PAR

J.-L. HEIBERG & H.-G. ZEUTHEN

[Johan Ludvig Heiberg and Hieronymous Georg Zeuthen.]

II

SCIENCES EXACTES DANS L’ANTIQUITE

1876-1884

 

1912

 

Entries in this set of volumes sometimes noted as:

“Extraits des Memoires de la Societe des sciences physiques et naturelles de Bordeaux.”

Or,

“Extrait de la Revue archeologique.”

 

 

Includes articles on the following:

 

1. [1876] Note sur le systeme astronomique d’Eudoxe [EUDOXUS].

[Assumed circular planetary orbits.]

2. [1876] Le nombre nuptial de Platon. [PLATO]

3. [1876] L’hypothese geometrique du Menon de Platon. [Plato]

4. [1878] Hippcrate de Chio et la quadrature des lunules [Hippocratus/Quadrature of the Lunes]

5. [1878]. Sur les solutions du probleme de Delos par Archytas et par Eudoxe

6. [1879]. A quelle epoque vivait Diophante. [DIOPHANTUS]

8. [1880] L’arithmetique des Grecs dans PAPPUS.

9. [1881] Sur l’age du pytharoricien Thymarids [PITAGORAS]

11. [1881] Sur le probleme des boeufs d’Archimede. [ARCHIMEDES]

14. [1882] Sur les fragments de Heron d’Alexandrie conserves par Proclus. [HERO; HULTSCH]

18. [1882] L’arithmetique des Grecs dans Heron d’Alexandrie. [HERO; HULTSCH]

19. [1882] Sur la mesure du cercle d’Archimede

20. [1882] De la solution geometrique des problemes du second degre avant Euclide. [EUCLID]

23. [1883] Sur une critique ancienne d’une demonstration d’Archimede.

24. [1883] Second note sur le systeme astronomique d’Eudoxe.

25. [1883] Le fragment d’Eudeme sur la quadrature des lunules [Hippocratus/Quadrature of the Lunes]

26. [1883] Aristarque de Samos [ARISTARCHUS]

27. [1883] Stereometrie de Heron d’Alexandrie. [HERO; HULTSCH]

28. [1883] Etudes heroniennes. [HERO; HULTSCH]

29. [1883] Sur le <<modius castrensis>>. [MODIUS; ASTRONOMY]

See p. 464-5

 

Notes from article 1:

Note sur le systeme astronomique d’Eudoxe.

About 400 BCE the influence of systems of astronomy similar to or yielded from the works of Eudoxus arise. Concentric orbits are considered perfect and beautiful and holy and as God is a perfect being he would build the heavens with circles. Sidereal and diurnal conflicts were noticed but not resolved by this theory. Callipus noted lunar movements inconsistent with the circle. Retrograde conflicts [mercury] further disproved circular orbits. A trigonometric lesson in how to attain cognizance of the fact that the orbits do not conform to circles and to find the quadrature of the Lunes [if they did], presented by Tannery and Schiaparelli is given on page 3 and ff.

 

Notes from article 29.

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

 

 

 

NOTES FROM V2:

PAUL TANNERY

 

MEMOIRES SCIENTIFIQUES

PUBLIES

PAR

J.-L. HEIBERG & H.-G. ZEUTHEN

 

II

SCIENCES EXACTES DANS L’ANTIQUITE

1883-1898

 

1912

 

Includes articles on the following:

31. [1884] Sur l’authenticite des axiomes d’Euclide [EUCLID]

32. [1884] Sur les manuscrits de Diophante a Paris [DIOPHANTUS]

33. [1884] La pert de sept livres de Diophante [DIOPHANTUS]

34. [1884] Sur la langue mathematique de Platon [PLATO]

38. [1885] Sur l’arithmetique pythagoricienne [PITAGORAS]

43. [1886] La coudee [CUBIT] astronomique et les anciennes divisions du cercle. [CALENDAR]

46. [1888] La grande annee d’Aristarque de Samos [Aristarchus; CALENDAR; CHINESE REMAINDER THEOREM]

47. [1887-8] Etudes sur Diophante. [DIOPHANTUS]

48. [1889] Le hypothese geometrique du Menon de Platon. [Plato]

49. [1889] L’art d’Eudoxe. [EUDOXUS]

50. [[1891] Les manuscrits de Diphante a l’Escorial. [DIOPHANTUS]

51. [1891] Sur une epigramme attribue a Diophante [DIOPHANTUS]

51b. [1892] Note sur un passage de Theon de Smyrne, De Musica

[See DIOPHANTUS]

53. [1894] Un fragment des Metriques de Heron. [HERO, HULTSCH]

54. [1894] Sur un fragment inedit des Metriques de Heron d’Alexandrie. [HERO, HULTSCH]

55. [1894] Sur Theon de Smyrne

56. [1895] Sur un passage de Theon de Smyrne

58. [1895] L’inscription astronomique de KESKINTO.

59. [1895] Sur l’inscription astronomique de KESKINTO.

60. [1895] Une inscription grecque astronomique.

61. [1895] Sur les subdivisions de l’heurs dans antiquite.

62. [[1896] Sur la religion des derniers mathematiques de l’antiquite.

 

Notes from article 58. [copy all]

L’inscription astronomique de KESKINTO.

 

The Astronomical inscription at Keskinto [Rhodes]

 

p. 487

Eudoxus is from Cnide?

 

The Keskinto [town] inscription at Rhodes [island] has been dated by its content in that the theories of heavenly bodies, to be interpreted from the accurate data [via astrolabe or similar devices] inscribed, is not still suggestive of a belief that the motions of these bodies lied in concentric circles. The introduction of eccentric epicycles about the time of Hipparchus abandoned Eudoxus and others’ principles in an effort to better resolve this refined data and harmonize the perpetual calendar. This change and this inscription therefore occurred after 250 BCE [in Greek territory].

 

[Tannery here refers to his work in [B_437]; 1893, p. 252 et suiv]

 

p. 488

The incompleteness of the inscriptions does not permit a clear demonstration of the extent to which the theory of eccentric heavenly orbits was defined.

 

This inscription is dated to the period between 150 BCE and 50 BCE.

 

Found by M. Hiller von Gaertringen, de Berlin, in June of 1893.

Image source text referenced.

By Hiller:

Inscriptiones Graecae insularum maris Aegaei, fasciculus I, No. 913.

Cf. les Corrigenda, p. 207.

CATNYP# JFE 99-13015

See IG; [O_001]

 

p. 489

Ask Melita what is Kleemachkthress [thanks-offerings]

(as per M. Cherepuhin) The word is Klee makh trios

Circle divided into 9720 parts yielding 27 parts per degree

i.e. 27x360=9720

 

p. 492 Use longitude in tr. in lieu of elongation.

 

p. 493

Precession of the equinoxes assumed not specifically known at time of this inscription.

 

p. 494

Great year assumed to correspond to 291,400 years of 365.25 days.

See DRESDEN CODEX.

 

p. 497

Paul Tannery notes his lack of confidence in the accurate date of the inscription.

 

p. 499, article: “L’Inscription Astronomique de Keskinto.”

A second reference to the source text: IG, I, item 913, cf. corrigenda p. 207

 

p. 502, article: “Une Inscription Grecque Astronomique.”

 

p. 503

Tannery notes that each surviving “number” on this inscription [Keskinto] has more than one possible interpretation.

 

p. 505

Some of the numbers appear based on an assumed constant.

 

p. 506

Hipparchus said to have made standard the cubit as a measurement of two degrees at the ecliptic.

180 cubits = 360 degrees of ecliptic

 

p. 507

The portion of the insciption likely to yield lunar data is absent or destroyed.

 

p. 512

Prior to Ptolemy [VII?] the work of Theon de Smyrne [Smyrna], which can be seen in Astronomie 27, do not give evidence of the precession of the equinoxes.

 

p. 515

291,400 [great year] = 2^3 x 5^2 x 31 x 47 = 200 x 31 x 47.

 

p. 517, article: “Sur les subdivisions de l’Heure.”

Chaldean influence on Greek Astronomy.

Reference: Uranologion de Petau, 137 D.?

 

p. 518

Showing more of the literary inscription at Keskinto.

 

p. 522

One LEPTA?=12 Minutes

One Point = 3 Minutes

One Point = 12 ICTUS

One ICTUS = 15 seconds

120 LEPTA = One day

 

Get Melita’s HELP!

Melita said Leptoh is the modern Greek for MINUTE!

Lepta is plural, i. e. minutes.

 

 

p. 523

1/5 hour [LEPTA or PUNCTI] may be a Sumerian division of the hour.

 

 

 

 

NOTES FROM V3:

PAUL TANNERY

 

MEMOIRES SCIENTIFIQUES

PUBLIES

PAR

J.-L. HEIBERG & H.-G. ZEUTHEN

 

III

SCIENCES EXACTES DANS L’ANTIQUITE

1889-1913

 

1915

 

Includes articles on the following:

68. [1900] Sur les problemes macaniques attribues a Aristote

69. [1901] Le Philosophe Aganis est-il identique a Geminus?

69b. [1902] Note sur le probleme de PAPPUS

71. [1902] Du role de la musique grecque dans le developpement de la mathematique pure. [MUSIC].

72. [1902] Sur un point d’histoire de la musique grecque. [MUSIC].

73. [1902] Sur les intervalles de la musique grecque. [MUSIC].

76. [1903] Heronis Alexandrini opera quoe supersunt omnia (vol. III) [HERO; HULTSCH]

78. [1903] Y-a-t-il un nombre geometrique de Platon? [PLATO]

79. [1904] Notes critiques sur les <<metrica>> de Heron. [HERO; HULTSCH]

81. [1904] Inauthenticite de la <<Division du Canon>> attribuee a Euclide [EUCLID]

82. [1904] A propos des Fragments Philolaiques sur la musique [MUSIC]

83. [1905] Un traite grec d’arithmetique anterieur a Euclide [EUCLID]

84. [1905] Notes sur trois manuscrits grecs mathematiques de Turin.

87. [1911] Sur le Spondiasme dans l’ancienne musique grecque. [MUSIC]

89. [1913] L’evolution des gammes antiques [GAMES]

90 Articles de la Grande Encyclopedie:

Anatolius d’Alexandri

Appolonius

Archimede

Arithmetique

Astronomie

Cleomede

Conon

Diophante

Eratosthene

Euclide

Eudoxe

Geometrie

Porisme

 

NOTES FROM V4:

PAUL TANNERY

 

MEMOIRES SCIENTIFIQUES

PUBLIES

PAR

J.-L. HEIBERG

 

IV

SCIENCES EXACTES CHEZ LES BYZANTINS

1884-1919

 

1920

 

Includes plates / descriptions of the following:

1. Manuscrit Grec 1928 de la Bibl. Nat. de Paris.

2. Manuscrit Arabe 2697 de la Bibl. Nat. de Paris.

3. and 4. Manuscrit Arabe 2631 de la Bibl. Nat. de Paris. [medicine]

5. and 6. Manuscrit Grec 2424 de la Bibl. Nat. de Paris. [astrological]

7. and 8. Manuscrit Latine 7354 de la Laurentienne.[Geomantiques?]

9. Manuscrit Francais 14778 de la Bibl. Nat. de Paris. [Jewish Astronomy; Levi; Goldstein]

See the following article numbers:

1. [1884] Manuel Moschopoulos et Nicholas Rhabdas [RHABDAS]

4. [1885] Notice sur les deux lettres arithmetiques de Nicolas Rhabdas/ Nicolas Artavasde de Smyrne, le Rhabdas

8. [1888] Notes critiques sur le traite de l’astrolabe de Philipon [AE influence]

9. [1892] Psellus sur la Grande Annee [Chinese remainder theorem; calendar]

 

 

[B_390b,pursue,KESKINTO]

“Scientific Memoires, Volume II, Exact Sciences in Antiquity, 1912.”

Reprint 1995

See KESKINTO in 1895 section of above work.

For sale via “Editions Jacques Gabay”

 

[B_537, cvr copy only,SIBL,NO KESKINTO IMG]

CATNYP# OSF (Herz, N. Geschichte der Bahnbestimmung von Planeten und Komenten)

“Geschichte der Bahnbestimmung von Planeten und Komenten / von Norbert Herz.”

Leipzig, two volumes, 1887-1894.

Primarily a discourse on ancient orbit theories but exclusive of analysis of the inscription from Keskinto.

Vol. 1: Die theoren des alterthums; Vol. 2: Die empirischen methoden

 

[B_540, NO KESKINTO IMG,8.5]

“Jahrbuch des Kaiserlich Deutschen Archaologischen Instituts”

“Band IX 1894”

“mit dem beiblatt Archaologischer Anzeiger”

“Berlin, Druck und Verlag von Georg Reimer, 1895”

CATNYP# MTGA (Archaologisches Institut des Deutschen Reiches. Jahrbuch). Berlin. 1890-1950; See old card catalog: V. 33; p. 318; card 15

Included on page 125 is a copy from “Archaologischer Anzeiger” of the preliminary notice of the discovery of the Keskinto inscription but no image. This brief detail of the inscription specifies again the division of the circle of 360 degrees into 9720 sub points. Note Keskinto shown as “Keskindos.”

An excerpt from the inscriptions’ content noted as follows:

                                                                        links                 rechts

Thainontos kata             mnxos swidiakoi            910000              ……

                                    Platos tropikoi               919216                98 

                                    Bados peridpomai          1007976              1760

                                    Oxnma diesodoi 1008158            2 1480

Note: These numerical entries are reasonably challenged by Paul Tannery in his corrigenda on p. 207 in Inscriptiones Graecae.

 

Also see similar continuation of this collection:

[B_540b,ignr]

CATNYP# M-10 8642

“Archaologischer Anzeiger”

Berlin, 1963-?

See numerous varied titles for previous collections.

 

See CLOCKS; [B_539,8.5,SIBL] by Derek Price.

This article [B_542] published by Norbert Herz [b. 1858, d. 1927] 1894:

“Uber eine unter den Ausgrabungen auf Rhodos gefundene astronomische inschrift.” Within [?!] S.B.

[probably sitzungsberichte] der math.-nat. Classe d. Kaiserl. Akad. D. Wiss. [Wien] 103, Abt. Ila (1894)

pp. 1135-1144 =[B_542]

With a source image; plate/photo on p. 1144 [upside down]!

[Note: Norbert Herz also wrote “Keplers Astrologie”, 1895]

[B_542=Y_017,ANNEX,INP_110702,NG_110902,rcvd010503 (from Minnesota)_poor IMG]

CATNYP# *EF A317=NOT AVAILABLE!

NOT IN CATNYP, see old catalog volume 13, p. 316 card 18 AND:

Volume 13, p. 317, card 3

“Akademie der Wissenschaften. Vienna. Mathematische-Naturwissenschafte Klasse. Sitzungsberichte. 1894” CATNYP COPY NOT IN SERVICE!

Requested copies from Summit/Syracuse University on 110902.

Also, possibly available at Princeton University.

Copies and critical source image acquired 010503 third party via NYPL and the University of Minnesota.

 

Of note: related text:

[in which Hiller v. G. is quoted and refers to the LOST KESKINTO inscription stone!]:

Hiller v. Gaertringen [1942] F. Hiller v. Gaertringen [rev. of] Chr. Blinkenberg et K. F. Kinch, Lindos II. Gottingische Gelehrte Anzeigen 204 (1942) pp. 161-169.

 

[B_543,IGNR,SIBL]

CATNYP# JSD 86-619

“Little science, big science—and beyond / Derek J. de Solla Price.”

New York, 1986.

No Keskinto references

 

[B_544,Pursue!,42nd st!]

CATNYP# KAV (Herz, N. Lehrbuch der Mathematischen Geographie)

“Lehrbuch der Mathematischen Geographie / von Norbert Herz.”

Wien, 1906.

Seek Keskinto references

 

http://www.kuffner.ac.at/eng/history/herz.html

Biographical information on Norbert Herz; [Huffner; Astronomical Society, Germany.]

 

My notes:

A Great year: 291400 years  /  1460     =          199.5890411

A Great year: 291400 years  /  1461     =          199.4524298

Almost 200 ancient egyptian Sothic cycles is this Great Year Period.

Determine these decimal extensions as a series of AE unit fractions!!!!!!

Two such 1460/1461 year periods desrcibe the duration of ancient egyptian history to this time!

100 BCE + 1460 + 1460 = 3020 years, this seems about right. The timeline length of known recorded

astronomical data.

It does seem reasonable to conjecture that from the 3000 year period of reconstructing temples for use in

astronomical alignments and measurement, that the Egyptians would have noticed the shifting trend of the

Temples'

alignments and hence were somewhat aware of the precession of the equinoxes.

 

Keskinto search status:

Note, as per Otto Neugebauer in HAMA: Prof. Derek Price [AKA Derek John de Solla Price [1922-1983] of

Yale University] obtained a new squeeze [of the Keskinto Inscription] after World War II.

Although I don't know if Mr. Price ever published this image, he may have. I hope so.

I cannot find any further data. Can your contacts assist?

 

Meanwhile the HAMA lead on the first published squeeze by Norbert Herz in 1894/5 is a dead end here in

NYC.

I may find this at Syracuse University, still digging.

Probable squeeze source by Norbert Herz [b. 1858, d. 1927] as follows:

CATNYP# *EF A317

[Finally found in Minnesota!]

NOT AVAILABLE!

"Akademie der Wissenschaften. Vienna. Mathematische-Naturwissenschafte Klasse. Sitzungsberichte. 1894"

FIND PAGE 1144!

 

In search of data on keskinto squeeze:

Digging for Norbert Herz, footnoted in HAMA by O.N., I find:

Catalog of Items in the Nietz Old Textbook Collection

Books listed in this catalog are located in Special Collections, University Library System, University of Pittsburgh, 363 Hillman Library (Telephone: 412-648-8190). Only 33 titles of this 16,000 volume print collection are available in digital form at this time.

http://digital.library.pitt.edu/nietz/biblio/search.html

Another work by Norbert Herz is noted.

 

Otto's HAMA footnote as it appears:

Herz, Norbert [1894] Uber eine unter den Ausgrabungen auf Rhodos gefundene astronomische inschrift.

S.B.

der math.-nat. Classe d. Kaiserl. Akad. D. Wiss. [Wien] 103, Abt. Ila (1894) pp. 1135-1144

 

[See HAMA]

Note HAMA pages 590ff is misc info and 698-705 is Keskinto specific!

 

“the last line of the text (preceeding the dedication) contains the statement

…] the circle (contains) 360 degrees (moipwv) 720 “points”

(stigmwv) of the circle [a drawn circle]. One degree contains [2] points.”

 

My note to readers: see how this differs from the IG analysis!

[9720 points and 27 sub-points!]

 

Neugebauer [Henceforth O.N.] states the planets are ordered thusly:

[Venus]-Mercury-Mars-Jupiter-Saturn; i.e. the same order found with Archimedes.

 

[O.N.] For each one of the outer planets are listed four sets of integers, called, respectively,

*kata mnkos lwdiakoi [zodiacal longitutes=L]

*kata platos tropikoi [latitudinal variations=B]

*kata bados peridpomai [rotations in depth=G]

*kata oxnma diesodoi [returns in phase=A]

 

*Note my approximation of the Greek is only for recognition purposes and is NOT phonetically viable. I

wish to avoid inserting a Greek font into my website. Persons requiring scans may contact me:

brucefriedmandcg@aol.com

 

p. 700:

 

Mars

n                      l0 n

L          [1]74[9]2                       174920

B          [17]436                         174360

G          [ ]                                 491680

A          [ ]                                 136480

 

Jupiter

n                      l0 n

 

L          [2157]                           21570

B          [215]6                           21560

G          24260                           242600

A          26690                           26[6900]

 

Saturn

n                      l0 n

L          [ ]                                 [ ]

B          [ ]                                 9810

G          [2]7176                         [27]1760

A          [2]8148                         2[8]1480

 

 

[O.N.] 1. In any planetary theory the revolutions of the planet in longitude (L) and the number of corresponding phases (A) should satisfy the following identity

number of sidereal rotations + number of synodic periods =

number of sidereal years

 

Consequently we should expect L + A = N0

 

With probably the same value N0 for all planets. This assumption is easily tested. We know, e.g., from the Babylonian “Goal-year texts” how many synodic periods S correspond to N years:

Mars: N=79   Jupiter: N=71  Saturn: N=59

          S=37                S=65               S=57

 

Hence we should expect that in our text

 

A*(N/S)~=N0

 

This is indeed nearly the case

 

Copies from SBAW or similar keskinto squeeze quest goodies may be available via CAS.

CAS=Chemical Abstracts Service P: 800 753-4227

[unrelated item]

Diesing, K. M. 1861. Revision der Nematoden. Sitzungsb. K. Akad. Wissensch. Wien, Math.-Naturw. Cl. 42 : 595. looks like same name as keskinto squeeze source!

 

Melita, thanks! Help arrives on 101703:
Review of the block Greek of the rest of [O_001].
Elias, thanks! More help arrives on 020404:

 

As follows:
Column E (probably repeated at Column A) on [O_001]
[as per P. Tannery interp.; MISSING from block text]
Phosphorooh=Radiant [a/p Elias]
Steehlvohndos=
Peeroh-endos=[endos=inside a/p Elias]
Peeroh-endos=
Peeroh-endos=
Peeroh-endos=
Fayathohndos=
Fayathohndos=
Fayathohndos=
Fayathohndos=
Fehnohndos=is seen/is showing
Fehnohndos=is seen/is showing
Fehnohndos=is seen/is showing
Fehnohndos=is seen/is showing

 

Column F (probably repeated at Column B) on [O_001]
?????????a= who knows?
Kata ???kos= who knows?
Kata platos= by the width (or length)
Kata vathos=
[looks like: KA ‘ ASXHMA]=
Kata sskheema= As per the plan (i. e. by design)
Kata meekhos=by the length [a/p Elias]
Kata platos= by the width (or length)
Kata vathos=very deep/in depth/detailed
Kata sskheema= As per the plan
Kata meekhos=
Kata platos= by the width (or length)
Katavathos=very deep/in depth/detailed
Kata sskheema= As per the plan
[as per P. Tannery interp.; MISSING from block text]
Kata meekhos=
Kata platos= by the width (or length)
Katavathos=very deep/in depth/detailed
Kata sskheema= As per the plan
Kata meekhos=
Kata platos= by the width (or length)
Katavathos=very deep/in depth/detailed
Kata sskheema= As per the plan

 

Column G (probably repeated at Column C) on [O_001]
The-ex-oh-thee=The exits? [a/p Elias]
Zoh-ee-thee ahkhee=[Zoh-ee=life]=
[looks like TROPIKOI]=Trohpeekee= a function of three {?}
Pehreethrohmeh=circumference?; Orbit?; Road/roundabout ?[a/p Elias]
Theeexohthee=
Zoh-ee-thee ahkhee=[Zoh-ee=life]=
Trohpeekee=
Pehreethrohmeh=
Theeexohthee=
Zoh-ee-thee ahkhee=[Zoh-ee=life]=
Trohpeekee=
Pehreethrohmeh=
Theeexohthee=

 

Column D (probably related at Column H) on [O_001]
*Column D is NOT identical to column H!
missing line

 

Mu [accented by Lambda? lost 2nd symbol?]=
meaning probably 10000 * (30?+?) = 300000?
Zeta? [accented by convex bowl?]= 7000?
meaning probably 1000 * (7?) = 7000?
Upsilon=400
?????=??
Beta accented’=2/3
TOTAL of MZU B’=307400? +2/3

 

Mu [accented by Lambda? lost 2nd symbol?]=
meaning probably 10000 * (30?+?) = 300000?
Theta? [accented by convex bowl?]= 9000?
meaning probably 1000 * (9?) = 9000?
Upsilon=400
Lambda=30
Stigma=6
TOTAL of MTULS=309436?
*Note: Zero Milesian symbol may follow? If so, adjust to 3094360?

 

Mu [accented by Lambda? lost 2nd symbol?]=
meaning probably 10000 * (30?+?) = 300000?
Damaged

 

Mu [accented by Lambda? lost 2nd symbol?]=
meaning probably 10000 * (30?+?) = 300000?
Damaged

 

Mu [accented by?]=
meaning probably 10000 * (?) = ?
Damaged

 

Mu [accented by?]=
meaning probably 10000 * (?) = ?
Damaged
Iota=10
Stigma=6 accented
TOTAL of M??IS’= ?? 16th

 

Mu [accented by Beta]=
meaning probably 10000 * (2) = 20000?
Delta [accented by convex bowl?]= 4000?
meaning probably 1000 * (4?) = 4000?
Sigma=200
Xi=60 accented
TOTAL of MDSX’=24260?

 

Mu [accented by Beta]=
meaning probably 10000 * (2) = 20000
Stigma [accented by convex bowl?]= 6000?
meaning probably 1000 * (6?) = 6000?
Chi=600
Qoppa=90 accented
TOTAL of MSXQ’=26690

 

Sampi Iota? (or Sampi Mu?)=
Meaning probably 910
[P. Tannery sugests 910000]

 

Sampi Mu Theta Sigma Iota Stigma zero symbol?=
Meaning probably 9491600
[P. Tannery sugests 919216] WHY?

 

Mu [accented by Pi]=
meaning probably 10000 * (80)= 800000
Zeta [accented by convex bowl?]= 7000?
meaning probably 1000 * (7?) = 7000?
Rho=100
Omicron=70
Stigma accented=6
TOTAL of MZROS’=807176
[P. Tannery sugests 1007176] WHY?

 

Mu [accented by Pi]=
meaning probably 10000 * (80)= 800000
Eta [accented by convex bowl?]= 8000?
meaning probably 1000 * (8?) = 8000?
Rho=100
Mu=40
Eta accented=8
TOTAL of MERME’=808148
[P. Tannery sugests 1008148] WHY?

 

Column H (probably related at Column D) on [O_001]
*Column H is NOT identical to column D!
qoppa eta ??[98?]

 

Mu [accented by Iota Zeta]=
meaning probably 10000 * (10+7) = 170000
Delta [accented by convex bowl]=
meaning probably 1000 * (4) = 4000
?Sampi=meaning probably 900
Kappa=20
TOTAL of MDSK=174920

 

Mu [accented by Iota Gamma]=
meaning probably 10000 * (10+3) = 130000
Delta [accented by convex bowl]=
meaning probably 1000 * (4) = 4000
Tau=300
Xi=60
TOTAL of MDTX=134360

 

Mu [accented by Mu]=
meaning probably 10000 * (40) = 400000
Alpha [accented by convex bowl]=
meaning probably 1000 * (1) = 1000
Chi=600
Pi=80
TOTAL of MACP=401680

 

Mu [accented by Iota Gamma]=
meaning probably 10000 * (10+3) = 130000
Stigma [accented by convex bowl]=
meaning probably 1000 * (6) = 6000
Upsilon=400
Pi=80
TOTAL of MSUP=136480

 

Mu [accented by Beta]=
meaning probably 10000 * (2) = 20000
Alpha [accented by convex bowl]=
meaning probably 1000 * (1) = 1000
Phi=500
?Omicron=70
TOTAL of MAPO= ?21570

 

Mu [accented by Beta]=
meaning probably 10000 * (2) = 20000
Alpha [accented by convex bowl]=
meaning probably 1000 * (1) = 1000
Phi=500
Xi=60
TOTAL of MAPX= 21560

 

Mu [accented by Kappa Delta?]=
meaning probably 10000 * (24) = 240000
Beta [accented by convex bowl]=
meaning probably 1000 * (2) = 2000
Chi=600
??Omicron=70
TOTAL of MBCO= ?242670

 

Mu [accented by Kappa Stigma]=
meaning probably 10000 * (26) = 260000
rest is damaged/missing

 

missing next line

 

Theta Omega Iota?
Meaning probably= 9 – 10 –800?
[P. Tannery suggests 9810]
Bruce to investigate source image (when found) to determine
if crescent appears over the Theta as noted in above
equality.

 

Mu Alpha Chi Xi
Meaning probably= 40 – 1 – 600 - 60?
[P. Tannery suggests .1760] WHY?
Bruce to investigate source image (when found) to determine
if fraction accent appears over the Mu and all symbols as
noted in above equality.

 

Mu [accented by Kappa Iota?]=
meaning probably 10000 * (20 + 10) = 300000
Alpha [accented by convex bowl]=
meaning probably 1000 * (1) = 1000
Epsilon=500
Pi=80
TOTAL of MAPX= 301580
[P. Tannery suggests 281480] WHY?
Bruce to investigate source image (when found) to determine
if Iota accent appears over the Mu or if this might be an Eta
as P. Tannery guesses as noted in above equality.

 

See also this relevant link:
http://www.calstatela.edu/faculty/hmendel/Ancient%20Mathematics/Philosophical%20Texts/Astronomy/Simplicius%20InDeCael.pdf

 

[B_590,SIBL, no copy]
CATNYP# *OAC (Sarton, G. A. L. Study of the History of Mathematics)
The Study of the History of Mathematics, and the Study of the History of Science.”
New York, Dover Publications, 1957 reprint, 1936.
Suggested by Judy Caruso, Librarian at SIBL.
See [B_595] below.

 

[B_595,SIBL, no copy,no keskinto img]
CATNYP# *OAC (Sarton, G. A. L. History of Science)
“A History of Science.”
Cambridge, Harvard University Press, 1952-1959.
A brief mention of the Keskinto incription in the second volume does not include any numerical data or a reference text for a source image.

 

Other Bruce thoughts; 111704:
How many seconds or decimal minutes is one part?
Given: (360*27=)9720 parts = 24 hours = 1440 minutes = 86400 seconds
1 part = 86400/9720 = 8 8/9 seconds per part
9 parts = 80 seconds = 1 1/3 minutes = 4/3 minutes
See HIBEH; EUDOXUS.
27 parts = 240 seconds = 4 minutes.
What typically occurs in four minute intervals.
Perhaps an astronomical/astrological sighting or other.

 

See:
http://www.br-online.de/alpha/forum/vor0304/20030422_i.shtml
Dr. Sylvia Schoske, director of the Staatliches Museum
Ägyptischer Kunst München, April 22, 2003 (transcript)
http://www.br-online.de/alpha/forum/vor0304/20030422_i.shtml

 

NOW translate corrigenda p. 207 KESKINTO!

 

Traianos Gagos,
{From: "traianos" <traianos@UMICH.EDU>}
Subject: (Con)Textual Encounters in Egypt: Bridging the Disciplinary
Divide Between Archaeology and Papyrology

 

Associate Professor of Greek and Papyrology,
Archivist of Papyrology, and
President, American Society of Papyrologists

Addresses:

Department of Classical Studies
The University of Michigan
2160 Angell Hall
Ann Arbor, MI 48109-1003, USA
Tel. +(734) 647-3290
Fax + (734) 763-4959

 

http://www.chass.utoronto.ca/~ajones/documents/Keskinto_Translation.htm

 

**FIND Mr. Asger Aaboe! He or his staff may have KESKINTO ACCESS.

 

 

KETTUBAH: See MARRIAGE

http://jnul.huji.ac.il/dl/ketubbot/

 

KHAEMWESE: (AE; MK) HPP

 A principal son (the 4th son) of Ramses II. AKA KHAEMWASET.

 

AKA Kahaemwat

http://www.ahram.org.eg/weekly/2001/553/tr4.htm

 

(as per K. Weeks) see the stories of Setne Khaemwese. These stories herald his intellect and magic. He ruled as (HPP) The High Priest of Ptah, and earlier in life as a lesser sem-priest.

A brother or half brother to Merenptah.

See Great Temple of Ptah at Memphis.

Examine stone (temple fragment) at the Royal Scottish Museum.

 

(as per Lesley-Ann Liddiard, Department of History and Applied Art, National Museums of Scotland)

The Royal Scottish Museum is now known as the Royal Museum, which is part of the National Museums of Scotland.

The fragment in question is registration number:

A.1908.364

Described: “Column, part of a clustered papyrus-bud column, limestone consisting of four deep flutings on the lower half; and above a lashing, three flutings on upper half with panel showing in low relief a figure of the King’s son Khaemwese wearing the side-lock and panther skin of a setem [sem] priest facing left…Excavated in the temple of Ptah at Memphis.

 

Origin: XIX Dynasty.

 

Published: See Petrie, [B_198], “Memphis I”, plate 10.

 

 

See also Serapeum re. Apis; the wrapping of the ceremonial deity bull.

 

[W_044,rvw] WATSON# 532T34 B21. "Notizia sommaria degli scavi della missione archeologica italiano in Egitto, anno 1903 : valle delle regine / F. Ballerini. Torino, 1903.

Note: Khaemwaset tomb at QV.

 

 

KHASEKHEM: (OK; AE) historical ruler

(as per J. Legon) Seek 2nd dynasty statue of Khasekhem,

 with number of 47,209 enemies slain.

Possible source for statue image:

Quibell 1900. J.E. Quibell. with note by W.M.F.P. Hierakonpolis I. London. BSAE 4

Kom El Ahmar= Hierakonpolis

http://www.casa.ucl.ac.uk/digital_egypt/chronology/kingkhasekhem.html

 

http://www.casa.ucl.ac.uk/digital_egypt/chronology/kingkhasekhemwy.html

 

~2700 BCE Statue image; without inscription analysis:

http://banners.konouz.net/popups/egipto_popup.html

 

http://members.xoom.it/francescoraf/hesyra/khaskhmsvi.jpg

 

 

KHAY: (Hieratic) Papyrus

See Amherst, BOTD.

 

 

KHENTY-IRTI: (AE; lesser) gods

(as per M. St. John) Study the Protector gods of the tomb of Senmut,

The Four Sons of Khenty-irti:

Khenty-irti is a god with a cult center at Khem (Letopolis).

Haqu (Haw).

Iriemowa (He who behaves as a thief).

Maanitef (He who looks at his father).

Irerenefdjesef (He who made his own name).

 

See CUBIT.

 

(as per M. St. John) The Chassinat book is the one with the most information. [about Khenty-irti]

Chassinat (Emile Gaston) 1868-1948
French. Director of
IFAO. Excavated at Meir, Dendera, Asyut and Abu Ruwash. Many publications including the "Edfu Texts".

 

See also Marshall Clagett's 'Ancient Egyptian Science' Volume II.

Find pictures on Plate III.4 and also on 65b and 65c.

[B_028,HOUSE] CATNYP# JFM 95-854 (see volume two)

 "Ancient Egyptian Science: a source book / by Marshall Clagett”

Philadelphia : American Philosophical Society, 1989-

Review this text again for the images of the four sons.

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

 

(as per M. St. John)

See Book of the Dead Chapter 99, Part III, about 2/3rds of way through.

“Tell me my name say the ribs which are in her timbers.”

“Imsety, Hapy, Duamutef and Qebehsenuef, Plunderer, He who takes by robbery, He who sees what he has brought, He who helps himself, are your names.”

 

Conceptual linkage with the other set of four sons (of Khenty-irti).

 

 

KHIRBET EL-KOM: (~275 BCE; Bilingual; Greek; Aramaic) ostracon

See the bilingual pottery shard from this area near Hebron.

With dates in the format of the Aramaic and Macedonian systems (~277 BCE).

See CALENDAR.

 

Seek: BASOR 220.

L.T.Geraty. The Khirbet el-Kom bilingual ostracon, BASOR 220, 195

 

(as per G. Ifrah; [B_359]) See p. 235:

“6th Year, the 12th of the month of Panemos [Tammuz], Nikeratos, son of Sobbathos, received from the moneylender 32 drachma”

 

Geraty, Lawrence T. 1975. The Khirbet el-Kôm bilingual ostracon. Bulletin of the American School of Oriental Research 220: 55-61.
See math content? Page 195?

 

 

KHIRBET ET-TANNUR: (Nabatean) temple

See ZODIAC in transjordan structure.

See winged Nike. ~200 CE.

 

A Nabatean summit shrine at GEBEL ET-TANNUR.

Near Wadi el-Laban and Wadi el-Hesa.

 

See Glueck, N. (1952) “The Zodiac of KHIRBET ET-TANNUR”, Bulletin of the American Schools of Oriental Research 126: 5-10.

[BASOR]

 

 

KHIRBET MIRD: (Greek; Aramaic; Arabic) Manuscripts from Israel

Manuscripts in Greek, Christian Palestinian Aramaic, and Arabic from the ruins of the monastery of Castellion were acquired from Bedouins and by a Belgian expedition in 1953. These seem to be mostly from the more recent Byzantine and Arab periods.

 

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

 

See also KHIRBET QUMRAN.

Images are available at JH.

 

 

KHONSU-HETEP: (AE; Hieratic) maxims of

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

See maxims of Ani.

 

See:

9. Maspero, Lectures Historiques, p. 16; Amélineau, op. cit., p. ix.]

http://www.sacred-texts.com/egy/ebod/ebod06.htm

 

 

KIDS: boiled or fried?

http://www.warnerbros.com

 

http://www.childrensmuseum.org/kids/games.htm

 

http://www.talesbyfloyd.com

 

 

KL. FORM.: (Greek) papyri

(as per E. G. Turner) See Stud. Pal. iii and viii.

 

See:

Griechische Papyrusurkunden kleineren Formats (P.Kl. Form. I), ed. C. Wessely. Nos. 1—701. 1904.

http://scriptorium.lib.duke.edu/papyrus/texts/clist_series.html

 

 

KLEPSYDRA: water clocks

AKA CLEPSYDRA; See SAK; GIESSEN; JEMDET-NASR

 

 

KMT: See KEMET

 

KNOSSOS: (Linear A) tablets

See LINEAR B

[B_609, 8.5, NO IMG] CATNYP# JFE 74-278

“The KNOSSOS Tablets; a transliteration by John Chadwick, J.T. Killen and J.-P. Olivier.”

Cambridge, 1971. [4th edition]

Compare symbolic items to PHAISTOS disc.

 

KOENEN (Greek) papyrus

See Michigan

[B_501,rvw] CATNYP# JFF 97-390

P. Michigan Koenen (=P. Mich. XVIII) : Michigan texts published in honor of Ludwig Koenen / edited by Cornelia E. Römer & Traianos Gagos ; consulting editors Ann E. Hanson & Pieter J. Sijpesteijn.”

Amsterdam, 1996.

See plates

 

 

KOLLER: (AE; Hieratic) papyrus

(as per A. H. Gardiner) seek Koller P.

[B_246,rvw=W_021=W_027,rvw] CATNYP# *OBR+ (Egyptian Hieratic texts) = WATSON# 533.6 G16, "Egyptian hieratic texts: series 1, literary texts of the New Kingdom / transcribed, translated and annotated by Alan H. Gardiner", Liepzig, 1911. A review of Anastasi I =BM 10247 and P. KOLLER.

Referred to by [B_039].

NYPL has Series I, Part 1.

 

See also ANASTASI.

 

 

KOLNER or KOLN: (Greek and Latin) papyri

KOLN, Germany sometimes referred to as: Cologne

http://www.uni-koeln.de/phil-fak/ifa/NRWakademie/pap_Col.html

 

P.Köln: Kölner Papyri. See COLOGNE.

P.Koeln 1.50. Purchase of arable land:

(Greek; 99 bce; from Pathyris)

http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0144

 

[B_463=O_032,rvw]

CATNYP# *OBKQ 75-868 v.7

BOBST# PJ1014 .P3 vol.7

Kolner Papyri: (P. Koln.) / bearbeseit von Barbel Kramer und Robert Hubner.”

Opladen : Westdeutscher Verlag, 1976-?

With German, Greek and Latin.

See KOLN.; COLOGNE

 

KOM OMBO: (Ptolemaic) theology text

derived from inscriptions at Temple near ASWAN.

 

(As per Y. Koenig) See t.47. refers to "Fondamentaux de la Theologie de Kom Ombo", (BdE XLVII), I p.242 et II p.224.

 

WATSONLINE yields nothing additional, but has the above text.

 

KOM OMBO AKA OMBOS.

 

KORAN: (Muslim) holy text

See KORANFRAGMENTE; QURAN; [B_450=O_018,8.5,IMG];

KORANFRAGMENTE: (Arabic) papyri

[B_450=O_018,8.5,IMG]

CATNYP# *OBKQ+ 77-689 Folge 14

BOBST# PA3308 .V52 Folge 14 Oversize

See BOBST Archive: O 1

Koranfragmente auf Pergament aus der Papyrussammlung der Osterreichischen Nationalbibliothek / herausgegeben von Helene Loebenstein.”

Wien, 1982.

See KORAN; QURAN; SAMMLUNG; TORAH; ERZ. RAIN.; PHILOSOPHY

 

 

KRALL: (Author; demotic); papyrus

[B_053,8.5,IMG] CATNYP# *OBKG+ 77-689 Folge 8, "Der Kamph um den Panzer des Inaros (Papyrus Krall). von Edda Bresciani. 1964.

(as per 2terres); demotic.

 

(as per R.A. Parker) Seek "Demotische Lesestucke. II.", Liepzig, 1903, by Author Jacob Krall.

 

[W_028,rvw] WATSON# 533.4 K85 "Ein neuer historischer Roman in demotischer Schrift", Wien, 1897. Related to SAMMLUNG and ERZHERHOG.

 

 

KROLL: (Greek) papyri

(as per E. G. Turner) P. Kroll = Eine ptolemaische Konigsurkunde, ed. L. Koenen, Weisbaden, 1957.

 

P.Kroll: Eine ptolemäische Königsurkunde

See P. Koeln [KOLN]

http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0145

 

 

KRONION: (Greek) archive; papyri

P.Kron.: L'Archivio di Kronion

P.Kron. 1. graphê pastofo/rwn: (Greek; AD 122; from TEBTYNIS)

http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0146

Some accounts; drachmas.

 

 

KUNSTBLATT: (Prussian publication) des Morgenblatt,

The long haul

Referred to by Lepsius in [B_149, ftnt. of p. 14; 1834, no. 70, p. 125]

as: Kunstblatt des Morgenlandes.

(Art Journal of the Near East)

Referred to by Bockh in [B_219, ftnt. a of p. 224; 1838]

 

[C_001;NO IMG;file with B_149] Kunstblatt des Morgenlandes

AKA Kunst-blatt des Morgenblatt.

I have learned via the NUC that this was a semi weekly publication included as a supplement in Morgenblatt fur gebildete Leser”

[not Morgenlandes]

Published in Stuttgart, by the Univ. of Tubingen, 1834.

Edited by: Ludwig Schorn, Franz Kugler and Ernst Foerster.

Access by permission of the NYPL reference Librarians via a pass to the Butler Library at Columbia University (Broadway and 116th Street).

I am searching for an entry by E.F. Jomard in Issue 70.

Also available in Hamburg Univ. Library.

Only available at Columbia University Library in NY City.

See images from M. Tilgner. Filed with [B_149].

 

 

 

KUNTILLET: (Hebrew and Phoenician) inscriptions; ostraca; graffiti

The earliest biblical reference to spoken Hebrew occurs in Genesis 31:47 where Laban and Jacob refer to a heap of stones in their own native speech. Laban calls it Jegarsahadutha, which is Aramaic [heap of testimony], but Jacob calls it Galeed, which is Hebrew [witness heap]. He also calls a nearby pillar by a Hebrew word, Mizpah. This could place spoken Hebrew in the eighteenth century B.C.

http://earth.vol.com/~lmartin/INTRODUC.HTM

In 1976 about seventy Hebrew and Phoenician inscriptions were found at Kuntillet `Ajrud in Sinai, and they are dated in the ninth and eighth centuries B.C. One text refers to God under his covenant name YHWH.

Samaritan ostraca of the ninth century have also been discovered. Although the question of early Hebrew dialects is uncertain these ostraca seem to show a northern dialect which differs somewhat from the southern dialect of the Gezer calendar.

An inscription of six lines was discovered in the tunnel between the Virgin's Spring and the Pool of Siloam at Jerusalem. It has come to be called the Siloam inscription and dates from the eighth century B.C.

About forty engraved seal-stones have been discovered. Some of them are pre-exilic. Other inscriptions, called the Lachish letters, have been found written on potsherds. They are dated at approximately 590 B.C., and consist largely of military communications.

Surveys Northwest Semitic inscriptions that bear significantly on our understanding of Biblical history and the Hebrew language. Texts studied include (among many others) the Moabite stone, Israelite ostraca, Siloam engraving, Gezer calendar, Deir Alla inscription (Gilead), the Asherah texts, Ammonite fragments, and Phoenician monuments.

http://faculty.washington.edu/snoegel/Heb42802.syll.html

Week Four: Kuntillet 'Ajrud, Khirbet el-Qom Inscriptions, Khirbet Beit Lei, Lachish, and Elephantine Ostraca.  

Kuntillet Ajrud was excavated by Ze'ev Meshel. There were Hebraic inscriptions on some of the clay storage vessels described as set aside for tithes. Some text about Ajrud has been published on the internet. The greater text of the discoveries at Ajrud might not be found on the internet due to copyright laws.

http://omega.cohums.ohio-state.edu/hyper-lists/anc-l/01-99-99/0003.html

pithoi (store jars) [see PITHOM] inscribed with a Hebrew script and decorated with figurine-like drawings of Jahweh and Ashera were found in Kuntillet 'Ajrud in the northeast Sinai peninsula.

http://pluto.mscc.huji.ac.il/~msjan/abstract.html

Significant Texts and Inscriptions:

Siloam tunnel inscription, “Annals of the Kings of Judah and Israel”, Assyrian and Babylonian annals, Ahiram sarcophagus inscription, Gezer calendar, Samaria ostraca, Lachish letters, Nineveh relief, Merneptah stella, Moabite stella / Mesha inscription, Shalmaneser III Black Obelisk, Medinet Habu relief, Arad letters, Sennacherib’s Prism, Cyrus Cylinder, “Tale of Wen-Amon,” Kuntillet ‘Ajrud graffiti, etc.

http://srv2.lycoming.edu/~knauth/226mid2rev.htm

 

The Kuntillet Ajrud Texts:

Kuntillet Ajrud is [about] 50 km south of Kadesh Barnea in the Sinai desert

In addition to these wall inscriptions, there are inscriptions on two storage jars written in red ink, dated [about] 750 BCE. They read:

I bless you by Yahweh of Teman and by his Asherah

May he bless you and keep you and be with (you), my Lord

I have blessed you by Yahweh smrn [of Samaria? Our guardian?] and by his asherah

These inscriptions raises very significant questions about the nature of Israel’s popular religion.

K.A.D. Smelik (1991) asks whether these inscriptions might give us a direct insight into the nature of the

popular religion that is so scathingly condemned by israel’s pre-exilic prophets?

Does it give us an insight into the religion that was subsequently and consciously suppressed by biblical writers and confirm that Yahweh did indeed have a consort Asherah - the Goddess of Israel?

http://www.dbi.edu/gt/genesis/bilag/yahwism.htm

See:

De Moor, Johannes C. The Rise of Yahwism. The Roots of Israelite Monotheism. BETL 91. Peeters, 1990. Important evidence and arguments for Israel's worship of one God in Mosaic and later times.

 

KUSH: (extinct; African) people of

See northern Sudan; extinct capital city of Kerma.

Conquered by AE ~1500 BCE.

See Old Testament; TORAH; TRADE.

 

 

KV5: a dig in progress of a fascinating tomb

See Kent Weeks’ text: [B_562].

 

[B_562,HOUSE] CATNYP# *OBLH 99-6533

“The lost tomb : the greatest discovery at the valley of the kings since Tutankhamun / Kent R. Weeks”

 

See TMP; MERENPTAH

http://www.kv5.com/html/index_progress.html

kv5 progress jun-2002

 

 

 

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